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Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: A critical review
Accepted Manuscript Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: A critical review Hai Nguyen Tran, Sheng-Jie You, Ahmad Hosseini-Bandegharaei, Huan-Ping Chao PII:
S0043-1354(17)30269-5
DOI:
10.1016/j.watres.2017.04.014
Reference:
WR 12811
To appear in:
Water Research
Received Date: 29 October 2016 Revised Date:
29 March 2017
Accepted Date: 6 April 2017
Please cite this article as: Tran, H.N., You, S.-J., Hosseini-Bandegharaei, A., Chao, H.-P., Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: A critical review, Water Research (2017), doi: 10.1016/j.watres.2017.04.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Mistakes and inconsistencies regarding adsorption of contaminants from aqueous
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solutions: A critical review
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Hai Nguyen Trana,b*, Sheng-Jie Youb, Ahmad Hosseini-Bandegharaeic,d, Huan-Ping Chaob*
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Department of Civil Engineering, Chung Yuan Christian University, Chungli 320, Taiwan
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Department of Environmental Engineering, Chung Yuan Christian University, Chungli 320, Taiwan Wastewater Division, Faculty of Health, Sabzevar University of Medical Sciences, PO Box 319, Sabzevar, Iran d Department of Engineering, Kashmar Branch, Islamic Azad University, PO Box 161, Kashmar, Iran
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Corresponding authors:
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H. N. Tran ([email protected]) and H.- P. Chao ([email protected])
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Department of Environmental Engineering, Chung Yuan Christian University, Chungli 320, Taiwan
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Abstract
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In recent years, adsorption science and technology for water and wastewater treatment has attracted substantial attention from the scientific community. However, the number of
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publications containing inconsistent concepts is increasing. Many publications either reiterate previously discussed mistakes or create new mistakes. The inconsistencies are reflected by the
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increasing publication of certain types of article in this field, including “short communications”, “discussions”, “critical reviews”, “comments”, “letters to the editor”, and
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“correspondence (comment/rebuttal)”. This article aims to discuss (1) the inaccurate use of
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technical terms, (2) the problem associated with quantities for measuring adsorption performance, (3) the important roles of the adsorbate and adsorbent pKa, (4) mistakes related to the study of adsorption kinetics, isotherms, and thermodynamics, (5) several problems related to adsorption mechanisms, (6) inconsistent data points in experimental data and model fitting, (7) mistakes in measuring the specific surface area of an adsorbent, and (8) other mistakes found in the literature. Furthermore, correct expressions and original citations of the relevant models (i.e., adsorption kinetics and isotherms) are provided. The authors hope that this work will be helpful for readers, researchers, reviewers, and editors who are interested in the field of adsorption studies.
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Keywords: Adsorption; mistake; comment; inconsistency; critical review
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Table of Contents 1. Introduction ........................................................................................................................5 2. Technical terms used in the study of adsorption ..................................................................6
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3. Quantities for measuring adsorption performance ...............................................................8 4. Incorrect assumptions regarding pKa ...................................................................................9
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5. Adsorption kinetics ...........................................................................................................11
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5.1. The important role of initial time............................................................................11
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5.2. Adsorption equilibrium time for porous materials ..................................................13 5.3. Pseudo-first-order (PFO) equation..........................................................................14
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5.3.1. Derivation of the PFO equation ...................................................................14 5.3.2. Problems in the application of the PFO equation..........................................15 5.4. Pseudo-second-order (PSO) equation .....................................................................17 5.4.1. Derivation of the PSO equation ...................................................................17 5.4.2. Problems in the application of the PSO equation..........................................20 5.5. Elovich equation ....................................................................................................23 5.5.1. Derivation of the Elovich equation ..............................................................23 5.5.2. Incorrect expression of the Elovich equation................................................24 5.6. Intra-particle diffusion model .................................................................................24 6. Adsorption isotherms ........................................................................................................25 6.1. Adsorption equilibrium ..........................................................................................25 6.2. Langmuir equation .................................................................................................29 6.2.1. Derivation of the Langmuir equation ...........................................................29 6.2.2. Derivation of the separation factor ...............................................................31 6.2.3. Mistakes concerning the Langmuir model and the separation factor.............31 6.3. Freundlich equation ...............................................................................................33 6.3.1. Derivation of the Freundlich equation ..........................................................33 6.3.2. Mistakes concerning the Freundlich equation ..............................................34 6.4. Redlich–Peterson equation .....................................................................................35 6.4.1. Derivation of the Redlich–Peterson equation ...............................................35 6.4.2 Mistakes concerning the Redlich–Peterson equation .....................................36 6.5. Dubinin–Radushkevich equation ............................................................................36 6.5.1. Derivation of the Dubinin–Radushkevich equation ......................................36 6.5.2. Mistakes concerning the Dubinin–Radushkevich equation ...........................37 7. Adsorption thermodynamics .............................................................................................38 7.1. Principles of adsorption thermodynamics ...............................................................38 7.2. Equilibrium constant derived from the Langmuir constant (KL) ..............................40 3
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7.3. Equilibrium constant derived from the Freundlich constant (KF) ............................44 7.4. Equilibrium constant derived from the partition coefficient (Kp).............................45 7.5. Equilibrium constant derived from the distribution coefficient (Kd) ........................47 8. Others mistakes ................................................................................................................49
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8.1. Inconsistent data points in experimental data and model fitting ..............................49 8.2. Oxidation state of chromium ..................................................................................51
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8.3. Incorrect labels.......................................................................................................53
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8.4. BET specific surface area of an adsorbent ..............................................................54
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8.5. Maximum absorption wavelength in dye adsorption studies ...................................57
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8.6. Cπ-cation and π-π interactions................................................................................57 8.6.1. Cπ-cation interactions ..................................................................................57 8.6.2. π-π interactions ............................................................................................59 8.7. Other miscellaneous errors .....................................................................................62 9. Nonlinear-optimization technique .....................................................................................66 10. Conclusions ....................................................................................................................68
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Acknowledgements ..............................................................................................................69
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1. Introduction Nowadays, the number of publications in international scientific journals has increasingly
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become a standard for the assessment of scientists (Geckeis and Rabung, 2004). As the number of
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scientific publications increase, mistakes and misconceptions enter scientific literature and some
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can also be repeated in subsequent publications. Once errors and mistakes enter the literature, it is
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difficult to eradicate them. The entrance of mistakes in scientific publications, as well as their
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propagation, can result from the subjectivity of the authors and/or objective reasons.
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A typical study on the adsorption of organic and inorganic contaminants comprises several
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sections, such as the effects of solution pH and ionic strength, studies of adsorption kinetics,
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isotherms, thermodynamics, desorption, and regeneration. Adsorption processes can be conducted
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using either batch or column techniques. It has been found that many scientific articles in the field
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of adsorption science and technology contain several mistakes and misconceptions including the
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use of technical terms, application of quantities, determining the roles of some constants like pKa,
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performing kinetic studies and modeling kinetic adsorption data, finding a suitable isotherm model
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to fit equilibrium data, calculating thermodynamic parameters, correct interpretation of adsorption
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mechanisms, and measuring the specific surface area of an adsorbent. Moreover, a survey of the
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scientific publications related to the adsorption of contaminants in aqueous solutions reveals that
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some less obvious inconsistencies and mistakes have unavoidably slipped the attention of authors
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and were repeated in subsequent publications.
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The observation of these inconsistencies and mistakes, regardless of their origin, along
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with comments and open discussions can prevent their propagation in scientific knowledge
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transfer. Therefore, the presentation of a comprehensive review on common mistakes in
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adsorption studies, besides introducing the most correct approaches to use and giving a source of 5
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up-to-date literature on this issue, seems to be valuable to both readers and researchers in this
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field. The main purpose of this review is to identify mistakes in past publications and prevent the
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propagation of such mistakes in future scientific literature. Herein, we present some common
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mistakes in various aspects of adsorption studies and analyze the reasons for their entrance into
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the literature. This was accomplished by discussing the published papers in the field of adsorption
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of contaminants from aqueous solutions, commonly including “comments on”, “reply for
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comments”, “response to”, “authors’ response to comments on”, “comments on the authors’
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response to comments on”, “comments on comment on”, “in reaction to”, “critical review”, and “a
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note on the comments” published works. In addition to our comprehensive review on the mistakes
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existing in publications, some correct approaches are suggested where necessary to avoid the
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propagation of such mistakes in the future scientific literature. This paper primarily focuses on
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three basic constituents of adsorption theory: adsorption equilibria, kinetics, and thermodynamics.
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2. Technical terms used in the study of adsorption
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Adsorption processes have their own vernacular. Therefore, correctly understandings the
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technical terms used in adsorption technology can prevent the introduction of several unexpected
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ambiguities and discrepancies. Some basic adsorption terms are summarized in Figure 1.
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Figure 1
To some extent, a thorough understanding of the properties of adsorbents might prevent
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common mistakes made in interpreting adsorption processes and adsorption mechanisms.
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Numerous techniques can be used to characterize an adsorbent (Figure 2). More information on the
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basic properties of adsorbents (i.e., biosorbent, biochar, hydrochar, and activated carbons) and the
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relations between these properties has been published in our recent work (Tran et al. 2017c). 6
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Figure 2 The appropriate use of technical words regarding the biosorption mechanism of heavy
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metals has been highlighted by Robalds et al. (2016). To avoid reader confusion, they
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recommended that “surface precipitation” be used instead of “microprecipitation” (also written as
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“micro-precipitation”). Similarly, it is necessary to distinguish between “chelation”,
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“complexation”, and “coordination”. The word “complexation” includes two meanings:
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“chelation” and/or “coordination”. For example, the incorrect sentence “in another sense, it can
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also be defined as a collective term for a number of passive accumulation processes which in any
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particular case may include ion exchange, coordination, complexation, chelation, adsorption and
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microprecipitation” should be revised as “biosorption may include ion exchange, complexation
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(including coordination and/or chelation), physisorption, or microprecipitation” (Robalds et al.,
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2016). In addition, the use of the term “electrostatic adsorption” may cause misunderstanding and
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confusion; therefore, depending on the intended meaning, the appropriate terms (i.e., “electrostatic
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attraction”, “electrostatic force”, or “electrostatic interaction”) are recommended. Notably, the
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authors also suggested a new classification system for the (bio)sorption mechanisms of heavy
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metals (Figure 3).
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Figure 3
The electrical state of an adsorbent’s surface in solution is usually characterized by either
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the point of zero charge (PZC) or the isoelectric point (IEP). Many authors have complained about
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the misuse of the terms IEP and PZC outside their normal meanings (Somasundaran, 1968;
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Kosmulski, 2009). The PZC is defined as the solution conditions under which the surface charge
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density equals zero. Potentiometric titration, or related methods, is used to determine the PZC by
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finding the point at which the apparent surface charge density in the presence of an inert electrolyte 7
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is not dependent on ionic strength (Figure 4a). The IEP occurs when the electrokinetic (ζ) potential
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at the shear plane equals zero; ζ is determined from measuring electrokinetic (electrophoresis and
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streaming potential) and electroacoustic phenomena (Figure 4b) (Kosmulski, 2009). IEP values
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clearly represent only the external surface charge of particles in solution, whereas the PZC varies
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in response to the net total (external and internal) surface charge of the adsorbent (as the
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characteristic of amphoteric surfaces). Therefore, the difference between the PZC and IEP values
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for a porous carbon system can be interpreted as a measure of the surface charge distribution. A
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difference (PZC − IEP) of greater than zero indicates that the external particle surface is more
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negatively charged than the internal particle surface, and a difference of close to zero corresponds
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to a more homogeneous distribution of surface charge. The PZC is only equal to the IEP in the
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absence of specific or counter ions. This means that equality between the PZC and IEP exists only
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if no specific adsorption of counter ions from the solution occurs (Radovic, 1999; Onjia and
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Milonjić, 2002).
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Figure 4
3. Quantities for measuring adsorption performance In the field of adsorption, adsorption performance can be expressed as the amount of
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adsorbate adsorbed at equilibrium or the percentage of removed adsorbate. The amount of
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adsorbate adsorbed at equilibrium (qe; mg/g) is often calculated using the material balance of an
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adsorption system; the adsorbate, which has disappeared from the solution, must be in the
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adsorbent (Volesky, 2007).
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qe =
(C o − C e ) V1 m1
(1)
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where C0 (mg/L) and Ce (mg/L) are the initial and equilibrium adsorbate concentration in solution,
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respectively; m (g) is the dried mass of used adsorbent; and V (L) is the volume of the adsorbate
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solution. Depending on the purpose of the study, the parameter qe may be expressed in different units
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as follows: (1) mg/g for evaluating practical and engineering processes, (2) mmol/g or meq/g for
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examining the stoichiometry of a process and for studying functional groups and metal-binding
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mechanisms, and (3) mmol/g for comparing the selective adsorption performance of various
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adsorbates (Volesky, 2007). Of these units, mg/g (milligrams of adsorbate adsorbed per gram of
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dried adsorbent) is used most commonly for qe in adsorption studies.
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In addition to qe, the adsorption performance can also be expressed as the percentage of
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removed adsorbate (%removal). However, the unit of %removal needs to be used cautiously, as it
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is very approximate and can cause misleading conclusions about relative adsorption performance.
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This unit is only appropriate for the purpose of crude measurements and perhaps for quick and
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very approximate screening of adsorbent materials (Kratochvil and Volesky, 1998; Hai, 2017) (C o − C e ) × 100 Co
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To some extent, the use of %removal in the study of adsorption equilibria can cause
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incorrect observations and, as a result, inaccurate conclusions (a detailed discussion is provided in
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Section 6.1).
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4. Incorrect assumptions regarding pKa
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A mistake regarding the fundamentals of chemistry was commented on by Rayne (2013).
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The commented paper reported the adsorption of n-perfluorooctanesulfonamide (PFOSA) onto
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multiwalled carbon nanotubes with differing oxygen content. However, PFOSA was mistakenly 9
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assumed to be an “organic base”, resulting in the following invalid interpretation: “for PFOSA
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(pKa = 6.52), when pH < pKa, protonation occurs on the amino group, and the decreased
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protonation leads to the increased adsorption, but when pH > pKa, PFOSA exists as neutral
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molecule in water.” In fact, PFOSA is an acid and, thus, is a neutral compound below its pKa value
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(estimated at between 6.0 and 7.0) and a dissociated anion at pH > pKa (Rayne, 2013).
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Recently, the effect of pH on the interaction of copper with the surface functional groups of raw pomegranate-peel biosorbent was reported as follows:
R–OH ↔ R–O− + H+ R–O− + Cu2+ ↔ R–OCu+ R–O− + Cu(OH)+ ↔ R–OCu(OH)
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(3) (4) (5) (6)
where –R represents the surface adsorbent; R–OH2+, R–OH, and R–O− represent protonated,
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neutral, and ionized surface hydroxyl functional groups, respectively; and R–OCu+ and R–
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OCu(OH) are the formed bonding complexes.
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The authors (Ben Ali et al., 2016) explained that, “the effect of pH could be also explained
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by considering the point of zero charge of the adsorbent (pHpzc). The adsorbent surface is
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positively charged for pH< 4.7 and it becomes negatively charged at pH value above 4.7.
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Therefore, for pH values < 4.7, the adsorption is unfavorable because of repulsive electrostatic
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interactions between metal ions and positively charged functional groups. The maximum
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adsorption of Cu(II) occurs at pH above pHpzc value when the adsorbent surface is negatively
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highly charged.” However, the important role of the pKa values of carboxylic acid groups (–
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COOH; pKa 1.7–4.7) and hydroxyl groups (–OH; pKa 9.5–13) was ignored (Volesky, 2007).
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Correspondingly, Eqs. 3–6 indicate a misunderstanding of the surface chemistry of the adsorbent.
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The authors investigated the effect of solution pH on the adsorption process of Cu(II) in solutions
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with pH values from 2.0 to 6.0. Therefore, dissociation of the –OH groups to –O− did not occur at
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these solutions pH values. Instead, the –COOH groups dissociated, forming negatively charged
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carboxylate groups (–COO‒) in the aforementioned pH range, and were the dominant groups that
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interacted with copper ions (Tran, 2017).
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Moreover, Bui and Choi (2010) made a critical comment that Oleszczuk et al (2010)
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mistyped the properties of two pharmaceuticals: oxytetracycline (logKow = 2.45, pKa = 7) and
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carbamazepine (logKow = −1.22, pKa = 3.27, 7.32, 9.11). The correct expression should be
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oxytetracycline (Sw = 121 mg/L, logKow = −1.22, pKa = 3.27, 7.32, 9.11; density = 1.63 g/cm3) and
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carbamazepine (Sw = 112 mg/L, logKow = 2.45, pKa = 7; density =1.15 g/cm3). Bui and Choi
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(2010) also emphasized that the pKa value of carbamazepine reported by Oleszczuk et al (2010) is
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still debated. Carbamazepine (CBZ) is commonly characterized with two pKa values: pKa1 (= 1 or
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2.3) for the equilibrium RCONH3+ ⇌ RCONH2 + H+ and pKa2 (= 13.9) for the equilibrium
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RCONH2 ⇌ RCONH− + H+. The misreporting of the CBZ pKa can cause inaccurate conclusions.
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For example, Oleszczuk et al. (2010) suggested that an electrostatic interaction occurred between
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CBZ and multiwalled carbon nanotubes (MWCNT) at pH < 7.0 because they opined that CBZ
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existed in its cationic form at pH < 7.0 (pKa = 7.0). However, CBZ with pKa1 < 2.3 and pKa2 ≥ 13.9
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actually exists entirely as a neutral species in the pH range of 1.9–11.9, as calculated using
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ACDLab. As a result, the electrostatic interaction was ruled out as a contributing interaction in the
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CBZ-adsorption mechanisms (Bui and Choi, 2010).
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5. Adsorption kinetics
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5.1. The important role of initial time
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In the study of adsorption kinetics, Azizian (2006) proposed that experiments should be 11
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started at t < 2 min (considered as the initial time). Adsorption kinetics data in the initial time
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periods play an important role in performing accurate modeling and drawing conclusions. Depending on the affinity between the adsorbent and adsorbate, the initial adsorption rate
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may be very fast. For the adsorption of heavy metals, Tran et al. (2015) investigated the adsorption
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of Cd2+ onto orange-peel-generated biochar, and found that equilibrium can be reached rapidly in
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kinetic experiments with a removal rate of 80.6–96.9% (within 1 min). An analogous performance
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was reported by Guo et al. (2015), with approximately 70.0–96.6% of the total Cd2+ in solution
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removed within the first minute of contact. Additionally, Müller et al. (2012) noted that
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approximately 90% of Zn(II) adsorption onto Lewatit S1468 occurs within 1 min, and this
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adsorption process reaches equilibrium in approximately 5 min.
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For the adsorption of organic contaminants, kinetic studies indicated that the adsorption
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equilibrium of methylene green 5 was quickly established, with a low activation energy required
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for adsorption (Ea; 3.30–27.8 kJ/mol), and activated carbons removed 50–73% of the dye from
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solution within 1 min (Tran et al., 2017d; Tran et al., 2017e). Similarly, Canzano et al. (2012)
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noted that the adsorption process of anionic Congo-red dye onto raw and acid-treated pine cone
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powder reached equilibrium in the first few minutes (< 5 min), during which no measurements
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were carried out.
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approaches that of at equilibrium (qe) and, therefore, plotting the kinetic data is bound to produce a
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straight line, independent of the real kinetic order followed by the system. In other words,
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equilibrium data does not describe the way by which the system reaches equilibrium. As a result,
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the use of data recorded over a significant time interval after the attainment of equilibrium, or very
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close to equilibrium, is likely to lead to erroneous conclusions regarding adsorption kinetics. 12
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5.2. Adsorption equilibrium time for porous materials The adsorption processes for inorganic and organic contaminants onto porous adsorbents
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(i.e., activated carbon, biochar, activated carbon spheres, zeolite, and macroreticular resin) can
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take longer (i.e., several days or weeks) to approach true equilibrium than nonporous adsorbents
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(i.e., biosorbent and hydrochar). This difference is attributed to the different adsorption
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mechanisms of these adsorbents. Pore filling is the most common adsorption mechanism for
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porous adsorbents, along with several other interactions (i.e., electrostatic attraction, hydrogen
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bonding, surface precipitation, π-π interaction, n-π interaction, and cation exchange) that depend
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on the characteristics of the porous adsorbents and adsorbates. Many studies have opted for a 24 h
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equilibrating time for isotherm adsorption experiments, without providing evidence that
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adsorption in their system attained true equilibrium within the appropriate timeframe.
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Therefore, it is necessary to provide the specified timeframe in which the adsorption
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process approaches a true equilibrium. Figures 5a–c represent the influence of contact time on the
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adsorption processes of various contaminants onto porous adsorbents (Hung and Lin, 2006;
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Masson et al.; 2016; Kim et al., 2016). Clearly, the amount of contaminant adsorbed onto the
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porous adsorbents continued to increase after 24 h. For example, Kim et al. (2016) speculated on
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the process of methyl violet (MV) adsorption onto synthesized granular mesoporous carbon
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(GMC) and commercial granular activated carbon (GAC). The results of their kinetic study
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demonstrated that MV adsorption reached an equilibrium state within 20 d for GMC-polyvinyl
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alcohol and 26 d for GMC-carboxymethyl cellulose, while adsorption onto GAC had not reached
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equilibrium even after 75 d. Furthermore, a phenomenon involving desorption from the adsorbent
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surface after reaching adsorption equilibrium (Figure 5d) has been reported in the literature
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(Sharma et al., 2013, Halder; Khan et al., 2016). Therefore, studies of the adsorption kinetics play
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an important role in identifying the required equilibration time and the optimal contact time and for
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an adsorption process.
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Figure 5 In aqueous-phase adsorption, two kinetic reaction models (i.e., pseudo-first-order and
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pseudo-second-order equations), the Elovich or Roginsky–Zeldovich model, and the intraparticle
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diffusion model have been widely applied to mathematically describe the intrinsic kinetic
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adsorption constant. Furthermore, most mistakes found and discussed in the literature correspond
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to the use of kinetic models. Therefore, the following sections (5.3–5.6) include a thorough
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discussion of these models.
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5.3. Pseudo-first-order (PFO) equation
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5.3.1. Derivation of the PFO equation
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Recently, Ho published a series of critical papers (Ho and McKay, 1998b; Ho, 2005, Ho,
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2014a; Ho, 2015; Ho, 2016e) discussing two main points. First, Ho (Ho and McKay, 1998b)
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claimed to offer the correct reference style for citing Lagergren’s paper, with the original
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translated from “Lagergren, S. (1898), Zur theorie der sogenannten adsorption gelöster stoffe.
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Kungliga Svenska Vetenskapsakademiens Handlingar, Band 24, No. 4, 1–39” into English as
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“Lagergren, S., About the theory of so-called adsorption of soluble substances, Kungliga Svenska
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Vetenskapsakademiens. Handlingar, Band 24, No. 4, 1898, pp. 1–39.” Second, Ho stated that
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Lagergren’s first-order rate equation has been called pseudo-first-order since 1998 (Ho, 2005) in
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order to distinguish kinetic equations based on the adsorption capacity of solids from those based
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on the concentration of a solution. However, the responses of many authors (Özacar; 2005, Kumar,
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2006d; Utomo et al., 2010) state that Lagergren’s first-order rate expression had been referred to as
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a pseudo-first-order equation before Ho’s publication in 1998. For example, in 1990, Sharma et al.
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(1990) studied the removal of Ni(II) from an aquatic environment by wollastonite. In the section
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on adsorption kinetics, they stated: “the adsorption of Ni (II) on wollastonite follows the first order
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adsorption rate expression of Lagergren (1898).” The great contributions of Ho toward correcting the citation style format for the PFO
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equation cannot be denied. However, the PFO equation was not originally proposed or initially
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expressed by Ho. In the scientific community, the authors who first propose a theoretical model
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should always be given credit for their contributions via correct citation (Kumar and Rattanaphani,
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2007; Wu, 2009; Utomo et al., 2010). Therefore, the original work by Lagergren (1898), who first
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presented the first-order-rate equation for the adsorption of oxalic acid and malonic acid onto
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charcoal, should be cited. The PFO equation can be expressed correctly in nonlinear (Eq. 7) and
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linear forms (Eq. 8 or Eq. 9).
log(qe − qt ) = log(qe ) −
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(7) (8)
(9)
where qe and qt are the amounts of adsorbate uptake per mass of adsorbent at equilibrium and at
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any time t (min), respectively; and k1 (1/min) is the rate constant of the PFO equation.
333
5.3.2. Problems in the application of the PFO equation
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334
EP
331
It cannot be denied that the PFO equation is widely applied in adsorption kinetics.
335
However, several problems related to the application of the PFO equation have been discussed in
336
the literature. First, many incorrect expressions for its linear forms have been published. Various
337
incorrect forms are shown in Eq. 10 (Alagumuthu et al., 2010), Eq. 11 (Fu et al., 2007; Jing et al.,
338
2014; Nekouei and Nekouei, 2017), Eq. 12 (Ho, 2014e; Ho, 2014a; Jing et al., 2014; Ho, 2016e; 15
ACCEPTED MANUSCRIPT
Ho, 2016b; Ho, 2016c; Ho, 2016a; Ho, 2016d; Ho, 2017), Eq. 13 (Ho, 2015), Eqs. 14 and 15 (Jing
340
et al., 2014), Eq. 16 (Kumar, 2006a), and Eq. 17 (Kumar and Porkodi, 2007b), which should be
341
avoided in future studies. As a result of these incorrect expressions, recalculation of the PFO
342
equation parameters was necessary to obtain the correct parameters (Wu et al., 2017). log(qe ) − k1 t 2.303
log(qe − qt ) =
log(qe ) − k1 2.303t
(10)
(11)
SC
log(qe − qt ) =
RI PT
339
log(qe − qt ) = log(qe )
Ci kt = 1 Ct 2.303
log(1 −
C i − Ct kt = 1 Ci − Ce 2.303
qe k1 = qe − qt 2.303t
EP
log
k1t 2.303
TE D
log
M AN U
1 k1 1 = + qt qet qe
log(qe − qt ) = log(qe ) −
k1 2.303
(12)
(13)
(14)
(15)
(16)
(17)
where Ci (mg/L), Ct (mg/L), and Ce (mg/L) are the concentrations of adsorbate at the initial time (t
344
= 0), any time t, and equilibrium, respectively.
345
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343
The second problem is the two unknown parameters (qe and k1). Furthermore, in most
346
cases, the PFO equation is only appropriate for the initial 20 to 30 min of contact time, not for the
347
whole range (Ho and McKay, 1998a). Thus, plots of Eq. 8 or Eq. 9 are only linear over
348
approximately the first 30 min; beyond this initial period, the experimental and theoretical data
16
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will not fit adequately (McKay et al., 1999). Another important problem is the selection of an
350
appropriate qe value. Notably, the adjusted qe value cannot be lower than the maximum measured
351
value of qt. This is because mathematical errors associated with taking the logarithm of a negative
352
number will occur when using Eq. 8 or Eq. 9 (Plazinski et al., 2009). Finally, the qe value
353
calculated using the PFO equation is not equal to the qe value obtained from experiments, which
354
further indicates the inability of the PFO equation to fit kinetic adsorption data (Febrianto et al.,
355
2009). The presence of a boundary layer or external resistance controlling the beginning of the
356
sorption process was argued to be responsible for this discrepancy (McKay et al., 1999).
SC
RI PT
349
Therefore, two methods have been recommended to obtain an accurate estimation of the
358
kinetic parameters in the PFO equation: (1) a trial and error process to obtain the optimal qe value
359
(Ho and McKay, 1998a), or (2) application of a nonlinear optimization technique. A simple guide
360
to using the nonlinear method is introduced in Section 9.
361
5.4. Pseudo-second-order (PSO) equation
362
5.4.1. Derivation of the PSO equation
TE D
M AN U
357
363
dn = K (no − n)2 dt
EP
removal of heavy metals from water using natural zeolites, as follows: (18)
AC C
364
In 1984, Blanchard et al. (1984) initially proposed a second-order rate equation for the
Integration of Eq. 18 gives: 1 − α = Kt no − n
(19)
After rearranging, Eq. 19 becomes: n=
Ktno + αno −1 Kt + α
(20)
17
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365
where n is the amount of M2+ fixed or the amount of NH4+ released at each instant; no is an
366
exchange capacity; and K is a rate constant. Plotting 1/(n0 − n) as a function of time (t) must produce a straight line, the slope of which
368
gives the rate constant K and the intercept leads to the exchange capacity. Considering the
369
boundary condition of n = 0 for t = 0, it follows that α = 1/n, and Eq. 20 can be rearranged to: (21)
If qt = no, qe = n, and k2 = K, Eq. 21 becomes: qt =
qe2k2t 1+ k2qet
M AN U
370
n2 + Kt 1 + Knt
SC
no =
RI PT
367
(22)
371
where qe (mg/g) and qt (mg/g) are the amount of adsorbate adsorbed at equilibrium and at any t
372
(min), respectively; and k2 (g/mg × min) is the rate constant of the PSO equation. The nonlinear form of the PSO equation (Eq. 22) has been applied elsewhere (Ho, 1995;
374
Ho; Wase et al., 1996). Recently, a series of comments made by Ho implied that the derivation and
375
first application of the PSO equation belongs to his work. Any application of the PSO equation in
376
the field of adsorption studies without citation of the original work or with a misquotation (i.e., the
377
citation of a secondary reference) might suffer from his comments. However, in reaction to Ho’s
378
comments, a series of notes were published by other scholars (Kumar, 2006d; Kumar, 2006c;
379
Kumar and Fávere, 2006; Kumar and Guha, 2006; Kumar and Rattanaphani, 2007) to clarify the
380
correct citation of the PSO equation. Thus, the nonlinear form of the PSO equation for solid-liquid
381
adsorption systems was not originally reported by Ho (1995) or first applied by Ho et al. (1996),
382
but initially proposed by Blanchard et al. (1984).
383
AC C
EP
TE D
373
In the literature, the PSO equation can be correctly expressed in four linear forms (Eqs. 23–
18
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384
26), and the initial adsorption rate (h) can be described by Eq. 29.
385
Expression for the linear form (Type 1) with a plot of t/qt versus t: t 1 1 = ( )t + qt qe k2qe2
RI PT
386
(23)
Expression of the linear form (Type 2) with a plot of 1/qt versus 1/t: 1 1 1 1 =( 2) + qt k2qe t qe
qt = − ( 388
SC
Expression of the linear form (Type 3) with a plot of qt versus qt/t: 1 qt ) + qe k 2 qe t
M AN U
387
(24)
Expression of the linear form (Type 4) with a plot of qt/t versus qt:
qt = −(k 2 qe )qt + k 2 qe2 t
rearranged to:
t 1 + 2 k 2 qe qe
(27)
Subsequently, when t approaches 0, Eqs. 23 and 27 can be expressed as Eq. 28. Setting h = qt/t, the initial adsorption rate (h; mg/g × min) can then be determined by Eq. 29.
AC C
392
1
EP
qt =
391
(26)
The initial adsorption rate (h) was proposed by Ho et al. (1996). First, Eq. 22 can be
TE D
389 390
(25)
t 1 = qt k 2 qe2
↔
qt = k 2 qe2 t
(28)
h = k 2 qe2
(29)
393
Clearly, only the linear form (Type 1, Eq. 23) might have been reported by Ho et al., (1996)
394
for the adsorption of dyes from waste streams by peat (Özacar, 2005; Kumar, 2006d; Kumar and
19
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Fávere, 2006; Wu, 2009). Kumar and Fávere (2006) hypothesized that, in adsorption research, the
396
Langmuir equation (Langmuir, 1918) has been the most widely used isotherm to describe
397
adsorption processes under equilibrium conditions. In the literature, four linear types of the
398
Langmuir isotherm have been reported. Irrespective of the linear expression reported, these
399
equations have been widely called the Langmuir isotherm. It is not correct to claim that the
400
Langmuir model was derived or proposed by other authors who transformed the original Langmuir
401
expression into a new linear expression (Kumar and Guha, 2006). In scientific literature, the names
402
of scientists (i.e., Langmuir or Freundlich) have always been presented, even after modification of
403
their equations (Arica, 2003). Similarly, Utomo et al. (2010) suggested that it might not be
404
necessary to cite papers that deal with mathematical modification and different mathematical
405
expressions of the models (i.e., PFO and PSO, and Langmuir). However, from the scientific point
406
of view, the authors who first proposed a theoretical model should be credited because of their
407
great contributions to the advancement of science. Therefore, the original work by Blanchard et al.
408
(1984) should be cited for the expression of the PSO equation (Özacar, 2005; Kumar, 2006d;
409
Kumar and Fávere, 2006; Plazinski et al., 2009; Wu, 2009; Utomo et al., 2010).
410
5.4.2. Problems in the application of the PSO equation
EP
TE D
M AN U
SC
RI PT
395
First, many incorrect expressions of the linear form of PSO equation are found in the
412
literature, as shown in Eq. 30 (Fu et al., 2007; Kumar and Porkodi, 2007b), Eq. 31 (Ho, 2014f),
413
Eqs. 32 and 33 (Ho, 2014g), Eq. 34 (Ho, 2013), Eq. 35 (Lin and Wang, 2009), Eq. 36 (Ho, 2014c),
414
Eq. 37 (Ho, 2014d), Eq. 38 (Ho, 2014), and Eq. 39 (Ho, 2015).
AC C
411
t 1 1 = + 2 qt k 2 qe qe t
(30)
20
ACCEPTED MANUSCRIPT
(31)
t 1 t = + qt k 2 q e q e
(32)
RI PT
t 1 1 = + qt 2k 2 qe
t 1 1 = ( qe2 ) + t qt k2 qe
(33)
t 1 1 = + t 2 qt k2 − qe qe
SC
(34)
M AN U
t 1 1 = ( )t 2 qt (k2 qe ) qe t 1 t = k2 qe2 + qt 2 qe
t 1 1 = + 2 qt k2 qe qe
(36)
(37)
(38)
(39)
EP
t kt t = 22 + qt k2 qe qe
TE D
1 1 1 = + 2 qt k2 qe qe
(35)
Second, based on the best fit of kinetic experimental data using the PSO model, many
416
authors have drawn controversial conclusions. For example, “the adsorption process is the
417
chemisorption, which involve valence forces through sharing electrons between adsorbate and
418
adsorbent”, “the best fit of experimental kinetic data in pseudo-second-order kinetics suggests the
419
chemisorption, which may involve valency forces through sharing of electrons between dye anion
420
and adsorbent”, and other similar conclusions. The problem with such conclusions has been
421
discussed by several researchers (Kumar, 2006a; Lima et al., 2015; Lima et al., 2016), who
AC C
415
21
ACCEPTED MANUSCRIPT
422
claimed that adsorption mechanisms cannot be directly assigned based on observing simple kinetic
423
experiments or by fitting kinetic models (i.e., the PFO and PSO models). Adsorption mechanisms can only be established by (1) using several analytical techniques
425
(i.e., FTIR, SEM, nitrogen adsorption-desorption isotherms, Raman spectroscopy, TGA/DTA,
426
DSC,
427
titration, and solution calorimetry), and (2) having a good sense of the chemical nature of the
428
adsorbate and adsorbent, adsorbent’s surface, and chemical or physical interactions between the
429
adsorbent and adsorbate (Volesky, 2007; Lima et al., 2015; Lima et al., 2016). The use of
430
analytical techniques together with adsorptive thermodynamic data (i.e., changes in enthalpy and
431
entropy) and activation and adsorption energies, are necessary to confirm whether the adsorption
432
of contaminants in aqueous solution is a chemical or physical process (Lima et al., 2015; Tran et
433
al., 2016).
Si and
13
C solid-state NMR, XRD, XPS, pHPZC, pHIEP, CHN element analysis, Boehm
M AN U
SC
29
RI PT
424
Finally, in most cases, experimental data for adsorption kinetics are well fitted by the linear
435
form of the PSO equation. However, caution should be taken in drawing conclusions based on
436
fitting to the linear form of the PSO equation. For example, Figure 6 presents a plot of t/qt versus t.
437
Clearly, the R2 values for the linear form of the PSO equation are very high (R2 > 0.99); however,
438
the corresponding R2 values for the nonlinear form of the PSO equation are significantly lower (R2
439
= 0.53–0.68). This finding means that the adsorption process of methylene green 5 (MG5) onto
440
synthesized activated carbon and commercial activated carbon (porous materials) is not
441
adequately described by the PSO equation. In fact, Tran et al. (2017a) concluded that the process
442
of MG5 adsorption onto these porous materials involved π-π interactions and pore filling, and was
443
not related to chemical adsorption. Obviously, the nonlinear method can be applied to obtain
444
kinetic model parameters that are more accurate than those obtained using the linear method.
AC C
EP
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434
22
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Figure 6
445 446
5.5. Elovich equation
447
5.5.1. Derivation of the Elovich equation An empirical equation was firstly proposed by Roginsky and Zeldovich (1934) for the
449
adsorption of carbon monoxide onto manganese dioxide. However, this equation is now generally
450
known as the Elovich equation and has been extensively applied to chemisorption data
451
(McLintock, 1967). This equation can be expressed mathematically as follows:
SC
RI PT
448
(40)
M AN U
dqt = α exp(− βqt ) dt 452
where qe and qt are the amounts of adsorbate uptake per mass of adsorbent at equilibrium and at
453
any time t (min), respectively; α (mg/g × min) is the initial rate constant because dqt/dt → α when
454
qt → 0; and β (mg/g) is the desorption constant during any one experiment.
become Eq. 41 (nonlinear). qt =
460
ln(1 + αβ t )
(41)
EP
linear form (Eq. 42) can be obtained: qt =
459
β
To simplify the Elovich equation, Chien and Clayton (1980) assumed αβt >> 1. Thus, a
457 458
1
AC C
456
By applying the boundary conditions of qt = 0 at t = 0, the integrated form of Eq. 40 will
TE D
455
1
β
ln(αβ ) +
1
β
ln(t )
(42)
and a plot of qt versus lnt should give a linear relationship with a slope of (1/β) and an
intercept of (1/β)ln(αβ).
23
ACCEPTED MANUSCRIPT
461
5.5.2. Incorrect expression of the Elovich equation Errors in the presentation of the nonlinear form of the Elovich model are common in the
463
literature. These incorrect equations (Eqs. 43–45) can be found in several previous papers (Ho and
464
McKay, 1998a; Lin and Wang, 2009; Alagumuthu et al., 2010; Ben Ali et al., 2016).
RI PT
462
qt = β ln(αβ ) + ln(t ) 1
β
ln(t )
(44)
SC
qt = β ln(αβ ) +
(43)
465 466 467
5.6. Intra-particle diffusion model
M AN U
qt = β ln(αβ ) + β ln(t )
(45)
The linearized transformation of the intra-particle diffusion model (Weber and Morris, 1963) is presented as follows: qt = k p t + C
(46)
where kp (mg/g × min) is the rate constant of the intra-particle diffusion model and C (mg/g) is a
469
constant associated with the thickness of the boundary layer, where a higher value of C
470
corresponds to a greater effect on the limiting boundary layer.
TE D
468
Generally, although the PSO model can adequately describe adsorption kinetic
472
experimental data, this model does not reveal the adsorption mechanisms. Similarly, the Elovich
473
equation seems to describe various reaction mechanisms, such as bulk diffusion and surface
474
diffusion. In contrast, the intra-particle diffusion model can be useful for identifying the reaction
475
pathways and adsorption mechanisms and predicting the rate-controlling step. In a solid-liquid
476
sorption process, adsorbate transfer is often characterized by film diffusion (also known as
477
external diffusion), surface diffusion, and pore diffusion, or combined surface and pore diffusion.
478
In short, if a plot of qt against t0.5 is linear and passes through the origin, the adsorption is entirely 24
AC C
EP
471
ACCEPTED MANUSCRIPT
479
governed by intra-particle diffusion. In contrast, if the intra-particle diffusion plot gives multiple
480
linear regions, then the adsorption process is controlled by a multistep mechanism. Four steps associated with transport processes during adsorption by porous adsorbents
482
were originally proposed in reference (Walter, 1984). The first stage is transport in the solution
483
phase (known as “bulk transport”; occurs quickly), which can occur instantaneously after the
484
adsorbent is transferred into the adsorbate solution; therefore, it does not control engineering
485
design. In most cases, this stage occurs too rapidly and its contribution is considered negligible.
486
The second stage is “film diffusion” (occurs slowly). In this stage, the adsorbate molecules are
487
transported from the bulk liquid phase to the adsorbent’s external surface through a hydrodynamic
488
boundary layer or film. The third stage involves diffusion of the adsorbate molecules from the
489
exterior of the adsorbent into the pores of the adsorbent, along pore-wall surfaces, or both (known
490
as “intraparticle diffusion”; occurs slowly). The last stage, adsorptive attachment, often occurs
491
very quickly; therefore, it is also not significant for design. These four steps are summarized in
492
Figure 7 (Weber and Smith, 1987).
TE D
M AN U
SC
RI PT
481
Figure 7
493
6. Adsorption isotherms
495
6.1. Adsorption equilibrium
EP
494
Milonjić (2009a) and Milonjić (2010) suggested that the amount of adsorbate adsorbed onto
497
an adsorbent depended on the equilibrium concentrations of metal ions, equilibrium solution pH,
498
and temperature. An adsorption isotherm should be given as the equilibrium adsorbed amounts
499
versus the equilibrium ion concentrations for a constant equilibrium solution pH and temperature.
500
Thus, environmental parameters in the sorption system (especially solution pH) must be carefully
501
controlled at the given value over the entire contact period until the sorption equilibrium is
AC C
496
25
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reached. These comments were in good agreement with the suggestion that metal-ion adsorption is
503
pH dependent (Volesky, 2003; Tien, 2007; Volesky, 2007; Tien, 2008). However, the pH effect
504
has invariably been examined in terms of the initial pH of the aqueous solution. Not a single case
505
has reported data demonstrating the changes in the solution pH during the course of an adsorption
506
experiment.
RI PT
502
In the scientific literature, adsorption equilibrium studies in batch experiments have been
508
conducted in different ways as follows: (1) solution pH values were not mentioned in the
509
manuscript, (2) initial pH values were neither measured nor adjusted and final pH values were
510
measured, (3) initial and final pH values were measured, (4) initial pH values were adjusted and
511
final pH values were not mentioned, (5) initial pH values were adjusted and final pH values were
512
measured, (6) initial and final pH values were adjusted, (7) pH was controlled several times during
513
the course of the reaction, (8) a constant pH was maintained throughout the equilibration time by
514
adding acidic or alkaline solutions, and (9) experiments were conducted at a constant pH using a
515
buffered solution (Smičiklas et al., 2009).
TE D
M AN U
SC
507
Kumar (2006a) recommended that presenting a plot of qe versus Ce for the complete
517
adsorption isotherm in an adsorption study plays a key role in identifying the regions (e.g., Henry,
518
Freundlich, Langmuir, and BET) in which the experimental data relating to adsorption equilibrium
519
are actually located. In contrast, plots of the Freundlich, Langmuir, or other adsorption isotherm
520
models do not help to identify these regions. Figures 8a and 8b provide typical complete
521
adsorption isotherms that should be presented in the investigation of liquid-phase adsorption.
522
Kumar and Sivanesan (2006) also recommended that using equilibrium data covering the
523
complete isotherm was the best way to obtain the parameters in isotherm expressions; equilibrium
524
data with a partial isotherm was not sufficient, instead equilibrium data that covers the complete
AC C
EP
516
26
ACCEPTED MANUSCRIPT
525
isotherm was required. Furthermore, an inconsistent definition of the adsorption isotherm plot in the literature was
527
recognized by Li and Pan (2007); the plot of qe against Ce/Wo (with Wo being a liquid/solid ratio) is
528
invisible with the traditional definition of the complete adsorption isotherm (the plot of qe versus
529
Ce).
RI PT
526
Recently, Senthil Kumar et al. (2014) presented a plot of %removal versus C0 in an
531
adsorption equilibrium study instead of presenting the complete adsorption isotherm (Figure 8a).
532
However, Hai (2017) made a critical note that it is clear that at every initial concentration of
533
methylene blue (MB; 50, 100, 150, 200, 250 mg/L), the removal percentage of MB by sulfuric
534
acid-treated orange peel (STOP) at 30 °C was always overwhelmingly higher than the
535
corresponding values at 40, 50, and 60 °C. This result revealed that increasing the temperature
536
from 30 to 60 °C resulted in a decrease in the adsorption capacity (qe) of MB dye onto STOP
537
(Figure 8a). However, the maximum adsorption capacities of STOP from the Langmuir model
538
(Qomax) exhibited the following order: 60 °C (83.333 mg/g) > 50 °C (71.428 mg/g) > 40 °C (62.5
539
mg/g) > 30 °C (50 mg/g). This logic problem might be caused by the adsorption process of MB
540
onto STOP not reaching equilibrium at the different temperatures (see adsorption isotherms in
541
Figure 8a) owing to the low initial MB concentrations (50–250 mg/L) used at a high solid/liquid
542
ratio of 4.0 g/L (Hai, 2017). Therefore, in adsorption equilibrium studies, presenting plots of
543
%removal versus Co, %removal versus Ce, or qe versus Co should be avoided, and a plot of qe
544
versus Ce for the complete adsorption isotherm must be presented.
M AN U
TE D
EP
AC C
545
SC
530
Figure 8b provides a typical example of the comparison of adsorption performance under
546
the same operating conditions (i.e., temperature and solution pH). Clearly, “adsorbent B” exhibits
547
a higher affinity than “adsorbent A” at low initial adsorbate concentrations (Co) and low
27
ACCEPTED MANUSCRIPT
548
equilibrium adsorbate concentrations (Ce), whereas the opposite order (“adsorbent A” >
549
“adsorbent B”) was found at higher Co and Ce values (Volesky, 2007). It was recently identified that many researchers have made questionable conclusions when
551
studying the effects of agitation rate or shaking speed on the adsorption capacity (qe) or maximum
552
adsorption capacity (Qomax) of an adsorbent toward an adsorbate. For example, Chu et al. (2005)
553
concluded that the adsorption capacity of vitamin E onto silica varies as a function of the agitation
554
rate (120–180 rpm). The Qomax values exhibited the following order: 43.71 mg/g at 180 rpm >
555
24.20 mg/g at 160 rpm > 24.20 mg/g at 140 rpm > 17.62 mg/g at 120 rpm. However, Choong and
556
Chuah (2005) made a critical remark that the agitation rate only impacts on the speed at which a
557
system reaches equilibrium, but not on the equilibrium itself. This means that when the adsorption
558
process obtains a true equilibrium (sufficient contact time between adsorbent and adsorbate), the
559
Qomax values at different agitation rates will be insignificantly different. This is because the
560
decrease of the boundary layer resistance a higher agitation rate will facilitate the transport of the
561
adsorbate to the adsorbent.
SC
M AN U
TE D
562
RI PT
550
Figure 8
Although adsorption isotherms can insignificantly contribute to elucidating adsorption
564
mechanisms, they are less helpful in this regard than data on adsorption kinetics and
565
thermodynamics (Volesky, 2003; Tien, 2007; Tien, 2008). However, collecting adsorption
566
isotherms is a useful strategy to both describe the relationship between the adsorbate concentration
567
in solution (liquid phase) and the adsorbent (solid phase) at a constant temperature and design
568
adsorption systems (Tran et al., 2016).
AC C
EP
563
569
A wide variety of models of adsorption isotherms have been applied in the literature. These
570
models can be classified as follows: (1) irreversible isotherms and one-parameter isotherms (i.e.,
28
ACCEPTED MANUSCRIPT
Henry isotherm); (2) two-parameter isotherms (i.e., Langmuir, Freundlich, Dubinin–
572
Radushkevich, Temkin, Flory–Huggins, and Hill); (3) three-parameter isotherms (i.e., Redlich–
573
Peterson, Sips, Toth, Koble–Corrigan, Khan, Fritz–Schluender, Vieth–Sladek, and Radke–
574
Prausnitz); and (4) more than three-parameter isotherms (i.e., Weber–van Vliet, Fritz–Schlunder,
575
and Baudu) (Kumar and Porkodi, 2006; Hamdaoui and Naffrechoux, 2007; Foo and Hameed,
576
2010). Of these, the Langmuir and Freundlich models are the most commonly used, followed by
577
the Dubinin–Radushkevich and Redlich–Peterson models, because of the usefulness of their
578
model parameters, their simplicity, and their easy interpretability.
579
6.2. Langmuir equation
580
6.2.1. Derivation of the Langmuir equation
M AN U
SC
RI PT
571
The theoretical Langmuir equation (Langmuir, 1918), which was originally applied to the
582
adsorption of gases on a solid surface, was developed using the following assumptions: (1) a fixed
583
number of accessible sites are available on the adsorbent surface and all active sites have the same
584
energy; (2) adsorption is reversible; (3) once an adsorbate occupies a site, no further adsorption
585
can occur on that site; and (4) there is no interaction between adsorbate species. The nonlinear
586
form of the Langmuir model is described in Eq. 47 and its four linearized forms are shown in Eqs.
587
48–51.
588
o Qmax + K L Ce 1 + K LCe
AC C
qe =
EP
TE D
581
(47)
Hanes–Woolf linearization of the Langmuir model (Type 1): Ce 1 1 = ( o )Ce + o qe Qmax Qmax K L
589
(48)
Lineweaver–Burk linearization of the Langmuir model (Type 2):
29
ACCEPTED MANUSCRIPT
1 1 1 1 =( o ) + o qe Qmax K L Ce Qmax Eadie–Hoffsiee linearization of the Langmuir model (Type 3): qe = ( 591
− 1 qe o ) + Qmax K L Ce
(50)
Scatchard linearization of the Langmuir model (Type 4): qe o = − K L qe + Qmax KL Ce
RI PT
590
(49)
SC
(51)
where Qomax (mg/g) is the maximum saturated monolayer adsorption capacity of an adsorbent, Ce
593
(mg/L) is the adsorbate concentration at equilibrium, qe (mg/g) is the amount of adsorbate uptake
594
at equilibrium, and KL (L/mg) is a constant related to the affinity between an adsorbent and
595
adsorbate. For a good adsorbent, a high theoretical adsorption capacity Qomax and a steep initial
596
sorption isotherm slope (i.e., high KL) are generally desirable (Kratochvil and Volesky, 1998;
597
Wang, 2009).
TE D
M AN U
592
The limitations of using the four linear forms of the Langmuir model have been
599
highlighted by Bolster and Hornberger (2007). The transformation of data for linearization can
600
result in modifications of error structure, introduction of error into the independent variable, and
601
alteration of the weight placed on each data point, which often leads to differences in the fitted
602
parameter values between linear and nonlinear versions of the Langmuir model. For the Type 1
603
linearization, because Ce and Ce/qe are not independent, the correlation between Ce and Ce/qe is
604
overestimated, i.e., this equation may provide good fits to data that do not conform to the
605
Langmuir model. For the Type 2 linearization, transformation leads to clustering of data points
606
near the origin and is extremely sensitive to variability at low values of qe (high values of 1/qe).
607
For the Type 3 linearization, the abscissa is not error free, and qe/Ce and qe are not independent. 30
AC C
EP
598
ACCEPTED MANUSCRIPT
Thus, the correlation between qe/Ce and qe is underestimated, i.e., this equation may provide poor
609
fits to data that do conform to the Langmuir model. Finally, the variables qe and qe/Ce are also
610
not independent in the Type 4 linearization. In this case, the correlation between qe and qe/ Ce is
611
underestimated, i.e., this equation may provide a poor fit to data that do conform to the Langmuir
612
model.
613
6.2.2. Derivation of the separation factor
RI PT
608
If the experimental data are adequately described by the Langmuir model, it is essential to
615
calculate the separation factor. Hall et al. (1966) originally proposed that the essential
616
characteristics of the Langmuir isotherm model can be expressed in terms of a dimensionless
617
constant called the separation factor or equilibrium parameter RL, which is defined as follows: RL =
M AN U
SC
614
1 1 + K LCo
(52)
where RL is a constant separation factor (dimensionless) of the solid-liquid adsorption system, KL
619
is the Langmuir equilibrium constant, and Co (mg/L) is the initial adsorbate concentration.
TE D
618
Notably, the isotherm shape can be predicted using the separation factor (RL) (Weber and
621
Chakravorti, 1974) and the Freundlich exponent n (Worch, 2012). Table 1 summarizes the various
622
isotherm shapes.
624 625
Table 1
AC C
623
EP
620
6.2.3. Mistakes concerning the Langmuir model and the separation factor Wan, et al. (2014) published a corrigendum because of a misapplication of the nonlinear
626
form of the Langmuir equation (Eq. 53). A similar mistake in presenting the nonlinear form of the
627
Langmuir equation (Eq. 54) was observed by Kumar and Porkodi, (2007b).
31
ACCEPTED MANUSCRIPT
(53)
Ce 1 1 = + o o qe K LQmax Qmax Ce
(54)
RI PT
Ce C K = oe + o L qe Qmax Qmax
Furthermore, an unexpected typographical error was made in reference (Egirani, 2004). As
629
a result, the sentence “a plot of Ce/qe versus Ce should indicate a straight line of slope 1/KLQomax
630
and an intercept of 1/Qomax” was corrected to “a plot of Ce/qe versus Ce should indicate a straight
631
line of slope 1/Qomax and an intercept of 1/ KLQomax” by Ho (2004a).
SC
628
The incorrect expression and inaccurate calculation of RL were recognized and discussed
633
by Kumar (2006a) and Kumar (2006b). First, the separation factor RL is not a Langmuir constant,
634
and is only employed for isotherms that obey the Langmuir model. Second, RL values will vary
635
with the initial adsorbate concentration, irrespective of the shape of the isotherm, and RL values at
636
different initial adsorbate concentrations cannot be calculated directly from the Langmuir
637
isotherm, but can be calculated from the Langmuir equilibrium constant KL. These
638
misunderstandings and mistakes are summarized in Table 2.
TE D
M AN U
632
Furthermore, a mistake related to the definition of RL compared with the original definition
639
was stated by Fu et al. (2007). The incorrect presentation is shown in Eq. 55.
641
1 o 1 + K LQmax Co
(55)
AC C
RL =
EP
640
Recently, Hai (2017) commented that “the authors’ conclusion about separation factor
642
(RL) was not valid. It is noted that there is no information or value of RL mentioned in the paper’s
643
results and discussion. It is impossible for the authors to conclude that the values of RL were found
644
to be between 0 and 1, indicating the favorable adsorption of MB dye onto STOP.”
645
Clearly, the separation factor is related to the Langmuir equation in the adsorption 32
ACCEPTED MANUSCRIPT
isotherm. Nevertheless, Goswami et al. (2016) recently described an incorrect relationship
647
between the separation factor and adsorption kinetic models (i.e., PFO, PSO, and intra-particle
648
diffusion) at different initial cadmium concentrations. This is a fundamental misunderstanding that
649
should be avoided.
651
6.3. Freundlich equation
652
6.3.1. Derivation of the Freundlich equation
SC
Table 2
650
RI PT
646
The Freundlich equation is one of the earliest empirical equations used to describe
654
equilibrium data and adsorption characteristics for a heterogeneous surface (Freundlich, 1906).
655
Unlike the Langmuir equation, the Freundlich isotherm can describe neither the (arithmetic)
656
linearity range at very low concentrations nor the saturation effect at very high concentrations.
657
Hence, the Freundlich isotherm does not describe the saturation behavior of an adsorbent (Wang,
658
2009). The nonlinear and linear forms of the Freundlich equation can be expressed as shown in
659
Eqs. 56 and 57, respectively.
qe = K F Cen
TE D
M AN U
653
log qe = n log Ce + log K F
(56)
EP
(57)
where qe (mg/g) is the amount of adsorbate uptake at equilibrium, Ce (mg/L) is the adsorbate
661
concentration at equilibrium, KF (mg/g)/(mg/L)n is the Freundlich constant, and n (dimensionless)
662
is the Freundlich intensity parameter, which indicates the magnitude of the adsorption driving
663
force or the surface heterogeneity.
AC C
660
33
ACCEPTED MANUSCRIPT
6.3.2. Mistakes concerning the Freundlich equation
665 666
Several investigators have identified an incorrect expression (Eq. 58) of the linear form of the Freundlich equation (Kumar and Porkodi, 2007b; Alagumuthu et al., 2010).
log qe =
1 + log K F n log Ce
RI PT
664
(58)
Furthermore, several discussions that are inconsistent with the original concepts of the
668
Freundlich theory have been identified in the literature (Lu, 2008; Hai, 2017). Hai (2017)
669
commented that the exponent n of the Freundlich equation must be dimensionless. Therefore, the
670
original authors incorrectly reported the units of the exponent n (g/L); and there is no validation for
671
the statement of the significance of the n value for the adsorption of MB dye onto STOP is as
672
follows: when n = 1 the adsorption is linear, when n < 1 the adsorption is a chemical process, and
673
when n > 1 the adsorption is a physical process. According to the Freundlich theory, the adsorption
674
isotherm becomes linear when n = 1, favorable when n < 1, and unfavorable when n > 1. Similarly,
675
Harsha et al. (2015) also made a basic mistake when they reported the units of the exponent n as
676
g/L.
TE D
M AN U
SC
667
Lu (2008) highlighted that in many cases KF is not the maximum adsorption capacity and
678
the KF value is only equal to the maximum adsorption capacity when n approaches infinity.
679
Although KF is not defined as the maximum adsorption capacity (Qomax), KF values and Qomax
680
values should be of the same order. Such a mistake has been discussed by Tran (2017), where the
681
reported KF values followed the order: 4.471 at 303 K > 3.439 at 313 and 323 K > 2.877 at 333 K,
682
while the Qomax values were 30.12 mg/g at 313 K > 21.367 mg/g at 323 K > 21.276 mg/g at 333 K
683
> 20.492 mg/g at 303 K. This mistake might be attributable to a miscalculation.
684
AC C
EP
677
Notably, Kumar (2006a) highlighted that values for the exponent n (Eq. 59) in the range of
34
ACCEPTED MANUSCRIPT
0–10 suggest favorable adsorption. If the experimental equilibrium data do not lie in the Henry
686
region, then the linear regression method will just check the hypothesis instead of verifying the
687
theory behind the Freundlich model; therefore, it is not possible in practice to obtain n > 10
688
(Kumar, 2006a). A corresponding error was also found in a published paper (Huang et al., 2014),
689
in which the n values reported for the removal of aniline and Cr(VI)/aniline + Cr(VI) by an
690
activated carbon/chitosan composite were 10.20 and 11.34, respectively.
RI PT
685
SC
qe = K F Ce1 / n 6.4. Redlich–Peterson equation
692
6.4.1. Derivation of the Redlich–Peterson equation
M AN U
691
(59)
A three-parameter Redlich–Peterson isotherm was proposed upon considering the
694
limitations of the Freundlich and Langmuir isotherms (Redlich and Peterson, 1959). This model
695
incorporates the features of the Freundlich and Langmuir models and might be applicable for
696
demonstrating adsorption equilibrium over a wide range of adsorbate concentrations. The
697
nonlinear form of this empirical model is given as follows:
K RPCe 1 + a RP Ceg
(60)
EP
qe =
TE D
693
where KRP (L/g) and aRP (mg/L)−g are the Redlich–Peterson constants and g (dimensionless) is an
699
exponent whose value must lie between 0 and 1.
700
AC C
698
Eq. 60 becomes a linear isotherm (Henry’s law equation) at low surface coverage (g = 0),
701
reduces to the Langmuir isotherm when g = 1, and transforms into the Freundlich isotherm when
702
KRP and aKP >> 1 and g = 1. Therefore, if the g value is outside the range of 0–1, the data is not
703
adequately explained by the Redlich–Person equation. Accurate calculation of g can be helpful in
704
expatiation of where the isotherm presentations, neither in the Freundlich or Langmuir (Kumar
35
ACCEPTED MANUSCRIPT
705
and Sivanesan, 2006).
706
6.4.2 Mistakes concerning the Redlich–Peterson equation A series of comments related to mistakes in calculating the exponent g have been reported
708
elsewhere (Inbaraj, 2006; Kumar and Porkodi, 2007a; Kumar et al., 2007; Kumar et al., 2007;
709
Kumar and Porkodi, 2008). These mistakes involved values of the exponent g that were outside the
710
range of 0–1 (Table 3). It is not easy to predict the parameters of the Redlich–Peterson equation
711
because there are three unknown parameters. Although a new linear form of the Redlich–Peterson
712
equation was published by Wu et al. (2010), the nonlinear form might be more appropriate for
713
accurately calculating the parameters of adsorption models with more than two unknown
714
parameters, such as the Redlich–Peterson model.
M AN U
SC
RI PT
707
Table 3
715
6.5. Dubinin–Radushkevich equation
717
6.5.1. Derivation of the Dubinin–Radushkevich equation
structure of an adsorbent (Dubinin and Radushkevich, 1947), and is expressed as follows:
qe = q DR e − K RDε
2
EP
719
The Dubinin–Radushkevich equation was developed to account for the effect of the porous
(61)
The linear form of the Dubinin–Radushkevich equation is:
AC C
718
TE D
716
ln q e = − K DR ε
ε = RT ln(1 +
2
+ ln q DR
(62)
1 ) Ce
(63)
By inserting Eq. 63 into Eq. 61, Eq. 64 can be obtained:
36
ACCEPTED MANUSCRIPT
2
2
2
ln q e = − K DR R T ln (1 +
1 ) + ln q DR Ce
(64)
The parameters qDR and KDR in Eq. 64 can be obtained as follows: (1) a plot of lnqe against
721
ln2(1 + 1/Ce) has a slope = −KDRR2T2 and an intercept = lnqRD, and the E value can be obtained
722
using Eq. 65, and (2) a plot of lnqe against R2T2ln2(1 + 1/Ce) has a slope = −KDR and an intercept =
723
lnqRD, and the E value can be obtained using Eq. 66. Notably, the E values obtained from Eqs. 65
724
and 66 are the same (Tran et al., 2016).
E=
1 1 = 2 K DR − 2slope
SC
1 RT = 2 K DR − 2 slope
M AN U
E=
RI PT
720
(65)
(66)
where qRD (mg/g) is the adsorption capacity, KRD (mol2/kJ2) is a constant related to the sorption
726
energy, ɛ is the Polanyi potential, E (kJ/mol) is the mean adsorption energy, R is the gas constant, T
727
is the temperature in Kelvin, and qe and Ce are obtained from Eq. 1.
728
6.5.2. Mistakes concerning the Dubinin–Radushkevich equation
731
equation (Cavas, 2008; Fu et al., 2008). These erroneous forms are shown in Eqs. 67–70.
EP
730
Some authors have highlighted erroneous expressions of the Dubinin–Radushkevich
Incorrect nonlinear form of the Dubinin–Radushkevich equation:
AC C
729
TE D
725
2
q e = q DR exp( − K DR ( RT (ln 1 + 1 / C e ) ) 732
Incorrect linear form of the Dubinin–Radushkevich equation:
ln q e = −2 K DR RT ln(1 + 733
(67)
1 ) + ln q DR Ce
(68)
Incorrect expressions for the Polanyi potential (ɛ):
37
ACCEPTED MANUSCRIPT
ε = RTe1/ C
(69)
1 ) Ce
(70)
e
RI PT
ε = RT ln(
Additionally, the magnitude of E may give useful information about the type of adsorption
735
process (physical or chemical) (Fu et al., 2008; Tran et al., 2016). Fu et al. (2008) commented that
736
the E values for the removal of phenolic compounds by organophilic bentonite can be categorized
737
as corresponding to ion exchange (E = 8–16 kJ/mol), whereas the original authors made an
738
inconsistent conclusion that the adsorption of two phenolic compounds could be regarded as
739
physical adsorption.
M AN U
SC
734
Recently, Tran (2017) made the following comment on the conclusions of the original
741
paper: “the obtained value of E in this work varies from 32.596 kJ/mol to 40.572 kJ/mol for studied
742
temperature which is higher than the adsorption energy values previously enumerated.” However,
743
these adsorption energy (E) values might not have been calculated correctly. Assuming the β
744
values at 303 K (β = 1.93 × 10−8 mol2/kJ2), 313 K (2.99 × 10−8), 323 K (2.00 × 10−8), and 333 K
745
(2.35 × 10−8) reported by these authors are correct, the recalculated adsorption energy (E) values
746
are 5090 kJ/mol at 303 K, 4089 kJ/mol at 313 K, 5000 kJ/mol at 323 K, and 4613 kJ/mol at 333 K.
747
Thus, the E values in this study ranged from 4089 to 5091 kJ/mol, which is impossible for a
748
heavy-metal biosorption process.
749
7. Adsorption thermodynamics
750
7.1. Principles of adsorption thermodynamics
AC C
EP
TE D
740
751
Thermodynamic studies are an indispensable component of predicting adsorption
752
mechanisms (e.g., physical and chemical). The key distinctions between physical and chemical
38
ACCEPTED MANUSCRIPT
753
adsorption were summarized in detail in a recent report (Tran et al., 2016). The thermodynamic
754
parameters can be computed according to the laws of thermodynamics using the following
755
equations: ∆G o = − RT ln K C
RI PT
756
(71)
The relationship between ∆G° and ∆H° and ∆S° is described as follows: ∆Go = ∆H 0 − T∆S 0
The well-known van’t Hoff equation is obtained by substituting Eq. 71 into Eq. 72 − ∆H o 1 ∆S o x + R T R
(73)
M AN U
ln KC =
SC
757
(72)
758
where R is the universal gas constant (8.3144 J/(mol × K)) and T is the absolute temperature in
759
Kelvin.
The Gibbs energy change (∆G°) is directly calculated from Eq. 71, whereas the enthalpy
761
change (∆H°) and entropy change (∆S°) are determined from the slope and intercept, respectively,
762
of a plot of lnKC versus 1/T (Eq. 73). The common units of ∆G°, the gas constant, and temperature
763
are J/mol, J/(mol × K), and K, respectively; therefore, the equilibrium constant KC in Eq. 73 must
764
be dimensionless (Milonjić, 2007; Milonjić, 2009b; Canzano et al., 2012; Dawood and Sen, 2012;
765
Zhou et al., 2012; Zhou and Zhou, 2014; Tran et al., 2016; Ghosal and Gupta, 2017; Hai, 2017;
766
Rahmani-Sani et al., 2017; Zhou, 2017).
EP
AC C
767
TE D
760
Eq. 72 describes the relationship of ∆G° with ∆H° and ∆S°, and it is useful for checking the
768
logic of calculated values for these thermodynamic parameters. Unfortunately, associated
769
mistakes have been found in the literature. Fu et al. (2008) substituted the values of ∆H° and ∆S°
770
into Eq. 72 to obtain ∆G°, but the obtained ∆G° values were significantly different from the ∆G°
771
values obtained using Eq. 71. Fu et al. (2008) highlighted that this mistake might result from
39
ACCEPTED MANUSCRIPT
772
incorrect application of the method for calculating the equilibrium constant. Clearly, accurate estimation of thermodynamic parameters is directly dependent on
774
accurate determination of the equilibrium constant between two phases (KC; dimensionless). In the
775
literature, the thermodynamic parameters can be calculated from KC values derived from
776
adsorption-isotherm constants (i.e., Langmuir, Freundlich, Frumkin, Flory–Huggins, and Henry)
777
or the partition coefficient (Liu, 2009; Doke and Khan, 2013; Tran et al., 2016). However, to
778
obtain an appropriate calculation method, several factors need to be considered thoroughly. First,
779
the equilibrium constant (KC) must be dimensionless. Second, the linear regression coefficient (R2)
780
of the van’t Hoff equation must be high. Third, the adsorbate in solution must have a high or low
781
concentration. In addition, the temperatures used for calculating the thermodynamic parameters
782
must have units of Kelvin (K), not degrees Celsius (°C). The incorrect use of temperature units led
783
to the publication of an erratum by Ho (2004a), with accurate recalculations.
M AN U
SC
RI PT
773
As the equilibrium constant KC can be derived using a number of approaches, considerable
785
variation in the thermodynamic parameters can be obtained; therefore, the most appropriate
786
approach should be determined. Here, we thoroughly discuss the derivation of the equilibrium
787
constant KC from adsorption isotherms (i.e., Langmuir, Freundlich, and Henry constants) and the
788
partition coefficient because of their popularity in the literature.
789
7.2. Equilibrium constant derived from the Langmuir constant (KL)
EP
AC C
790
TE D
784
The Langmuir equation was initially derived from a kinetic study and then subsequently
791
from a thermodynamic study. The derivation of the Langmuir equation from the thermodynamic
792
perspective can be described as follows (Crittenden et al., 2012; Tran et al., 2016). The
793
relationship between vacant surface sites on the surface of an adsorbent (Sv; mmol/m2), adsorbate
794
species in solution (A; mmol), and adsorbate species bound to surface sites (SA; mmol/m2) can be
40
ACCEPTED MANUSCRIPT
795
described by the following reaction:
SV + A ↔ SA
(74)
On the basis of the Langmuir expression, it is assumed that the reaction has a constant
797
Gibbs energy change (∆G°; J/mol) for all sites, so the thermodynamic equilibrium constant (KC;
798
dimensionless) can be expressed as:
RI PT
796
− ∆G o
⇔ KC = e
∆G = − RT ln K C
RT
(75)
SC
o
Another Langmuir assumption is that each site is capable of binding at most one adsorbate
800
molecule (monolayer). According to the equilibrium condition, the thermodynamic equilibrium
801
constant may be written as:
SA KC = =e SV [ A]
M AN U
799
− ∆G o
RT
(76)
where [A] is the concentration of adsorbate A in solution at equilibrium (mg/L), R is the universal
803
gas constant (8.314 J/mol × K), and T is absolute temperature K (273 + °C).
TE D
802
The critical problem with Eq. 76 is that there are two unknown parameters (i.e., SV and
805
[A]). However, this problem can be solved if the total sites available or monolayer coverage (ST;
806
mol/m2) are fixed:
807
SA + SA KC [ A]
AC C
ST = SV + SA =
EP
804
⇔
SA =
K C [ A]ST 1 + K C [ A]
(77)
The expression of SA in units of mmol/m2 is not useful in mass balance, and units of mass
808
of adsorbate adsorbed per unit mass of adsorbent (qe; mg/g) are much more useful. The mass
809
loading (qe) can be obtained in units of mg/g (Eq. 1) by multiplying both sides of Eq. 71 by the
810
surface area (SBET; m2/g) of the adsorbent and the molecular weight of the adsorbate (Mw; g/mol).
41
ACCEPTED MANUSCRIPT
811
Thus, Eq. 77 becomes:
K [ A]ST S BET M w SA.S BET .M w = C 1 + K C [ A]
⇔
o Qmax K L Ce qe = 1 + K L Ce
(78)
where qe (mg/g) = SA × SBET × Mw is described by Eq. 1; Ce (mg/L) = [A] is the concentration of
813
adsorbate in solution at equilibrium; Qomax (mg/g) = ST × SBET × Mw is the maximum monolayer
814
adsorptive capacity of the adsorbent when the surface sites are saturated with adsorbate; the
815
relationship between KL and KC is described in the following discussion.
SC
RI PT
812
However, the main problem is that the Langmuir constant KL is dimensional with common
817
units of L/mmol or L/mg, while the equilibrium constant KC is dimensionless (without units).
818
Thus, the direct application of KL (L/mmol or L/mg) in the calculation of thermodynamic
819
parameters produces incorrect results, as discussed by many authors (Milonjić, 2007; Milonjić,
820
2009b; Canzano et al., 2012; Dawood and Sen, 2012; Zhou et al., 2012; Zhou and Zhou, 2014;
821
Anastopoulos and Kyzas, 2016; Tran et al., 2016; Ghosal and Gupta, 2017; Hai, 2017,
822
Rahmani-Sani et al., 2017). To solve this unit problem, several methods have been recommended
823
(Milonjić, 2007; Zhou and Zhou, 2014; Tran et al., 2016). Depending on the units of KL, the
824
equilibrium constant KC can easily be obtained as a dimensionless constant.
EP
TE D
M AN U
816
When an adsorption study is conducted in aqueous solution and KL has units of L/mmol, KC
826
can be easily obtained as a dimensionless parameter by multiplying KL by 55.5 and then by 1,000
827
(Eq. 79). This method was originally proposed by Milonjić (2007) and then developed by Zhou
828
and Zhou (2014) and Tran et al. (2016). The values of the parameters ∆G°, ∆H°, and ∆S° can be
829
calculated using the following equations:
AC C
825
KC = 55.5×1,000× KL
(79)
42
ACCEPTED MANUSCRIPT
∆Go = −RT ln(55.5×1,000× KL ) ln(55 .5 × 1,000 × K L ) =
(80)
− ∆H o 1 ∆S o × + R T R
(81)
where the factor 55.5 is the number of moles of pure water per liter (1,000 g/L divided by 18
831
g/mol) and the term 55.5 × 1,000 × KL is dimensionless.
RI PT
830
In the case of KL with units expressed in L/mg, Milonjić (2007 and 2009b) stated that KL
833
could be obtained as a dimensionless parameter by multiplying KL by 106 (Eq. 82). However, Zhou
834
and Zhou (2014) recommended that KC could be obtained as a dimensionless parameter by
835
multiplying KL by the molecular weight of the adsorbate (Mw; g/mol), by 1000, and then by 55.5
836
(Eq. 85).
M AN U
SC
832
KC = 106 K L ∆G o = − RT ln(106 K L )
TE D
− ∆H o 1 ∆S o ln(10 K L ) = x + R T R 6
(82) (83) (84)
where the factor 106 is the solution density (assuming the density of pure water is 1.0 g/mL) and
838
the term 106 × K is dimensionless.
EP
837
K C = M w × 55.5 ×1,000 × K L
AC C
(85)
∆Go = −RT ln(Mw × 55.5×1,000× KL )
(86)
− ∆ H o 1 ∆S o ln( M w × 55.5 ×1,000 × K L ) = × + R T R
(87)
839
where the factor 55.5 is the number of moles of pure water per liter and the term Mw × 55.5 × 1,000
840
× KL is dimensionless.
43
ACCEPTED MANUSCRIPT
In a recent paper, Tran et al. (2016) applied Eqs. 79–87 to compare thermodynamic
842
parameters calculated from the Langmuir constants derived from four linear forms of the
843
Langmuir model. They concluded that (1) both the recommendations of Milonjić (2007 and
844
2009b) and Zhou and Zhou (2014) provide the same methods for calculating the thermodynamic
845
parameters, and (2) there is some deviation between these methods for the results from Types 1, 3,
846
and 4; only Type 2 produces identical results.
847
7.3. Equilibrium constant derived from the Freundlich constant (KF)
SC
RI PT
841
The Freundlich equation is consistent with the thermodynamics of heterogeneous
849
adsorption (Crittenden, et al., 2012). The Freundlich constant KF can be obtained as a
850
dimensionless value using Eq. 88 (Ghosal and Gupta, 2015; Tran et al., 2016).
M AN U
848
K ρ 106 (1− ) KC = F ( ) n 1000 ρ 1
K ρ 106 (1− ) ∆G o = − RT ln( F ( ) n ) 1000 ρ
K F ρ 10 6 (1− n ) − ∆ H o 1 ∆S o x + ( ) )= R T R 1000 ρ 1
ln(
(89)
(90)
where ρ is the density of pure water (assumed as ~1.0 g/mL).
EP
851
TE D
1
(88)
It is noted that the units of KF rely on the units used for the liquid-phase concentration (C)
853
and solid-phase concentration (q). Units of mg/L or mmol/L for C and mg/g or mmol/g for q are
854
used most frequently to demonstrate adsorption from water solutions. The differing units of KF can
855
be reciprocally converted using Eq. 91 (Worch, 2012).
AC C
852
K F = K F' ( M w )1−1 / n 856
(91)
where the units of the Freundlich constant KF are (mg/g)/(mg/L)1/n, with Co and Ce (mg/L) and qe
44
ACCEPTED MANUSCRIPT
857
(mg/g); the units of KF′ are (mmol/g)/(mmol/L)1/n, with Co and Ce (mmol/L) and qe (mmol/g); and
858
Mw is the molecular weight of the adsorbate. The exponent 1/n is not affected by the units of the
859
liquid-phase concentration (C) and solid-phase concentration (q) Based on a comparison of the thermodynamic parameters calculated from the Freundlich
861
constant (dimensionless) and Langmuir constant (dimensionless), Tran et al., (2016) concluded
862
that the signs and magnitudes of ∆G°, ∆H°, and ∆S° calculated from KF were consistent with those
863
calculated from KL. Of course, the experimental data in the adsorption isotherms must be fitted
864
well by the Langmuir and Freundlich models, and the R2 value of the van’t Hoff equation must be
865
higher than 0.90 (Tran et al., 2016). It is also evident that, to some extent, the application of KF to
866
estimate the thermodynamic parameters should be approached with caution.
867
7.4. Equilibrium constant derived from the partition coefficient (Kp)
M AN U
SC
RI PT
860
868
reported by Biggar and Cheung (1973). The equilibrium constant can be defined as follows:
Kp =
as γ s C s = ae γ eCe
TE D
869
Changes in the thermodynamic partition coefficient with changes in temperature were first
(92)
where as is the activity of the adsorbate adsorbed onto the adsorbent, ae is the activity of the
871
adsorbate in solution at equilibrium, γs is the activity coefficient of the adsorbate adsorbed onto the
872
adsorbent, γe is the activity coefficient of the adsorbate in solution at equilibrium, Cs is the
873
concentration of adsorbate adsorbed onto the adsorbent at equilibrium (mg/L), and Ce is the
874
concentration of adsorbate in solution at equilibrium (mg/L). Cs is defined by the mass balance of
875
adsorbate that disappears from the solution, which should appear on the adsorbent.
876 877
AC C
EP
870
When the concentration of adsorbate in the solution approaches zero, which results in Cs → 0 and Ce → 0, the activity of coefficient γ approaches unity, and Eq. 92 can be written as:
45
ACCEPTED MANUSCRIPT
Cs
Lim C Cs →0
e
=
as = Kp ae
(93)
Kp values can be obtained plotting ln(Cs/Ce) versus Cs and extrapolating Cs to zero. If a
879
straight line fits the data with a high regression coefficient (R2) and its intersection with the vertical
880
axis provides the value of Kp, the partition coefficient will be in unison with the equilibrium
881
constant. The ∆G° value can be directly calculated using Eq. 71, while the values of ∆H° and ∆S°
882
are determined from the slope and intercept, respectively, of Eq. 73.
SC
RI PT
878
This method has been widely applied in the literature. A summary of the applications of
884
this method can found in the critical review in reference (Doke and Khan, 2013). However,
885
incorrect applications of Biggar and Cheung’s definition have also been identified in the literature.
886
In a typical experiment, Senthil Kumar et al. (2014) made a mistake in the application of Kp during
887
calculation of the thermodynamic parameters for the adsorption of MB onto STOP (Table 4). Hai
888
(2017) highlighted that it is impossible to obtain an equilibrium constant, Gibbs energy change
889
(∆G°), enthalpy change (∆H°), and entropy change (∆S°) for the adsorption process at every initial
890
MB concentration, as shown in Table 4. Assuming that the experimental data reported by Senthil
891
Kuma et al. (2014) are correct, Hai (2017) recalculated the thermodynamic parameters based on
892
the method of Biggar and Cheung (1973), and the corrected thermodynamic parameters are also
893
listed in Table 4. Likewise, Lima et al. (2015) also determined the value of the adsorption
894
equilibrium constant (KC) from the value of the best fit nonlinear isotherm equilibrium model
895
instead of using the equilibrium constant (Kp) calculated from the initial and equilibrium
896
concentrations of the adsorbate.
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TE D
M AN U
883
897
Table 4
898
Importantly, according to the United States Environmental Protection Agency (USEPA,
46
ACCEPTED MANUSCRIPT
1999), the partition coefficient is only appropriate for calculating the thermodynamic parameters
900
if the initial adsorbate concentration is low. Analogous conclusions can be found in the literature
901
(Liu, 2009; Salvestrini et al., 2014; Lima et al., 2015; Tran et al., 2016; Hai, 2017). It has been
902
highlighted that the partition coefficient is only equal to the thermodynamic equilibrium constant
903
when the adsorbed concentrations in the solutions are very low. In this situation, the partition
904
coefficient can be used to calculate the thermodynamic parameters. Recently, Tran et al. (2016),
905
who compared the thermodynamic parameters calculated from the Langmuir constant and the
906
partition coefficient, concluded that although the signs of the calculated ∆G°, ∆H°, and ∆S°
907
parameters were the same, the partition coefficient might not be appropriate for calculating the
908
thermodynamic parameters owing to the low regression coefficient of the van’t Hoff equation (R2
909
= 0.53).
910
7.5. Equilibrium constant derived from the distribution coefficient (Kd)
M AN U
SC
RI PT
899
In 1987, Khan and Singh (1987) proposed a method for calculating thermodynamic
912
parameters (Eq. 94) based on the method of Biggar and Cheung (1973). The distribution
913
coefficient (Kd) can be defined as follows:
(94)
In this method, Kd values are obtained by plotting ln(qe/Ce) against Ce and extrapolating to
AC C
914
qe Ce
EP
Kd =
TE D
911
915
zero Ce. If a straight line fits the data with a high regression coefficient (R2), then its intersection
916
with the vertical axis provides the value of Kd. Fundamentally, Eq. 94 can be derived from the
917
Freundlich and Langmuir equations. If n = 1, the Freundlich equation (Eq. 56) will become
918
Henry’s equation for a linearized isotherm (Eq. 95), and the Freundlich constant (KF) will be equal
919
to the Henry constant (KH). For very low concentrations of adsorbate (KL and Ce << 1), the
47
ACCEPTED MANUSCRIPT
920
Langmuir equation (Eq. 47) will become Henry’s equation (Eq. 95), and the Henry constant (KH)
921
will become QomaxKL. The Henry constant (KH) is also referred to as the distribution coefficient
922
(Kd).
qe = K H Ce
RI PT
(95)
This method has been widely applied to calculating thermodynamic parameters in the
924
literature. Unfortunately, the units of Kd in Eq. 94 are L/g as Ce has units of mg/L and qe has units
925
of mg/g. Therefore, it is impossible to directly employ Kd as the equilibrium constant for the
926
calculation of ∆G°, ∆H°, and ∆S°. This problem associated with the units has been discussed by
927
several scientists (Patrickios and Yamasaki, 1997; Milonjić, 2007; Canzano et al., 2012; Dawood
928
and Sen, 2012; Tran et al., 2016; Zhou, 2017). Canzano, Iovino et al. (2012) suggested that the
929
partition coefficient Kd (L/g) could be converted to KC (dimensionless) by multiplying Kd by a
930
factor of 1,000, as originally proposed by Milonjić (2007 and 2009b).
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SC
923
Similar to the partition coefficient, the distribution coefficient may be appropriate for
932
estimating the thermodynamic parameters when the initial concentration of the adsorbate is low
933
(Salvestrini et al., 2014; Tran et al., 2016). Tran et al. (2016) concluded that the signs of ∆G°, ∆H°,
934
and ∆S° estimated from the distribution coefficient and the Langmuir constant are the same.
935
However, the units of Kd (L/g) are different from those of KL (L/mg), and the adsorption
936
equilibrium data do not fit Henry’s adsorption isotherm. As a result, application of the distribution
937
coefficient was not appropriate for calculating the thermodynamic parameters in this study; the
938
low regression coefficient of the van’t Hoff equation (R2 = 0.42) is further evidence of the
939
inappropriateness of this approach.
AC C
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931
940
In summary, to determine accurate thermodynamic parameters, several points should be
941
thoroughly considered. First, the equilibrium constant (KC) must be dimensionless. Second, if the 48
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concentrations of adsorbate used to obtain the adsorption isotherm are very low (diluted solutions),
943
the partition (Kp) or distribution coefficients (Kd) are appropriate for calculation of the
944
thermodynamic parameters; otherwise, the Langmuir (KL) or Freundlich (KF) constant models may
945
be more appropriate. Third, the plot of lnKC against 1/T corresponding to the van’t Hoff equation
946
must be linear with a high regression coefficient (R2). Additionally, it is necessary to consider
947
whether the adsorption process can reach equilibrium and consideration of the adsorption isotherm
948
shapes and the adsorption model fit are also recommended. Thus, presentation of the complete
949
adsorption isotherm (plot of qe versus Ce) is strongly recommended. Finally, the determined
950
thermodynamic parameters must have a logical relationship with the experimental data.
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942
Notably, numerous recent studies have reported methods of calculating thermodynamic
952
parameters from the partition coefficient (Kp) or distribution coefficient (Kd) that differed from the
953
traditional concepts defined in Sections 7.4 and 7.5, respectively. A typical mistake is present in
954
the work of Nekouei et al. (2016). They studied the adsorption thermodynamics at only one initial
955
adsorbate concentration and different temperatures instead of using a range of adsorbate
956
concentrations (i.e., from 100 mg/L to 1,000 mg/L) and different temperatures (i.e., 10 °C, 20 °C,
957
30 °C, and 50 °C). This mistake led to invalid conclusions regarding the adsorption
958
thermodynamics.
959
8. Others mistakes
960
8.1. Inconsistent data points in experimental data and model fitting
EP
AC C
961
TE D
951
Significant differences between the number of data points in an experiment and those used
962
for model fitting should be avoided. For example, Azizian (2008a) made the following critical
963
comments about the paper of Karadag et al. (2007): there were six experimental data points
964
regarding the adsorption kinetics (plots of qt versus t), but only five experimental data points were
49
ACCEPTED MANUSCRIPT
used for fitting of the experimental data to the PSO model (plot of t/qt versus t). This omission
966
resulted in inaccurate calculations and questionable conclusions. The R2 values of the PSO model
967
were very high (0.992–1.000), but the difference between the experimental (qe,exp) and calculated
968
(qe,cal) values was more than 100% (for example qe,exp = 6.720 mg/g and qe,cal = 15.526 mg/g).
969
Clearly, the qe values calculated from the experimental data and the model were significantly
970
different, but the authors (Karadag et al., 2007) concluded that “The pseudo-second-order kinetic
971
model agrees very well with the dynamic behavior for the adsorption of dyes RR239 and RB5 onto
972
CTAB-zeolite under several different dye concentrations, temperatures, and pH values”; the
973
validity of this conclusion is very questionable.
M AN U
SC
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965
Lima et al. (2015) observed a change in kinetic parameters when five experimental points
975
were deleted to achieve a good R2 value. They concluded that the strategy of deleting some data
976
points to improve the R2 value caused serious errors in the values of qe and k1 in the PFO equation
977
or k2 in the PSO equation.
TE D
974
Azizian (2008) pointed out that in reference (Karadag et al., 2007), a comparison was made
979
between the results of fitting four experimental equilibrium data points to the Langmuir model and
980
fitting five experimental equilibrium data points to the Freundlich model. Therefore, it is
981
impossible for the authors (Karadag et al., 2007) to conclude that “the Freundlich model exhibited
982
a slightly better fit than the Langmuir model.” To compare the fits of two different models, the
983
same experimental data (including the same number of experimental data points) should be used
984
(Azizian, 2008a). Likewise, Harsha et al. (2015) examined adsorption isotherms using seven
985
experimental data points. However, in the plots for calculating the Langmuir, Freundlich, and
986
Dubinin–Radushkevich models, only three experimental points were used. It is impossible to
AC C
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978
50
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987
obtain the Langmuir, Freundlich, and Dubinin–Radushkevich parameters from only three
988
experimental points. A similar mistake was found in reference (Goswami et al., 2016).
989
8.2. Oxidation state of chromium Many investigators (Aoyama, 2003; Park et al., 2006a; Park et al., 2006b; Park et al.,
991
2006c) have commented that mistakes in analyzing chromium species in aqueous solution have
992
resulted in the incorrect elucidation of hexavalent chromium adsorption, attributing Cr(VI)
993
removal from an aqueous solution to “anionic adsorption”. Generally, when Cr(VI) comes into
994
contact with organic substances or reducing agents, especially in an acidic medium, it is easily or
995
spontaneously reduced to Cr(III), as Cr(VI) has a high redox potential (above +1.3 V under
996
standard conditions). Therefore, there is a strong possibility that the mechanism of Cr(VI) removal
997
by biomaterials or biomaterial-based activated carbon is not “anionic adsorption” but
998
“adsorption-coupled reduction”. Various authors (Aoyama, 2003; Park et al., 2006a; Park et al.,
999
2006b; Park et al., 2006c) also suggested that in Cr(VI) adsorption studies, it is necessary to
1000
analyze both the Cr(VI) and total Cr in aqueous solution, as well as determining the oxidation state
1001
of chromium bound to the biomaterial or activated carbon.
TE D
M AN U
SC
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990
The authors (Aoyama, 2003; Park et al., 2006a; Park et al., 2006b; Park et al., 2006c)
1003
pointed out that in most papers, only Cr(VI) in aqueous solutions was analyzed by the standard
1004
colorimetrical method; the pink colored complex formed from between 1,5-diphenycarbazide and
1005
Cr(VI) in an acidic solution can be spectrophotometrically analyzed at 540 nm. Similarly, the total
1006
Cr in aqueous solutions has been analyzed using atomic absorption spectroscopy (AAS) or
1007
inductively coupled plasma-atomic emission spectroscopy (ICP-AES), which cannot distinguish
1008
Cr(VI) from the total Cr. Additionally, Aoyama (2003) underlined that the total Cr present in a
1009
solution can be determined by oxidizing any Cr(III) formed with KMnO4, followed by the same
AC C
EP
1002
51
ACCEPTED MANUSCRIPT
procedures described for the determination of Cr(VI). The adsorption density can be calculated
1011
from the difference between the initial concentration of Cr(VI) and the final concentration of total
1012
Cr. In contrast, the Cr(III) concentration is calculated from the difference between the final total Cr
1013
and final Cr(VI) concentrations.
RI PT
1010
Several techniques have been applied in the literature to ascertain the oxidation state of
1015
chromium on an adsorbent, such as X-ray photoelectron spectroscopy (XPS) and X-ray absorption
1016
spectroscopy (XAS). For example, Dambies et al. (2001) investigated the characterization of
1017
Cr(VI) interactions with chitosan using XPS. On the basis of their XPS data, they concluded that
1018
Cr(VI) was entirely reduced to Cr(III) on glutaraldehyde crosslinked beads, while only 60% of
1019
Cr(VI) was found in its reduced form on raw beads. Additionally, Cr(VI) binding and reduction to
1020
Cr(III) by agricultural byproducts of Avena monida (oat) biomass was characterized by
1021
Gardea-Torresdey et al. (2000). Their XAS studies further corroborated that, although Cr(VI)
1022
could bind to oat biomass, it was easily reduced to Cr(III) by positively charged functional groups,
1023
and Cr(III) was subsequently adsorbed by available carboxyl groups.
TE D
M AN U
SC
1014
A study on using fermentation waste for detoxification of Cr(VI) contaminated aqueous
1025
solutions was published by Park et al. (2008). In this study, the colorimetric method was used in
1026
combination with excess potassium permanganate to analyze both the Cr(VI) and total Cr in
1027
aqueous solution, and XPS was used to ascertain the oxidation state of the chromium bound on the
1028
biomass. Park et al. (2008) concluded that the mechanism of Cr(VI) removal by the fermentation
1029
waste involved reduction of Cr(VI) to Cr(III) (redox reaction). As a result, kinetic and equilibrium
1030
models based on the “reduction” mechanism were used to describe the behavior of Cr(VI) and total
1031
Cr in aqueous solution.
1032
AC C
EP
1024
Two main mechanisms for removal of Cr(VI) from aqueous solution by nonliving
52
ACCEPTED MANUSCRIPT
biomass were proposed by Park et al. (2005). In the first mechanism (direct reduction), Cr(VI)
1034
was directly reduced to Cr(III) in the aqueous phase by contact with electron-donor groups of the
1035
biomass, i.e., groups with lower reduction potentials than that of Cr(VI) (+1.3 V). However, the
1036
second mechanism comprised three steps: (1) binding of anionic Cr(VI) ion species to positively
1037
charged groups on the biomass surface, (2) reduction of Cr(VI) to Cr(III) by adjacent
1038
electron-donor groups, and (3) release of the Cr(III) ions into the aqueous phase, owing to
1039
electronic repulsion between the positively charged groups and the Cr(III) ions, or complexation
1040
of Cr(III) with adjacent groups capable of binding chromium. If there are a small number of
1041
electron-donor groups in the biomass or a low concentration of protons in the aqueous phase,
1042
chromium bound on the biomass can remain in the hexavalent state. Therefore, the extent to
1043
which mechanisms I and II operate depends on the nature of the biosorption system, including
1044
solution pH, temperature, functional groups on the biomass, and biomass and Cr(VI)
1045
concentrations (Park et al., 2006b; Park et al., 2006a). These two main mechanisms are
1046
summarized in Figure 9.
Figure 9
1047
8.3. Incorrect labels
EP
1048
TE D
M AN U
SC
RI PT
1033
Incorrect labeling of compounds should also be avoided. A publication entitled “Selenite
1050
adsorption and desorption in main Chinese soils with their characteristics and physicochemical
1051
properties” included such a mistake, as pointed out by Goldberg (2016). The purpose of this work
1052
was to study the adsorption of Se(IV) (selenite), not Se(VI) (selenate); however, the paper reported
1053
that the authors prepared Se solutions using Na2SeO4 (hexavalent Se(VI)). This mistake was
1054
explained by the incorrect labeling of Na2SeO3 as Na2SeO4 in the Materials and Methods section.
AC C
1049
53
ACCEPTED MANUSCRIPT
Similarly, the author of the paper entitled “Adsorption sequence of toxic inorganic anions
1056
on a soil” prepared solutions from Na2HAsO4·7H2O as As(V) species. However, they mislabeled
1057
Na2HAsO4·7H2O as NaAsO2, a trivalent As(III) species (Goldberg, 2009).
1058
8.4. BET specific surface area of an adsorbent
RI PT
1055
Using the Brunauer–Emmett–Teller (BET) surface area of pahokee peat (0.88 m2/g) and
1060
assuming that the atrazine molecule is a sphere with a radius (r) of 4.16 × 10−10 m, Borisover and
1061
Graber (1997) estimated the maximum adsorption capacity of pahokee peat for atrazine. First, the
1062
cross-section area (A) of atrazine can be obtained as 3.14 × (4.16 × 10−10)2 = 54.4 × 10−20 m2;
1063
subsequently, the surface covered by 1 mol of atrazine (MA) can be calculated as (54.4 × 10−20 m2)
1064
× (6.023 × 1023/mol) = 3.3 × 105 m2/mol. Second, the maximum possible concentration of atrazine
1065
on the surface area (Qomax,covered; maximum adsorption capacity) was obtained by dividing the BET
1066
surface area (0.88 m2/g) by the surface covered by 1 mol of atrazine (3.3 × 105 m2/mol) to give 2.7
1067
× 10−6 mol/g. Finally, Qomax,covered was converted into weight units using (2.7 × 10−6 mol/g) ×
1068
(215.7 g/mol) to give 582 µg/g. This value (582 µg/g) is substantially higher than the maximum
1069
adsorption capacity obtained from the Langmuir equation (161 µg/g). Although these calculations
1070
are correct, these inconsistent values might originate from a misunderstanding by the authors
1071
(Borisover and Graber, 1997) who state that “N2 BET measured external surface area”, and thus
1072
attributed the value of 582 µg/g to the maximal possible atrazine concentration on the external
1073
surface of pahokee peat.
M AN U
TE D
EP
AC C
1074
SC
1059
According to the 2011 guide for the accelerated surface area and porosimetry (ASAP)
1075
system, the definition of the BET specific surface area (m2/g) includes both the t-Plot external
1076
surface area (m2/g) and the t-Plot micropore area (m2/g). Table 5 gives a typical example of correct
1077
and incorrect use of the Micromeritics report (experimental data measured using a Micromeritics
54
ACCEPTED MANUSCRIPT
ASAP 2020 sorptometer at 77 K). Although there were no problems found in the N2
1079
adsorption/desorption isotherms, the report results for BET analysis of the prepared activated
1080
carbon in Table 5 contain discrepancies, as the BET specific surface area value is less than the
1081
external surface area. This error resulted from calculation of the specific surface area (SBET) in the
1082
range 0.38 < p/p0 < 0.57, instead of 0.05 < p/p0 < 0.3.
Table 5
1083
RI PT
1078
Recently, Ben Ali et al. (2016) used the “iodine number” to determine the surface area of a
1085
biosorbent without any treatment (pomegranate peel; PGP) and concluded that “the specific
1086
surface area obtained is equal to 598.78 m2/g. Iodine number is generally used as an
1087
approximation for surface area and microporosity of active carbons with good precision”. Tran
1088
(2017) commented that there are two serious misconceptions in this work that need to be
1089
discussed.
M AN U
SC
1084
First, the iodine number of activated carbon is often determined following the internal
1091
method, ASTM D4607-14 (D4607-14 2014). According to the ASTM, the iodine number (mg/g;
1092
amount of iodine adsorbed (mg) by 1.0 g of activated carbon) is a relative indicator of porosity in
1093
activated carbon. Iodine molecules (≈0.27 nm) can be adsorbed into the micropores (pore width >
1094
1 nm) of porous materials. However, the iodine number does not necessarily provide a measure of
1095
the ability of activated carbon to adsorb other species. Although the iodine number may be used to
1096
approximate the surface area for several types of activated carbon, it must be realized that the
1097
relationship between surface area and iodine number cannot be generalized, as it varies with
1098
changes in the raw carbon material, processing conditions, and pore volume distribution.
1099
Biosorbents that have not undergone any treatment have never been defined as porous materials;
1100
thus, the porosity of a biosorbent is negligible.
AC C
EP
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1090
55
ACCEPTED MANUSCRIPT
Therefore, the iodine number cannot be applied for the determination of porosity for any
1102
biosorbent. Moreover, it is impossible to obtain the very high iodine number reported for PGP
1103
(602 mg/g). The high iodine number for PGP can be attributed to the high sulfur content (0.89%)
1104
and prolonged contact time (>30 s) (Tran, 2017). According to the ASTM (D4607-14 2014), after
1105
transferring activated carbon (g) into hydrochloric acid solution (5 wt%), the mixture should be
1106
boiled gently for 30 s to remove any sulfur that may interfere with the test results. Therefore, it is
1107
clear that the iodine number is greatly affected by high sulfur contents. Notably, the contact time
1108
between activated carbon and iodine solution (0.1 N) strongly impacts the determined iodine
1109
number. The contact time recommended by the ASTM was approximately 30 s, while the contact
1110
time used by Ben Ali et al. was approximately 4 min. Recently, Tran et al. (2017c) prepared
1111
activated carbons from golden shower using different chemical activation methods with K2CO3
1112
(GSAC, GSBAC, and GSHAC). Their results indicated that the iodine numbers (mg/g) of the
1113
prepared activated carbons at a contact time of 30 s were significantly lower than those at 5 min;
1114
GSAC (2,604 mg/g < 2,883 mg/g), GSBAC (1,568 mg/g < 2,296 mg/g), GSHAC (2,695 mg/g <
1115
4,842 mg/g).
TE D
M AN U
SC
RI PT
1101
Second, the textural properties of an adsorbent (i.e., specific surface area, total pore
1117
volume, and micropore volume) can be obtained from conventional analysis of nitrogen
1118
adsorption-desorption isotherms, which are measured at 77 K using a sorptometer (e.g.,
1119
Micromeritics ASAP 2020). The BET method is widely employed to compute specific surface
1120
area (SBET) (Marsh and Reinoso, 2006). Therefore, it is impossible to measure the surface area of
1121
an adsorbent using the iodine number method. This mistaken assumption will lead to incorrect
1122
result, such as the extremely high surface area of PGP (598.78 m2/g). The BET surface areas of
1123
various biosorbents are approximately 40 m2/g for yellow passion-fruit shell, 20 m2/g for orange
AC C
EP
1116
56
ACCEPTED MANUSCRIPT
peel, 8.17 m2/g for wheat straw, 8.13 m2/g for sargassum, 4.01 m2/g for Moringa oleifera lamarck
1125
seed powder, 1.31 m2/g Spirogyra species, 1.21 m2/g for waste pomace from an olive oil factory,
1126
0.76 m2/g for soy meal shells, 0.48 m2/g for rubber tree leaves, and 0.48 m2/g for rice bran (Farooq
1127
et al., 2010; Tran et al., 2016). Thus, the discussions and conclusions regarding the surface area of
1128
PGP made by Ben Ali et al. (2016) are not valid, as they are inconsistent with the ASTM
1129
definitions and fundamental understanding of the porosities of materials.
1130
8.5. Maximum absorption wavelength in dye adsorption studies
SC
RI PT
1124
A comment on the method of using the maximum absorption wavelength (λmax) to calculate
1132
Congo red (CR) solution concentrations was published by Zhou et al. (2011). They pointed out that
1133
CR is very sensitive to pH and changes from red to blue owing to a π-π* transition of the azo group
1134
following protonation (Figure 10a). At lower pH values, CR is protonated and cationic CR shows
1135
two tautomeric forms: ammonium rich variety and azonium variety. Therefore, the maximum
1136
absorption wavelength used to calculate the concentration of CR in solution is strongly dependent
1137
on the solution pH (both initial and final) (Figure 10b); for example, λmax was 576 nm at pH 2.18–
1138
3.16, 567 nm at pH 3.86, and 496 nm at pH ≥ 4.71.
TE D
Figure 10
EP
1139
M AN U
1131
Tien (2007) and Tien (2008) highlighted that commercial dyes are often mixtures of active
1141
ingredients and filler materials are often not recognized. Therefore, the possibility that
1142
experiments may involve bi-solute adsorption is often not considered.
1143
8.6. Cπ-cation and π-π interactions
1144
8.6.1. Cπ-cation interactions
AC C
1140
1145
Recently, Morosanu et al. (2016) investigated the biosorption of lead ions onto rapeseed
1146
biomass that was used as a biosorbent without any treatments. On the basis of FTIR measurements
57
ACCEPTED MANUSCRIPT
before and after adsorption, they concluded that the disappearance of the peak at 1710 cm−1, which
1148
is characteristic of C=O stretching, indicated surface complexion through Cπ-cation interactions.
1149
Similarly, Medellin-Castillo et al. (2017) examined the biosorption of Pb2+ and Cd2+ onto a
1150
biosorbent derived from industrial chili seeds. They also found changes in the intensity of the
1151
absorbance peak at 1657 cm−1 in heavy-metal-loaded chili seeds, suggesting that the adsorption of
1152
Cd2+ and Pb2+ involved π-cation interactions between the aromatic rings of the lignin and the
1153
Cd2+ and Pb2+ cations in the solution.
SC
RI PT
1147
In general, Cπ-cation interactions are attributed to electrostatic interactions between the
1155
aromatic rings of basic carbonaceous materials (i.e., biochar, carbon foam, carbon nanotubes,
1156
activated carbon, and graphene) and metallic cations. For example, Tran et al. (2015) used
1157
orange-peel-derived biochar, which was produced through a carbonization process under
1158
limited-oxygen conditions (also known as pyrolysis) at a high temperature (>400 °C). Biochar is
1159
known as a carbon-enriched porous material, similar to activated carbon. Thus, biochar also
1160
possesses a graphitic structure (C=C bonds; π-electrons). As a result, Cπ-cation interactions played
1161
a primary role in the adsorption of heavy metals onto biochar. Analogous conclusions were
1162
reached by other scholars (Swiatkowski et al., 2004; Uchimiya et al., 2010; Rivera-Utrilla and
1163
Sánchez-Polo, 2011).
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The contribution of Cπ-cation interactions to the mechanism of heavy-metal adsorption
AC C
1164
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1165
onto carbonaceous material cannot be denied. However, unlike biochar and activated carbon,
1166
biosorbents (commonly derived from lignocellulose materials) do not possess a graphitic
1167
structure. In addition, although hydorchar prepared through hydrothermal carbonization (i.e., 150–
1168
250 °C controlled temperature for 2–72 h at a specific pressure) exhibits an aromatic carbon
1169
network, its properties are similar to those of biosorbents (Tran et al., 2017c). Therefore, the
58
ACCEPTED MANUSCRIPT
1170
presence of Cπ-cation interactions in heavy-metal adsorption onto biosorbents and hydrochar is
1171
still controversial and needs to be further investigated. Bui and Choi (2010) considered the role of cation-π bonding between the protonated
1173
amino group of oxytetracycline (OTC) and the graphitic π electrons of multiwalled carbon
1174
nanotubes (MWCNTs). Essentially, the cation-π bonding is dominated by the electrostatic forces
1175
between the cation and the permanent quadrupole of the π-electron-rich aromatic structure and
1176
cation-induced polarization (Ji et al., 2009). Like π-π interactions, cation-π bonding would be
1177
suppressed with increasing pH. This is because at a higher pH, deprotonation of the charged amino
1178
group and protonation of the enol groups will be enhanced and so the electron-acceptor ability of
1179
the oxytetracycline molecule is weaker (Ji et al., 2009). Bui and Choi (2010) opined that
1180
Oleszczuk et al. (2010) ignored the important roles of Ca2+ in the solution; for example,
1181
Ca2+ possibly forms a complex with OTC in the solution or Ca2+ can act as a cation bridge between
1182
the negatively charged OTC and the negative charges of the MWCNTs. Therefore, Bui and Choi
1183
(2010) suggested that Ca2+ may simultaneously bind with the negatively charged OTC and interact
1184
either with the negative charges or the graphitic π electrons of the MWCNTs via cation-π bonding.
1185
As pH is increased, both MWCNTs and OTC become more negatively charged and, consequently,
1186
probably interact more strongly with Ca2+, leading to lower desorption of OTC. This hypothesis
1187
could be further verified by studying the desorption of OTC in the presence of NaCl, instead of
1188
CaCl2.
1189
8.6.2. π-π interactions
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1172
1190
π-π interactions (also known as π-π electron donor-acceptor interactions) between
1191
the π-electrons in a carbonaceous adsorbent and the π-electron in the aromatic ring of an adsorbate
1192
were initially proposed by Coughlin and Ezra (1968). In short, the addition of
59
ACCEPTED MANUSCRIPT
electron-withdrawing groups (i.e., oxygen-containing and nitrogen-containing functional groups)
1194
at the edges of the individual graphene layers within a carbonaceous solid causes a considerable
1195
drop in the π-electron density. Positive holes are consequently created in the conduction π-band of
1196
the individual graphene layers, and the interactions between the π-electrons of a carbonaceous
1197
adsorbent and the π-electrons of the adsorbate aromatic rings become weaker.
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1193
Recently, Tran et al. (2017b), and Tran et al. (2017d) investigated the mechanisms of
1199
methylene green 5 (MG5) adsorption by commercial activated charcoal, synthesized activated
1200
carbons, and prepared biochars. They proposed that the primary mechanisms in MG5 adsorption
1201
were π-π interactions and pore filling, while hydrogen bonding and n-π interactions were minor
1202
contributors (Figure 11). To identify the existence of π-π interactions, they used two pieces of
1203
experimental evidence. First, FTIR analysis showed that a peak corresponding to the skeletal
1204
vibration of aromatic C=C bonds decreased in intensity and upshifted after MG5
1205
adsorption. Secondly, oxygenation of the surface of the carbonaceous solids (i.e., biochar and
1206
activated carbon) through a hydrothermal process with acrylic acid resulted in a decrease in MG5
1207
adsorption and indicated the importance of π-π interactions to the adsorption process.
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1198
As discussed in Section 8.6.1, hydrochar also possesses an aromatic carbon network;
1209
therefore, π-π interactions might be expected between the π-electrons of the aromatic C=C bonds
1210
in hydrochar and the π-electrons of an adsorbate. However, a recent study (Tran et al., 2017e)
1211
demonstrated that oxygenation of a hydrochar surface through a hydrothermal process with acrylic
1212
acid contributed to increasing MG5 adsorption and indicated the negligible role of π-π interaction
1213
in the adsorption process. FTIR analysis demonstrated that the aromatic C=C peak did not
1214
significantly decrease in intensity or shift toward higher/lower wavenumbers after adsorption,
1215
which further confirms the insignificant contribution of π-π interactions. Electrostatic attraction
AC C
EP
1208
60
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played a major role in the adsorption mechanism, while hydrogen bonding and n-π interactions
1217
were minor contributors. The primary adsorption mechanisms of MG5 onto hydrochar were
1218
similar to those on biosorbents, but dissimilar to biochar and activated carbon (i.e., π-π interaction
1219
and pore filling). An identical result was obtained in the investigation of phenol, MG5, and acid
1220
read 1 adsorption onto a commercial glucose-derived spherical hydrochar functionalized with
1221
triethylenetetramine (Tran, et al., 2017a). Therefore, it can be concluded that the addition of
1222
oxygen- and nitrogen-containing functional groups (electron-withdrawing groups) on the surface
1223
of hydrochar does not cause a considerable drop in the π-electron density, but this process provides
1224
abundant adsorption sites on the hydrochar surface.
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1216
Jiang et al. (2009) and Chen et al. (2009) argued over the primary adsorption mechanisms
1226
of hydroxyl- and amino-substituted aromatics on carbon nanotubes and graphite (CNTs/graphite).
1227
Chen et al. (2009) proposed that π-π interactions played a major role in the adsorption mechanism.
1228
However, Jiang et al. (2009) remarked that the experiments of Chen et al. (2009) were
1229
insufficient to support the presence of π-π electron-donor−acceptor (EDA) interactions between
1230
hydroxyl-substituted aromatics and CNTs/graphite. According to Jiang et al. (2009), phenolic
1231
compounds were not appropriate candidates to assess the presence of π-π EDA interactions
1232
between π-electron-donating aromatics and CNTs because of the significant effects of oxygen.
1233
Therefore, the oxygen effect should be considered in more detail in order to gain in-depth insights
1234
into the adsorption mechanisms of environmentally relevant phenolic compounds onto
1235
carbonaceous materials.
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Figure 11
1236 1237
8.7. Other miscellaneous errors Azizian (2007) commented that the theoretical development of empirical PFO and PSO
1239
kinetic adsorption models using statistical rate theory (SRT) was first reported by Azizian (2004),
1240
not by Rudzinski and Plazinski (2007). Furthermore, the idea that the PFO model can only be
1241
derived theoretically at a nearly constant bulk concentration was proposed by Azizian (2004). In
1242
addition, the conclusion that the PFO and PSO models are simplified forms of a more general
1243
equation was also proposed by Azizian (2004), not Rudzinski and Plazinski (2007). Similarly,
1244
mistakes related to either no citation of the original paper or incorrect citation were pointed out by
1245
Azizian (2008b).
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1238
A series of mistakes related to incorrectly digitized data, typos, inaccurate calculations,
1247
incorrect use of conditional equilibrium constants, incorrect units, incorrect references, incorrect
1248
application of modeling procedures, and other miscellaneous errors have been highlighted by
1249
Gustafsson and Lumsdon (2014).
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1246
The distinction between heat of adsorption, adsorption energy, and activation energy in
1251
adsorption was reported elsewhere (Inglezakis and Zorpas, 2012). The authors concluded that it is
1252
important to distinguish the differential enthalpy at zero coverage (∆Hdo) from the differential
1253
enthalpy or isosteric heat (∆Hd) and the standard heat of complete coverage or integral enthalpy
1254
(∆H°), which expresses the total heat generation for the adsorption and is related to the
1255
thermodynamic equilibrium constant.
AC C
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Li et al. (2010) pointed out that (1) although the cited documents were solid and sound in
1257
their scientific aspects, the reviewers seemed to fail to take full advantage of the intrinsically
1258
contained information; (2) there were some critical errors in the main text; and (3) the writing style
62
ACCEPTED MANUSCRIPT
1259
of the paper was misleading and, to some extent, lacked cautiousness. They focused on 11
1260
comments and concluded that the original paper’s conclusions were not optimistic. However, most
1261
of these comments were rejected by the original authors (Mohan and Pittman, 2011). Regarding the correct citation for determining pHPZC using the batch equilibration method,
1263
Milonjić (2009a) commented that this method was originally proposed by Milonjić et al. (1975).
1264
Furthermore, Milonjić (2009a) noted that using correct and updated citations were very important
1265
for researchers to find relevant information, pioneer ideas, and make progress in a particular
1266
subject. Additionally, from a scientific point of view, it is always necessary to give credit to the
1267
authors who first proposed a method or theoretical model. Recently, Tran et al. (2017b) applied the
1268
“drift method” to determine the pHPZC of commercial activated charcoal (CAC). The effects of
1269
various operation conditions (i.e., different degassing times with N2, background electrolytes,
1270
concentrations of an electrolyte, solid/liquid ratios, and contact times) on the pHPZC were
1271
investigated. The results demonstrated that the pHPZC (9.81 ± 0.07) of CAC was insignificantly
1272
dependent on the operation conditions.
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1262
Geckeis and Rabung (2004) pointed out that photon correlation spectroscopy (PCS) is a
1274
method for colloid size determination, not for zeta-potential analysis. Methods that have been
1275
correctly applied for zeta-potential analysis include electrophoretic light scattering and laser
1276
Doppler velocimetry (LDV), and the units for the measured zeta potentials are mV, not eV.
AC C
1277
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Lee (2017) considered the potential effects of flow velocity on the concentration and
1278
distribution of triphenyltin chloride (TPT) on nano zinc oxide (nZnO). The author remarked that
1279
TPT was possibly re-suspended by the hydraulic flow that occurs during hydrant flushing in a
1280
reactor because TPT can be loosely deposited on the nZnO surface. As reported in the literature,
1281
the flow velocity in a wastewater treatment system is one of the factors affecting the removal
63
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efficiency for a tested pollutant. The distribution of TPT on nZnO might vary during the
1283
adsorption process according to the time of hydrant flushing; therefore, the process of TPT
1284
adsorption onto nZnO might be affected by the operating conditions of a reactor. However, the
1285
authors of the commented paper replied that the application of nZnO for the removal of TPT from
1286
dockyard wastewater was examined using a batch adsorption technique. As a result, the effects of
1287
flow velocity on the adsorption process conducted in the batch experiments were negligible
1288
compared to that in pilot studies and/or column experiments.
SC
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1282
Kamagaté et al. (2016) and Komárek et al. (2016) considered the influence of Si species
1290
originating from the partial dissolution of quartz on the competitive adsorption of Cd(II), Cr(VI),
1291
and Pb(II) onto nanomaghemite- and nanomaghemite-coated quartz. They recommended that to
1292
accurately assess the interfacial reaction mechanisms occurring at the Fe-oxide/water interface in
1293
the presence of Si-complex mineral assemblages or Fe-coated sand systems, more attention should
1294
be paid to the possible release of silicate from Si-bearing minerals and its subsequent adsorption on
1295
reactive phases.
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A critical paper entitled “comments on “zirconium-carbon hybrid sorbent for removal of
1297
fluoride from water: oxalic acid mediated Zr(IV) assembly and adsorption mechanism”” was
1298
published by Zhao (2015). The authors of the original paper concluded that the fluoride adsorption
1299
occurs on the surface sites of ZrOx-AC (commercial activated carbon modified with Zr together
1300
with oxalic acid) with –OH displacement and/or interacts with the positive charge of zirconium to
1301
form –COOH groups in the oxalate acid; however, Zhao (2015) suggested that if the fluoride
1302
concentration is high enough, it would completely desorb the oxalate acid from the ZrOx-AC
1303
surface. According to the results of previous experiments, Zhao (2015) suggested that it is
AC C
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64
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1304
necessary to further consider or add the exchangeable role of chloride and oxalic acid in the
1305
proposed fluoride-adsorption mechanism. Fan et al. (2007) additionally discussed the mechanisms of fluoride adsorption by calcined
1307
Mg-Al-CO3 layered double hydroxides (CLDH). Based on the experimental data published in the
1308
original paper and analysis of other literature results, they concluded that XRD measurements
1309
indicated that mixed Mg-Al oxides, as well as partially restored LDH, was present in
1310
fluoride-loaded CLDH after freeze-drying treatment. Furthermore, fluoride can be effectively
1311
adsorbed onto MgO, demonstrating that fluoride adsorption over the mixed oxide along with a
1312
memory effect accounts for the effective removal of fluoride by CLDH.
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1306
An analytical article on the magnitude of estimated maximum surface-area-normalized
1314
adsorption capacities (Qmax*) for the adsorption of polycyclic aromatic hydrocarbons (PAHs) and
1315
polychlorobiphenyls (PCBs) on soot and soot-like carbon materials was published by Werner and
1316
Karapanagioti (2005). The original authors (van Noort et al., 2005) used the Langmuir isotherm to
1317
extrapolate Qmax* at the solubility limit from solid-water distribution coefficients (Ks) measured in
1318
the pg/L to ng/L range along with estimated Langmuir affinities for adsorption (b) on a
1319
carbonaceous surface. After comparison with estimated surface-area-normalized monolayer
1320
adsorption capacities (Qmono*) and with empirical sorption data from the literature, Werner and
1321
Karapanagioti (2005) concluded that the Langmuir isotherm cannot be used to extrapolate
1322
maximum sorption capacities (Qmax*) near the aqueous-sorbate saturation limit from distribution
1323
coefficients measured at extremely low aqueous-sorbate concentrations. Adsorption sites in
1324
carbon materials are not uniform and other processes, such as multilayer adsorption, condensation
1325
in capillary pores, and absorption into the polymeric matrix, may be relevant near the solubility
1326
limit.
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1313
65
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Müller et al. (2017) analyzed strong conflicts between the XPS and XRD data and their
1328
interpretation by the original author in a study on the synthesis of Yb doped CuFe2O4 nanoferrite
1329
adsorbents (i.e., CuYb0.5Fe1.5O4) and the application of such adsorbents in the removal of different
1330
pollutants (e.g. methyl orange, safranin, Cr3 +, and Pb2 +). After a polemical discussion, Müller et
1331
al. (2017) concluded that because any experimental study stands and falls on the reliability of the
1332
investigated specimen the lack of any significance therefore holds for this study as a whole.
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1327
Interestingly, a series of recommendations and suggestions were written by the editor of
1334
Carbon for improving manuscript quality and avoiding mistakes (Thrower, 2007; Thrower,
1335
2008b; Thrower, 2008a; Thrower, 2010; Thrower, 2011). The author focused on five main topics:
1336
titles and abstracts, introduction and references, experimental, results and discussion, and
1337
language.
1338
9. Nonlinear-optimization technique
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1333
To calculate the parameters of kinetic and isotherm models accurately in both batch and
1340
column experiments, application of the nonlinear method instead of the linear method has been
1341
recommended by many researchers (Porter, 1985; Ho, 2004b; Ho et al., 2005; Bolster and
1342
Hornberger, 2007; Han et al., 2007; Kumar, 2007; El-Khaiary et al., 2010; Chowdhury and Das
1343
Saha, 2011; Lima et al., 2015; Tran et al., 2015; Tran et al., 2017d).
EP
Furthermore, to identify the best-fit model, calculation of the chi-squared (χ2, Eq. 96) value
AC C
1344
TE D
1339
1345
is recommended in addition to calculating the coefficient of determination (R2, Eq. 97) for the
1346
nonlinear method. In the chi-squared test, the squares of the differences between the experimental
1347
data and data calculated using the models are divided by the corresponding data obtained and then
1348
summed. If the data obtained using a model are similar to the experimental data, χ2 is close to zero.
1349
High χ2 values indicate high bias between the experiment and model. Therefore, analyzing the data
66
ACCEPTED MANUSCRIPT
set using the chi-squared test is necessary to confirm the best-fit isotherm for a given sorption
1351
system (Ho, 2004b; Ho et al., 2005; Chowdhury and Das Saha, 2011; Lima et al., 2015; Tran et al.,
1352
2015; Tran et al., 2017b; Tran et al., 2017d; Tran et al., 2017e).
χ =∑ 2
R
2
(qe,exp − qe,cal ) 2 qe,cal
∑(q =1 − ∑ (q
e, exp
− qe, mean)2
=
∑ (q ∑ (q
e, cal
-q
e, cal 2 e, mean
- qe,mean)2
) + ∑(qe, cal - qe,exp )2
(96)
(97)
SC
e,exp
− qe,cal )2
RI PT
1350
where qe,exp (mg/g) is the amount of adsorbate uptake at equilibrium obtained from Eq. 1, qe,cal
1354
(mg/g) is the amount of adsorbate uptake achieved from the model using the Solver add-in, and
1355
qe,mean (mg/g) is the mean of the qe,exp values.
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1353
Lima et al. (2015) confirmed that the use of nonlinear equilibrium and kinetic adsorption
1357
models gives values that are reliable and statistically relevant for modeling the isotherm and
1358
kinetics of adsorption. Moreover, they did not suggest using linearized equilibrium and kinetic
1359
adsorption models, even in the cases of the linearized Langmuir Type 1 and linearized PSO Type 1
1360
equations that provide R2 values close to unity. The linearization of equilibrium and kinetic
1361
adsorption models could make the parameters determined from these models meaningless.
EP
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1356
Owing to the wide application of the nonlinear method in the study of adsorption
1363
processes, we provide here a short introduction to the application of this method using the “Solver
1364
add-in” in Microsoft Office Excel (2013 version). First, it is necessary to load the Solver add-in in
1365
Microsoft Excel: File → Excel options → Add-ins (select Excel Add-ins in Manage box) → select
1366
the Solver Add-in check box. Second, all Ce and qe values obtained experimentally are considered
1367
as input data, and the qe values from the Langmuir equation are calculated based on two variables
1368
(Qomax and KL ≠ 0). Using the Solver Add-in (Figure 12), the Qomax, KL, and R2 values can be
AC C
1362
67
ACCEPTED MANUSCRIPT
1369
obtained. Notably, other programs (i.e., Origin) also provide similar results and can accurately
1370
calculate the parameters of kinetic and isotherm models.
1371
Figure 12 10. Conclusions
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1372
In scientific publications, the correct use of technical terms and accurate calculations are
1374
essential. According to the viewpoints discussed in this review, we put forward the following key
1375
conclusions and perspectives:
1378 1379 1380 1381 1382
Adsorption performance should be expressed as qe (mg/g), while the use of
the unit of %removal for qe should be avoided or used cautiously. ii.
M AN U
1377
i.
The use of accurate citations and correct mathematical expressions in
original works is also recommended. iii.
Measurements of adsorption kinetics should be started at an initial time of
less than 2 min and finish when the adsorption process reaches true equilibrium. iv.
TE D
1376
SC
1373
A complete adsorption isotherm (plotting qe versus Ce) should be presented
1383
when investigating liquid-phase adsorption to identify the regions in which the
1384
experimental data relating to adsorption equilibrium are actually located. v.
Differences between the number of data points in an experiment and those
EP
1385
used for model fitting (i.e., the pseudo-second-order or Langmuir models) should be
1387
avoided.
1388
AC C
1386
vi.
For adsorption thermodynamics, the equilibrium constant (KC) must be
1389
dimensionless. The optimal method for calculating thermodynamic parameters should
1390
be appropriately selected according to the data from the adsorption equilibrium
1391
experiment. Notably, it is impossible to calculate thermodynamic parameters from an
1392
experiment using one initial adsorbate concentration at different temperatures. 68
ACCEPTED MANUSCRIPT
1393
vii.
To accurately estimate the parameters of adsorption kinetic and isotherm
models, the nonlinear optimization technique should be applied to decrease the bias
1395
between the qe values calculated from the experimental data and those estimated from
1396
the models. The chi-squared (χ2) test should be used alongside the nonlinear
1397
determination coefficient (R2) to obtain the best-fit models for adsorption kinetics and
1398
isotherms.
1399
viii.
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1394
An in-depth understanding of the models applied to adsorption kinetics and
isotherms is necessary to avoid misapplication of these models, as well as inaccurate
1401
discussions, calculations, and conclusions. ix.
More attention should be paid to various common misunderstandings about
M AN U
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1400
1403
fundamental adsorption and chemistry concepts. Understanding the unique properties
1404
of adsorbents and target adsorbates can help avoid mistakes made when explaining
1405
adsorption mechanisms.
Although the comments and recommendations of some authors are not always correct, their
1407
observations and suggestions should be acknowledged because of their great contributions in
1408
transferring scientific knowledge.
1409
Acknowledgements
1410
This current work was financially supported by Chung Yuan Christian University (CYCU) in
1411
Taiwan. The first author would like to thank CYCU for the Distinguished International Graduate
1412
Students (DIGS) scholarship to pursue his doctoral studies. The authors gratefully acknowledge
1413
the editor and anonymous reviewer for their invaluable insight and helpful suggestion.
1414
Reference
1415
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1416
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1435
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Azizian, S. (2008a). "Comments on “Adsorption Equilibrium and Kinetics of Reactive Black 5
1437
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1438
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1442
Ben Ali, S., I. Jaouali, S. Souissi-Najar and A. Ouederni (2016). "Characterization and adsorption
1443
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1444
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1445
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"Adsorption
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1447
Thermodynamic Approach to the Adsorption Mechanism1." Soil Science Society of
1448
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1450 1451 1452
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1449
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Bolster, C. H. and G. M. Hornberger (2007). "On the Use of Linearized Langmuir equation." Soil Science Society of America Journal 71(6): 1796-1806.
Borisover, M. D. and E. R. Graber (1997). "Comment on “Competitive Sorption between
1454
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1455
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1456
Bui, T. X. and H. Choi (2010). "Comment on “Adsorption and Desorption of Oxytetracycline
1457
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Canzano, S., P. Iovino, S. Salvestrini and S. Capasso (2012). "Comment on “Removal of anionic
1460
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1461
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1462
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1463
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Cavas, L. (2008). Comment on Equilibrium sorption isotherm studies of Cd(II), Pb(II) and Zn (II) ions detoxification from waste water using unmodified and EDTA-modified maize
1465
husk.
1467 1468
Chen, W., L. Duan, L. Wang and D. Zhu (2009). "Response to Comment on “Adsorption of
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Table captions Table 1. Relationship between isotherm parameters and isotherm shape
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Table 2. Mistakes in the presentation and calculation of the separation factor (RL) Table 3. Incorrect values of the exponent g in the Redlich–Peterson equation
Table 4. Comparison of incorrect and correct thermodynamic parameters for methylene blue
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adsorption onto sulfuric acid-treated orange peel
Table 5. A typical example of correct and incorrect use of a Micromeritics report (data not
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published)
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Table 1. Relationship between isotherm parameters and isotherm shape
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Freundlich exponent Separation factor Isotherm shapes Remarks n=0 RL = 0 Irreversible Horizontal n<1 RL < 1 Favorable Concave n=1 RL = 1 Linear Linear n>1 RL > 1 Unfavorable Convex Note: Information was adapted from Worch (2012). Copyright (2012), with permission from De Gruyter. RL and n were calculated from equations 52 and 56, respectively.
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Table 2. Mistakes in the presentation and calculation of the separation factor (RL)
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Typical examples Remakes Langmuir parameters The RL is not the Langmuir o Q max KL RL constant, so it is mistake for Orange peel 54.5 0.101 0.01–0.17 presentation. OP Biochar 115 0.019 0.08–0.57 Langmuir parameters The RL values must be calculated RL o Q max KL at different range of initial adsorbate concentration, so it is Orange peel 54.5 0.101 0.17 mistake for calculation. OP Biochar 115 0.019 0.57 Langmuir parameters RL Qomax KL Correction presentation and calculation. Orange peel 54.5 0.101 0.01–0.17 OP Biochar 115 0.019 0.08–0.57 Note: The data were modified from our previous publication (Tran, You et al. 2015).
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Table 3. Incorrect values of the exponent g in the Redlich–Peterson equation Adsorbate
Sawdust
Reactive black
1.10
(Inbaraj, 2006)
Sawdust
Reactive red
1.04
(Inbaraj, 2006)
Congo red
2.91
(Kumar and Porkodi, 2008)
Xad-4 resin
4-chlorophenol at 303 K
1.07
(Kumar and Porkodi, 2007)
Xad-4 resin
4-chlorophenol at 318 K
1.19
(Kumar and Porkodi, 2007)
2+
–0.35
(Vasanth Kumar et al., 2007)
2+
–1.23
(Kumar et al., 2007
Tectona grandis
Cu
Syzygium cumini
Pb
Activated carbon/ chitoshan composite Activated carbon/ chitoshan composite Activated carbon
Aniline/aniline + Cr(VI)
1.04
(Huang et al., 2014)
Cr(VI)/aniline + Cr(VI)
1.04
(Huang et al. 2014)
Cr(VI)
1.02
(Huang et al. 2014)
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/chitoshan composite
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xerogel
Reference
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g
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Adsorbent
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Table 4. Comparison of incorrect and correct thermodynamic parameters for methylene blue adsorption onto sulfuric acid-treated orange peel Incorrect thermodynamic parameters reported by Senthil Kumar et al. (2014)
50 100 150 200 250
Temperature
30 °C –12.5 –10.1 –8.86 –8.03 –7.29
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40 °C 50 °C 60 °C –53.7 –137 –10.4 –8.87 –8.49 –37.4 –90.3 –9.15 –8.04 –7.46 –32.9 –79.4 –8.19 –7.27 –6.52 –27.5 –64.2 –7.54 –6.64 –6.19 –23.7 –54.4 –6.61 –6.17 –5.64 KC values 30 °C 40 °C 50 °C 60 °C 142 54.9 27.2 21.5 54.8 33.6 19.9 14.8 33.7 23.3 14.9 10.5 24.2 18.1 11.9 9.35 18.1 12.7 9.97 7.66 Correct thermodynamic parameters suggested by Hai (2017) ∆Go ∆Ho ∆So KC van't Hoff equation (kJ/mol) (kJ/mol) (J/mol) 5.25
40 °C
4.33
50 °C
3.54
60 °C
3.27
-4.18 -3.81 -3.40
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30 °C
13.65
-31.39 y = 1642 – 3.78 R2 = 0.978
-3.28
The unit of J/mol/K was expressed as the original paper; the correction unit might be kJ/mol.
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∆Go (kJ/mol)
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Co (mg/L)
∆So (J/mol/K)a
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∆Ho (kJ/mol)
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Table 5. A typical example of correct and incorrect use of a Micromeritics report Correct data
Prepared activated carbon
Prepared Biochar
BET surface area
613
536
Langmuir surface area
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Micropore area
NA
External surface area
698
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Incorrect data
660
348
188
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NA: The micropore area is not reported because either the micropore volume is negative or the calculation of external surface area is larger than the total surface area (BET surface area). The unit is m2/g. Data is not published.
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Figure captions Figure 1. Some basic terms used in adsorption science and technology
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Figure 2. Basic properties of an adsorbent determined by various common techniques Figure 3. Schematic illustration of a new classification system for metal biosorption mechanisms
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Figure 4. A typical example of difference between (a) point of zero charge and (b) zeta potential of glucose-derived spherical biochar prepared from 800 °C
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Figure 5. Effect of contact time on the adsorption process of (a) methyl violet onto granulated mesoporous carbon (GMC) and granular activated carbon (GAC); (b) methyl tert-butyl ether onto carbonaceous resin (Ambersorb 563); (c) ibuprofen (IBP), carbamazepine (CBZ), ofloxacin (OFX), bisphenol-A (BPA), diclofenac (DFN), mecoprop (MCP), pentachlorophenol (PCP), benzotriazol (BZT), and caffeine
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(CAF) onto activated carbon cloths (resin phenolic precursor); and (d) methyl blue onto graphene oxide
Figure 6. Fits of kinetic adsorption data to the linear pseudo-second-order equation (the study
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of methylene green 5 adsorption onto commercial activated carbon (CAC) and synthesized activated carbons prepared from golden shower through different
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chemical activation methods (GSAC, GSBAC, GSHAC, and GSHBAC))
Figure 7. Transport processes during adsorption by a porous adsorbent Figure 8. (a) non-equilibrium adsorption isotherms of methylene blue onto sulfuric acid-treated orange peel (STOP) at various temperatures, and (b) comparison of adsorption isotherm curves; adsorbent B performs better (higher qe at q10) than adsorbent A at lower equilibrium concentrations (e.g., Ce = 10 mg/L)
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Figure 9. Proposed mechanisms for Cr(VI) biosorption by nonliving biomass Figure 10. (a) Chemical structure of Congo Red and (b) UV-vis spectra of Congo Red
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solutions at different solution pH values Figure 11. An example of a graphene layer and proposed mechanisms of methylene adsorption green 5 onto biochar, synthesized activated carbon, and commercial
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activated charcoal
Figure 12. A simple guide to the nonlinear method of calculating the Langmuir parameters
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(RSS: residual sum of squares, TSS: total sum of squares)
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Figure 1. Some basic terms used in adsorption science and technology
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Figure 2. Basic properties of an adsorbent determined by various common techniques
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Figure 3. Schematic illustration of a new classification system for metal (bio)sorption mechanisms
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(Adapted from Robalds et al., 2016. Copyright (2016), with permission from Elsevier)
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Figure 4. A typical example of difference between (a) point of zero charge and (b) zeta
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potential of glucose-derived spherical biochar prepared from 800 °C (Data unpublished)
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Figure 5. Effect of contact time on the adsorption process of (a) methyl violet onto granulated mesoporous carbon (GMC) and granular activated carbon (GAC) (Reprinted from Kim et al.
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2016. Copyright (2016), with permission from Elsevier); (b) methyl tert-butyl ether onto carbonaceous resin (Ambersorb 563) (Reprinted from Hung and Lin 2006. Copyright (2006), with permission from Elsevier); (c) ibuprofen (IBP), carbamazepine (CBZ), ofloxacin (OFX),
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bisphenol-A (BPA), diclofenac (DFN), mecoprop (MCP), pentachlorophenol (PCP), benzotriazol (BZT), and caffeine (CAF) onto activated carbon cloths (resin phenolic precursor) (Reprinted from Masson et al. 2016. Copyright (2016) with permission from Elsevier); and (d) methyl blue onto graphene oxide (Reprinted with permission from Sharma et al. 2013. Copyright (2013) American Chemical Society)
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Figure 6. Fits of kinetic adsorption data to the linear pseudo-second-order equation (the study of methylene green 5 adsorption onto commercial activated carbon (CAC) and synthesized
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activated carbons prepared from golden shower through different chemical activation methods (GSAC, GSBAC, GSHAC, and GSHBAC)) (Adapetd from Tran et al., 2017d.
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Figure 7. Transport processes during adsorption by a porous adsorbent (Adapted with
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permission from Weber and Smith, 1987. Copyright (1987) American Chemical Society)
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Figure 8. (a) non-equilibrium adsorption isotherms of methylene blue onto sulfuric acid-treated orange peel (STOP) at various temperatures (Adapted from Hai 2016. Copyright (2016) Taylor and Francis), and (b) comparison of adsorption isotherm curves: adsorbent B performs better (higher qe at q10) than adsorbent A at lower equilibrium concentrations (e.g., Ce = 10 mg/L) (Adapted from Volesky 2007. Copyright (2007), with permission from Elsevier)
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Figure 9. Proposed mechanisms for Cr(VI) biosorption by nonliving biomass
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(Adapted from Park et al., 2005. Copyright (2005), with permission from Elsevier).
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Figure 10. (a) Chemical structure of Congo Red and (b) UV-vis spectra of Congo Red solutions at different solution pH values (Adapted from Zhou et al., 2011. Copyright (2011), with permission from Elsevier)
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Figure 11. An example of a graphene layer and proposed mechanisms of methylene
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adsorption green 5 onto biochar, synthesized activated carbon, and commercial activated
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Figure 12. A simple guide to the nonlinear method of calculating the Langmuir parameters (RSS:
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residual sum of squares, TSS: total sum of squares)
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Highlights • This study summarizes common literature mistakes in the field of
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adsorption • Reiteration and propagation of such mistakes in future publications should be avoided.
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• Correct expression and citation of the models used in adsorption studies are provided
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further investigated
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• We also highlight some problems that need to be thoroughly discussed or
S0043-1354(17)30269-5
DOI:
10.1016/j.watres.2017.04.014
Reference:
WR 12811
To appear in:
Water Research
Received Date: 29 October 2016 Revised Date:
29 March 2017
Accepted Date: 6 April 2017
Please cite this article as: Tran, H.N., You, S.-J., Hosseini-Bandegharaei, A., Chao, H.-P., Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: A critical review, Water Research (2017), doi: 10.1016/j.watres.2017.04.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Mistakes and inconsistencies regarding adsorption of contaminants from aqueous
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solutions: A critical review
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Hai Nguyen Trana,b*, Sheng-Jie Youb, Ahmad Hosseini-Bandegharaeic,d, Huan-Ping Chaob*
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Department of Civil Engineering, Chung Yuan Christian University, Chungli 320, Taiwan
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Department of Environmental Engineering, Chung Yuan Christian University, Chungli 320, Taiwan Wastewater Division, Faculty of Health, Sabzevar University of Medical Sciences, PO Box 319, Sabzevar, Iran d Department of Engineering, Kashmar Branch, Islamic Azad University, PO Box 161, Kashmar, Iran
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Corresponding authors:
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H. N. Tran ([email protected]) and H.- P. Chao ([email protected])
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Department of Environmental Engineering, Chung Yuan Christian University, Chungli 320, Taiwan
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Abstract
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In recent years, adsorption science and technology for water and wastewater treatment has attracted substantial attention from the scientific community. However, the number of
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publications containing inconsistent concepts is increasing. Many publications either reiterate previously discussed mistakes or create new mistakes. The inconsistencies are reflected by the
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increasing publication of certain types of article in this field, including “short communications”, “discussions”, “critical reviews”, “comments”, “letters to the editor”, and
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“correspondence (comment/rebuttal)”. This article aims to discuss (1) the inaccurate use of
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technical terms, (2) the problem associated with quantities for measuring adsorption performance, (3) the important roles of the adsorbate and adsorbent pKa, (4) mistakes related to the study of adsorption kinetics, isotherms, and thermodynamics, (5) several problems related to adsorption mechanisms, (6) inconsistent data points in experimental data and model fitting, (7) mistakes in measuring the specific surface area of an adsorbent, and (8) other mistakes found in the literature. Furthermore, correct expressions and original citations of the relevant models (i.e., adsorption kinetics and isotherms) are provided. The authors hope that this work will be helpful for readers, researchers, reviewers, and editors who are interested in the field of adsorption studies.
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Keywords: Adsorption; mistake; comment; inconsistency; critical review
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Table of Contents 1. Introduction ........................................................................................................................5 2. Technical terms used in the study of adsorption ..................................................................6
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3. Quantities for measuring adsorption performance ...............................................................8 4. Incorrect assumptions regarding pKa ...................................................................................9
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5. Adsorption kinetics ...........................................................................................................11
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5.1. The important role of initial time............................................................................11
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5.2. Adsorption equilibrium time for porous materials ..................................................13 5.3. Pseudo-first-order (PFO) equation..........................................................................14
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
5.3.1. Derivation of the PFO equation ...................................................................14 5.3.2. Problems in the application of the PFO equation..........................................15 5.4. Pseudo-second-order (PSO) equation .....................................................................17 5.4.1. Derivation of the PSO equation ...................................................................17 5.4.2. Problems in the application of the PSO equation..........................................20 5.5. Elovich equation ....................................................................................................23 5.5.1. Derivation of the Elovich equation ..............................................................23 5.5.2. Incorrect expression of the Elovich equation................................................24 5.6. Intra-particle diffusion model .................................................................................24 6. Adsorption isotherms ........................................................................................................25 6.1. Adsorption equilibrium ..........................................................................................25 6.2. Langmuir equation .................................................................................................29 6.2.1. Derivation of the Langmuir equation ...........................................................29 6.2.2. Derivation of the separation factor ...............................................................31 6.2.3. Mistakes concerning the Langmuir model and the separation factor.............31 6.3. Freundlich equation ...............................................................................................33 6.3.1. Derivation of the Freundlich equation ..........................................................33 6.3.2. Mistakes concerning the Freundlich equation ..............................................34 6.4. Redlich–Peterson equation .....................................................................................35 6.4.1. Derivation of the Redlich–Peterson equation ...............................................35 6.4.2 Mistakes concerning the Redlich–Peterson equation .....................................36 6.5. Dubinin–Radushkevich equation ............................................................................36 6.5.1. Derivation of the Dubinin–Radushkevich equation ......................................36 6.5.2. Mistakes concerning the Dubinin–Radushkevich equation ...........................37 7. Adsorption thermodynamics .............................................................................................38 7.1. Principles of adsorption thermodynamics ...............................................................38 7.2. Equilibrium constant derived from the Langmuir constant (KL) ..............................40 3
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7.3. Equilibrium constant derived from the Freundlich constant (KF) ............................44 7.4. Equilibrium constant derived from the partition coefficient (Kp).............................45 7.5. Equilibrium constant derived from the distribution coefficient (Kd) ........................47 8. Others mistakes ................................................................................................................49
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8.1. Inconsistent data points in experimental data and model fitting ..............................49 8.2. Oxidation state of chromium ..................................................................................51
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8.3. Incorrect labels.......................................................................................................53
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8.4. BET specific surface area of an adsorbent ..............................................................54
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8.5. Maximum absorption wavelength in dye adsorption studies ...................................57
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8.6. Cπ-cation and π-π interactions................................................................................57 8.6.1. Cπ-cation interactions ..................................................................................57 8.6.2. π-π interactions ............................................................................................59 8.7. Other miscellaneous errors .....................................................................................62 9. Nonlinear-optimization technique .....................................................................................66 10. Conclusions ....................................................................................................................68
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Acknowledgements ..............................................................................................................69
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1. Introduction Nowadays, the number of publications in international scientific journals has increasingly
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become a standard for the assessment of scientists (Geckeis and Rabung, 2004). As the number of
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scientific publications increase, mistakes and misconceptions enter scientific literature and some
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can also be repeated in subsequent publications. Once errors and mistakes enter the literature, it is
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difficult to eradicate them. The entrance of mistakes in scientific publications, as well as their
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propagation, can result from the subjectivity of the authors and/or objective reasons.
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A typical study on the adsorption of organic and inorganic contaminants comprises several
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sections, such as the effects of solution pH and ionic strength, studies of adsorption kinetics,
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isotherms, thermodynamics, desorption, and regeneration. Adsorption processes can be conducted
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using either batch or column techniques. It has been found that many scientific articles in the field
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of adsorption science and technology contain several mistakes and misconceptions including the
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use of technical terms, application of quantities, determining the roles of some constants like pKa,
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performing kinetic studies and modeling kinetic adsorption data, finding a suitable isotherm model
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to fit equilibrium data, calculating thermodynamic parameters, correct interpretation of adsorption
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mechanisms, and measuring the specific surface area of an adsorbent. Moreover, a survey of the
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scientific publications related to the adsorption of contaminants in aqueous solutions reveals that
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some less obvious inconsistencies and mistakes have unavoidably slipped the attention of authors
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and were repeated in subsequent publications.
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The observation of these inconsistencies and mistakes, regardless of their origin, along
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with comments and open discussions can prevent their propagation in scientific knowledge
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transfer. Therefore, the presentation of a comprehensive review on common mistakes in
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adsorption studies, besides introducing the most correct approaches to use and giving a source of 5
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up-to-date literature on this issue, seems to be valuable to both readers and researchers in this
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field. The main purpose of this review is to identify mistakes in past publications and prevent the
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propagation of such mistakes in future scientific literature. Herein, we present some common
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mistakes in various aspects of adsorption studies and analyze the reasons for their entrance into
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the literature. This was accomplished by discussing the published papers in the field of adsorption
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of contaminants from aqueous solutions, commonly including “comments on”, “reply for
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comments”, “response to”, “authors’ response to comments on”, “comments on the authors’
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response to comments on”, “comments on comment on”, “in reaction to”, “critical review”, and “a
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note on the comments” published works. In addition to our comprehensive review on the mistakes
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existing in publications, some correct approaches are suggested where necessary to avoid the
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propagation of such mistakes in the future scientific literature. This paper primarily focuses on
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three basic constituents of adsorption theory: adsorption equilibria, kinetics, and thermodynamics.
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2. Technical terms used in the study of adsorption
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Adsorption processes have their own vernacular. Therefore, correctly understandings the
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technical terms used in adsorption technology can prevent the introduction of several unexpected
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ambiguities and discrepancies. Some basic adsorption terms are summarized in Figure 1.
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Figure 1
To some extent, a thorough understanding of the properties of adsorbents might prevent
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common mistakes made in interpreting adsorption processes and adsorption mechanisms.
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Numerous techniques can be used to characterize an adsorbent (Figure 2). More information on the
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basic properties of adsorbents (i.e., biosorbent, biochar, hydrochar, and activated carbons) and the
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relations between these properties has been published in our recent work (Tran et al. 2017c). 6
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Figure 2 The appropriate use of technical words regarding the biosorption mechanism of heavy
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metals has been highlighted by Robalds et al. (2016). To avoid reader confusion, they
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recommended that “surface precipitation” be used instead of “microprecipitation” (also written as
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“micro-precipitation”). Similarly, it is necessary to distinguish between “chelation”,
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“complexation”, and “coordination”. The word “complexation” includes two meanings:
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“chelation” and/or “coordination”. For example, the incorrect sentence “in another sense, it can
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also be defined as a collective term for a number of passive accumulation processes which in any
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particular case may include ion exchange, coordination, complexation, chelation, adsorption and
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microprecipitation” should be revised as “biosorption may include ion exchange, complexation
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(including coordination and/or chelation), physisorption, or microprecipitation” (Robalds et al.,
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2016). In addition, the use of the term “electrostatic adsorption” may cause misunderstanding and
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confusion; therefore, depending on the intended meaning, the appropriate terms (i.e., “electrostatic
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attraction”, “electrostatic force”, or “electrostatic interaction”) are recommended. Notably, the
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authors also suggested a new classification system for the (bio)sorption mechanisms of heavy
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metals (Figure 3).
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Figure 3
The electrical state of an adsorbent’s surface in solution is usually characterized by either
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the point of zero charge (PZC) or the isoelectric point (IEP). Many authors have complained about
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the misuse of the terms IEP and PZC outside their normal meanings (Somasundaran, 1968;
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Kosmulski, 2009). The PZC is defined as the solution conditions under which the surface charge
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density equals zero. Potentiometric titration, or related methods, is used to determine the PZC by
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finding the point at which the apparent surface charge density in the presence of an inert electrolyte 7
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is not dependent on ionic strength (Figure 4a). The IEP occurs when the electrokinetic (ζ) potential
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at the shear plane equals zero; ζ is determined from measuring electrokinetic (electrophoresis and
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streaming potential) and electroacoustic phenomena (Figure 4b) (Kosmulski, 2009). IEP values
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clearly represent only the external surface charge of particles in solution, whereas the PZC varies
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in response to the net total (external and internal) surface charge of the adsorbent (as the
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characteristic of amphoteric surfaces). Therefore, the difference between the PZC and IEP values
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for a porous carbon system can be interpreted as a measure of the surface charge distribution. A
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difference (PZC − IEP) of greater than zero indicates that the external particle surface is more
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negatively charged than the internal particle surface, and a difference of close to zero corresponds
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to a more homogeneous distribution of surface charge. The PZC is only equal to the IEP in the
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absence of specific or counter ions. This means that equality between the PZC and IEP exists only
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if no specific adsorption of counter ions from the solution occurs (Radovic, 1999; Onjia and
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Milonjić, 2002).
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Figure 4
3. Quantities for measuring adsorption performance In the field of adsorption, adsorption performance can be expressed as the amount of
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adsorbate adsorbed at equilibrium or the percentage of removed adsorbate. The amount of
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adsorbate adsorbed at equilibrium (qe; mg/g) is often calculated using the material balance of an
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adsorption system; the adsorbate, which has disappeared from the solution, must be in the
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adsorbent (Volesky, 2007).
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qe =
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where C0 (mg/L) and Ce (mg/L) are the initial and equilibrium adsorbate concentration in solution,
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respectively; m (g) is the dried mass of used adsorbent; and V (L) is the volume of the adsorbate
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solution. Depending on the purpose of the study, the parameter qe may be expressed in different units
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as follows: (1) mg/g for evaluating practical and engineering processes, (2) mmol/g or meq/g for
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examining the stoichiometry of a process and for studying functional groups and metal-binding
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mechanisms, and (3) mmol/g for comparing the selective adsorption performance of various
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adsorbates (Volesky, 2007). Of these units, mg/g (milligrams of adsorbate adsorbed per gram of
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dried adsorbent) is used most commonly for qe in adsorption studies.
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In addition to qe, the adsorption performance can also be expressed as the percentage of
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removed adsorbate (%removal). However, the unit of %removal needs to be used cautiously, as it
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is very approximate and can cause misleading conclusions about relative adsorption performance.
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This unit is only appropriate for the purpose of crude measurements and perhaps for quick and
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very approximate screening of adsorbent materials (Kratochvil and Volesky, 1998; Hai, 2017) (C o − C e ) × 100 Co
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To some extent, the use of %removal in the study of adsorption equilibria can cause
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incorrect observations and, as a result, inaccurate conclusions (a detailed discussion is provided in
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Section 6.1).
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4. Incorrect assumptions regarding pKa
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A mistake regarding the fundamentals of chemistry was commented on by Rayne (2013).
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The commented paper reported the adsorption of n-perfluorooctanesulfonamide (PFOSA) onto
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multiwalled carbon nanotubes with differing oxygen content. However, PFOSA was mistakenly 9
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assumed to be an “organic base”, resulting in the following invalid interpretation: “for PFOSA
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(pKa = 6.52), when pH < pKa, protonation occurs on the amino group, and the decreased
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protonation leads to the increased adsorption, but when pH > pKa, PFOSA exists as neutral
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molecule in water.” In fact, PFOSA is an acid and, thus, is a neutral compound below its pKa value
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(estimated at between 6.0 and 7.0) and a dissociated anion at pH > pKa (Rayne, 2013).
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Recently, the effect of pH on the interaction of copper with the surface functional groups of raw pomegranate-peel biosorbent was reported as follows:
R–OH ↔ R–O− + H+ R–O− + Cu2+ ↔ R–OCu+ R–O− + Cu(OH)+ ↔ R–OCu(OH)
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(3) (4) (5) (6)
where –R represents the surface adsorbent; R–OH2+, R–OH, and R–O− represent protonated,
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neutral, and ionized surface hydroxyl functional groups, respectively; and R–OCu+ and R–
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OCu(OH) are the formed bonding complexes.
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The authors (Ben Ali et al., 2016) explained that, “the effect of pH could be also explained
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by considering the point of zero charge of the adsorbent (pHpzc). The adsorbent surface is
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positively charged for pH< 4.7 and it becomes negatively charged at pH value above 4.7.
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Therefore, for pH values < 4.7, the adsorption is unfavorable because of repulsive electrostatic
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interactions between metal ions and positively charged functional groups. The maximum
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adsorption of Cu(II) occurs at pH above pHpzc value when the adsorbent surface is negatively
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highly charged.” However, the important role of the pKa values of carboxylic acid groups (–
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COOH; pKa 1.7–4.7) and hydroxyl groups (–OH; pKa 9.5–13) was ignored (Volesky, 2007).
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Correspondingly, Eqs. 3–6 indicate a misunderstanding of the surface chemistry of the adsorbent.
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The authors investigated the effect of solution pH on the adsorption process of Cu(II) in solutions
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with pH values from 2.0 to 6.0. Therefore, dissociation of the –OH groups to –O− did not occur at
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these solutions pH values. Instead, the –COOH groups dissociated, forming negatively charged
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carboxylate groups (–COO‒) in the aforementioned pH range, and were the dominant groups that
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interacted with copper ions (Tran, 2017).
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Moreover, Bui and Choi (2010) made a critical comment that Oleszczuk et al (2010)
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mistyped the properties of two pharmaceuticals: oxytetracycline (logKow = 2.45, pKa = 7) and
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carbamazepine (logKow = −1.22, pKa = 3.27, 7.32, 9.11). The correct expression should be
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oxytetracycline (Sw = 121 mg/L, logKow = −1.22, pKa = 3.27, 7.32, 9.11; density = 1.63 g/cm3) and
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carbamazepine (Sw = 112 mg/L, logKow = 2.45, pKa = 7; density =1.15 g/cm3). Bui and Choi
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(2010) also emphasized that the pKa value of carbamazepine reported by Oleszczuk et al (2010) is
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still debated. Carbamazepine (CBZ) is commonly characterized with two pKa values: pKa1 (= 1 or
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2.3) for the equilibrium RCONH3+ ⇌ RCONH2 + H+ and pKa2 (= 13.9) for the equilibrium
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RCONH2 ⇌ RCONH− + H+. The misreporting of the CBZ pKa can cause inaccurate conclusions.
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For example, Oleszczuk et al. (2010) suggested that an electrostatic interaction occurred between
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CBZ and multiwalled carbon nanotubes (MWCNT) at pH < 7.0 because they opined that CBZ
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existed in its cationic form at pH < 7.0 (pKa = 7.0). However, CBZ with pKa1 < 2.3 and pKa2 ≥ 13.9
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actually exists entirely as a neutral species in the pH range of 1.9–11.9, as calculated using
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ACDLab. As a result, the electrostatic interaction was ruled out as a contributing interaction in the
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CBZ-adsorption mechanisms (Bui and Choi, 2010).
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5. Adsorption kinetics
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5.1. The important role of initial time
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In the study of adsorption kinetics, Azizian (2006) proposed that experiments should be 11
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started at t < 2 min (considered as the initial time). Adsorption kinetics data in the initial time
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periods play an important role in performing accurate modeling and drawing conclusions. Depending on the affinity between the adsorbent and adsorbate, the initial adsorption rate
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may be very fast. For the adsorption of heavy metals, Tran et al. (2015) investigated the adsorption
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of Cd2+ onto orange-peel-generated biochar, and found that equilibrium can be reached rapidly in
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kinetic experiments with a removal rate of 80.6–96.9% (within 1 min). An analogous performance
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was reported by Guo et al. (2015), with approximately 70.0–96.6% of the total Cd2+ in solution
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removed within the first minute of contact. Additionally, Müller et al. (2012) noted that
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approximately 90% of Zn(II) adsorption onto Lewatit S1468 occurs within 1 min, and this
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adsorption process reaches equilibrium in approximately 5 min.
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For the adsorption of organic contaminants, kinetic studies indicated that the adsorption
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equilibrium of methylene green 5 was quickly established, with a low activation energy required
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for adsorption (Ea; 3.30–27.8 kJ/mol), and activated carbons removed 50–73% of the dye from
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solution within 1 min (Tran et al., 2017d; Tran et al., 2017e). Similarly, Canzano et al. (2012)
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noted that the adsorption process of anionic Congo-red dye onto raw and acid-treated pine cone
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powder reached equilibrium in the first few minutes (< 5 min), during which no measurements
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were carried out.
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approaches that of at equilibrium (qe) and, therefore, plotting the kinetic data is bound to produce a
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straight line, independent of the real kinetic order followed by the system. In other words,
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equilibrium data does not describe the way by which the system reaches equilibrium. As a result,
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the use of data recorded over a significant time interval after the attainment of equilibrium, or very
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close to equilibrium, is likely to lead to erroneous conclusions regarding adsorption kinetics. 12
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5.2. Adsorption equilibrium time for porous materials The adsorption processes for inorganic and organic contaminants onto porous adsorbents
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(i.e., activated carbon, biochar, activated carbon spheres, zeolite, and macroreticular resin) can
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take longer (i.e., several days or weeks) to approach true equilibrium than nonporous adsorbents
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(i.e., biosorbent and hydrochar). This difference is attributed to the different adsorption
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mechanisms of these adsorbents. Pore filling is the most common adsorption mechanism for
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porous adsorbents, along with several other interactions (i.e., electrostatic attraction, hydrogen
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bonding, surface precipitation, π-π interaction, n-π interaction, and cation exchange) that depend
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on the characteristics of the porous adsorbents and adsorbates. Many studies have opted for a 24 h
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equilibrating time for isotherm adsorption experiments, without providing evidence that
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adsorption in their system attained true equilibrium within the appropriate timeframe.
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Therefore, it is necessary to provide the specified timeframe in which the adsorption
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process approaches a true equilibrium. Figures 5a–c represent the influence of contact time on the
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adsorption processes of various contaminants onto porous adsorbents (Hung and Lin, 2006;
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Masson et al.; 2016; Kim et al., 2016). Clearly, the amount of contaminant adsorbed onto the
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porous adsorbents continued to increase after 24 h. For example, Kim et al. (2016) speculated on
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the process of methyl violet (MV) adsorption onto synthesized granular mesoporous carbon
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(GMC) and commercial granular activated carbon (GAC). The results of their kinetic study
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demonstrated that MV adsorption reached an equilibrium state within 20 d for GMC-polyvinyl
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alcohol and 26 d for GMC-carboxymethyl cellulose, while adsorption onto GAC had not reached
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equilibrium even after 75 d. Furthermore, a phenomenon involving desorption from the adsorbent
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surface after reaching adsorption equilibrium (Figure 5d) has been reported in the literature
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(Sharma et al., 2013, Halder; Khan et al., 2016). Therefore, studies of the adsorption kinetics play
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an important role in identifying the required equilibration time and the optimal contact time and for
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an adsorption process.
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Figure 5 In aqueous-phase adsorption, two kinetic reaction models (i.e., pseudo-first-order and
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pseudo-second-order equations), the Elovich or Roginsky–Zeldovich model, and the intraparticle
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diffusion model have been widely applied to mathematically describe the intrinsic kinetic
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adsorption constant. Furthermore, most mistakes found and discussed in the literature correspond
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to the use of kinetic models. Therefore, the following sections (5.3–5.6) include a thorough
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discussion of these models.
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5.3. Pseudo-first-order (PFO) equation
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5.3.1. Derivation of the PFO equation
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Recently, Ho published a series of critical papers (Ho and McKay, 1998b; Ho, 2005, Ho,
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2014a; Ho, 2015; Ho, 2016e) discussing two main points. First, Ho (Ho and McKay, 1998b)
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claimed to offer the correct reference style for citing Lagergren’s paper, with the original
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translated from “Lagergren, S. (1898), Zur theorie der sogenannten adsorption gelöster stoffe.
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Kungliga Svenska Vetenskapsakademiens Handlingar, Band 24, No. 4, 1–39” into English as
313
“Lagergren, S., About the theory of so-called adsorption of soluble substances, Kungliga Svenska
314
Vetenskapsakademiens. Handlingar, Band 24, No. 4, 1898, pp. 1–39.” Second, Ho stated that
315
Lagergren’s first-order rate equation has been called pseudo-first-order since 1998 (Ho, 2005) in
316
order to distinguish kinetic equations based on the adsorption capacity of solids from those based
317
on the concentration of a solution. However, the responses of many authors (Özacar; 2005, Kumar,
318
2006d; Utomo et al., 2010) state that Lagergren’s first-order rate expression had been referred to as
319
a pseudo-first-order equation before Ho’s publication in 1998. For example, in 1990, Sharma et al.
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320
(1990) studied the removal of Ni(II) from an aquatic environment by wollastonite. In the section
321
on adsorption kinetics, they stated: “the adsorption of Ni (II) on wollastonite follows the first order
322
adsorption rate expression of Lagergren (1898).” The great contributions of Ho toward correcting the citation style format for the PFO
324
equation cannot be denied. However, the PFO equation was not originally proposed or initially
325
expressed by Ho. In the scientific community, the authors who first propose a theoretical model
326
should always be given credit for their contributions via correct citation (Kumar and Rattanaphani,
327
2007; Wu, 2009; Utomo et al., 2010). Therefore, the original work by Lagergren (1898), who first
328
presented the first-order-rate equation for the adsorption of oxalic acid and malonic acid onto
329
charcoal, should be cited. The PFO equation can be expressed correctly in nonlinear (Eq. 7) and
330
linear forms (Eq. 8 or Eq. 9).
log(qe − qt ) = log(qe ) −
ln(qe − qt ) = ln(qe ) − k1t
k1 t 2.303
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qt = qe (1 − e −k1t )
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323
(7) (8)
(9)
where qe and qt are the amounts of adsorbate uptake per mass of adsorbent at equilibrium and at
332
any time t (min), respectively; and k1 (1/min) is the rate constant of the PFO equation.
333
5.3.2. Problems in the application of the PFO equation
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It cannot be denied that the PFO equation is widely applied in adsorption kinetics.
335
However, several problems related to the application of the PFO equation have been discussed in
336
the literature. First, many incorrect expressions for its linear forms have been published. Various
337
incorrect forms are shown in Eq. 10 (Alagumuthu et al., 2010), Eq. 11 (Fu et al., 2007; Jing et al.,
338
2014; Nekouei and Nekouei, 2017), Eq. 12 (Ho, 2014e; Ho, 2014a; Jing et al., 2014; Ho, 2016e; 15
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Ho, 2016b; Ho, 2016c; Ho, 2016a; Ho, 2016d; Ho, 2017), Eq. 13 (Ho, 2015), Eqs. 14 and 15 (Jing
340
et al., 2014), Eq. 16 (Kumar, 2006a), and Eq. 17 (Kumar and Porkodi, 2007b), which should be
341
avoided in future studies. As a result of these incorrect expressions, recalculation of the PFO
342
equation parameters was necessary to obtain the correct parameters (Wu et al., 2017). log(qe ) − k1 t 2.303
log(qe − qt ) =
log(qe ) − k1 2.303t
(10)
(11)
SC
log(qe − qt ) =
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339
log(qe − qt ) = log(qe )
Ci kt = 1 Ct 2.303
log(1 −
C i − Ct kt = 1 Ci − Ce 2.303
qe k1 = qe − qt 2.303t
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log
k1t 2.303
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log
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1 k1 1 = + qt qet qe
log(qe − qt ) = log(qe ) −
k1 2.303
(12)
(13)
(14)
(15)
(16)
(17)
where Ci (mg/L), Ct (mg/L), and Ce (mg/L) are the concentrations of adsorbate at the initial time (t
344
= 0), any time t, and equilibrium, respectively.
345
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The second problem is the two unknown parameters (qe and k1). Furthermore, in most
346
cases, the PFO equation is only appropriate for the initial 20 to 30 min of contact time, not for the
347
whole range (Ho and McKay, 1998a). Thus, plots of Eq. 8 or Eq. 9 are only linear over
348
approximately the first 30 min; beyond this initial period, the experimental and theoretical data
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will not fit adequately (McKay et al., 1999). Another important problem is the selection of an
350
appropriate qe value. Notably, the adjusted qe value cannot be lower than the maximum measured
351
value of qt. This is because mathematical errors associated with taking the logarithm of a negative
352
number will occur when using Eq. 8 or Eq. 9 (Plazinski et al., 2009). Finally, the qe value
353
calculated using the PFO equation is not equal to the qe value obtained from experiments, which
354
further indicates the inability of the PFO equation to fit kinetic adsorption data (Febrianto et al.,
355
2009). The presence of a boundary layer or external resistance controlling the beginning of the
356
sorption process was argued to be responsible for this discrepancy (McKay et al., 1999).
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Therefore, two methods have been recommended to obtain an accurate estimation of the
358
kinetic parameters in the PFO equation: (1) a trial and error process to obtain the optimal qe value
359
(Ho and McKay, 1998a), or (2) application of a nonlinear optimization technique. A simple guide
360
to using the nonlinear method is introduced in Section 9.
361
5.4. Pseudo-second-order (PSO) equation
362
5.4.1. Derivation of the PSO equation
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363
dn = K (no − n)2 dt
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removal of heavy metals from water using natural zeolites, as follows: (18)
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In 1984, Blanchard et al. (1984) initially proposed a second-order rate equation for the
Integration of Eq. 18 gives: 1 − α = Kt no − n
(19)
After rearranging, Eq. 19 becomes: n=
Ktno + αno −1 Kt + α
(20)
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365
where n is the amount of M2+ fixed or the amount of NH4+ released at each instant; no is an
366
exchange capacity; and K is a rate constant. Plotting 1/(n0 − n) as a function of time (t) must produce a straight line, the slope of which
368
gives the rate constant K and the intercept leads to the exchange capacity. Considering the
369
boundary condition of n = 0 for t = 0, it follows that α = 1/n, and Eq. 20 can be rearranged to: (21)
If qt = no, qe = n, and k2 = K, Eq. 21 becomes: qt =
qe2k2t 1+ k2qet
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n2 + Kt 1 + Knt
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no =
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(22)
371
where qe (mg/g) and qt (mg/g) are the amount of adsorbate adsorbed at equilibrium and at any t
372
(min), respectively; and k2 (g/mg × min) is the rate constant of the PSO equation. The nonlinear form of the PSO equation (Eq. 22) has been applied elsewhere (Ho, 1995;
374
Ho; Wase et al., 1996). Recently, a series of comments made by Ho implied that the derivation and
375
first application of the PSO equation belongs to his work. Any application of the PSO equation in
376
the field of adsorption studies without citation of the original work or with a misquotation (i.e., the
377
citation of a secondary reference) might suffer from his comments. However, in reaction to Ho’s
378
comments, a series of notes were published by other scholars (Kumar, 2006d; Kumar, 2006c;
379
Kumar and Fávere, 2006; Kumar and Guha, 2006; Kumar and Rattanaphani, 2007) to clarify the
380
correct citation of the PSO equation. Thus, the nonlinear form of the PSO equation for solid-liquid
381
adsorption systems was not originally reported by Ho (1995) or first applied by Ho et al. (1996),
382
but initially proposed by Blanchard et al. (1984).
383
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In the literature, the PSO equation can be correctly expressed in four linear forms (Eqs. 23–
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384
26), and the initial adsorption rate (h) can be described by Eq. 29.
385
Expression for the linear form (Type 1) with a plot of t/qt versus t: t 1 1 = ( )t + qt qe k2qe2
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386
(23)
Expression of the linear form (Type 2) with a plot of 1/qt versus 1/t: 1 1 1 1 =( 2) + qt k2qe t qe
qt = − ( 388
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Expression of the linear form (Type 3) with a plot of qt versus qt/t: 1 qt ) + qe k 2 qe t
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387
(24)
Expression of the linear form (Type 4) with a plot of qt/t versus qt:
qt = −(k 2 qe )qt + k 2 qe2 t
rearranged to:
t 1 + 2 k 2 qe qe
(27)
Subsequently, when t approaches 0, Eqs. 23 and 27 can be expressed as Eq. 28. Setting h = qt/t, the initial adsorption rate (h; mg/g × min) can then be determined by Eq. 29.
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1
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qt =
391
(26)
The initial adsorption rate (h) was proposed by Ho et al. (1996). First, Eq. 22 can be
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(25)
t 1 = qt k 2 qe2
↔
qt = k 2 qe2 t
(28)
h = k 2 qe2
(29)
393
Clearly, only the linear form (Type 1, Eq. 23) might have been reported by Ho et al., (1996)
394
for the adsorption of dyes from waste streams by peat (Özacar, 2005; Kumar, 2006d; Kumar and
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Fávere, 2006; Wu, 2009). Kumar and Fávere (2006) hypothesized that, in adsorption research, the
396
Langmuir equation (Langmuir, 1918) has been the most widely used isotherm to describe
397
adsorption processes under equilibrium conditions. In the literature, four linear types of the
398
Langmuir isotherm have been reported. Irrespective of the linear expression reported, these
399
equations have been widely called the Langmuir isotherm. It is not correct to claim that the
400
Langmuir model was derived or proposed by other authors who transformed the original Langmuir
401
expression into a new linear expression (Kumar and Guha, 2006). In scientific literature, the names
402
of scientists (i.e., Langmuir or Freundlich) have always been presented, even after modification of
403
their equations (Arica, 2003). Similarly, Utomo et al. (2010) suggested that it might not be
404
necessary to cite papers that deal with mathematical modification and different mathematical
405
expressions of the models (i.e., PFO and PSO, and Langmuir). However, from the scientific point
406
of view, the authors who first proposed a theoretical model should be credited because of their
407
great contributions to the advancement of science. Therefore, the original work by Blanchard et al.
408
(1984) should be cited for the expression of the PSO equation (Özacar, 2005; Kumar, 2006d;
409
Kumar and Fávere, 2006; Plazinski et al., 2009; Wu, 2009; Utomo et al., 2010).
410
5.4.2. Problems in the application of the PSO equation
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First, many incorrect expressions of the linear form of PSO equation are found in the
412
literature, as shown in Eq. 30 (Fu et al., 2007; Kumar and Porkodi, 2007b), Eq. 31 (Ho, 2014f),
413
Eqs. 32 and 33 (Ho, 2014g), Eq. 34 (Ho, 2013), Eq. 35 (Lin and Wang, 2009), Eq. 36 (Ho, 2014c),
414
Eq. 37 (Ho, 2014d), Eq. 38 (Ho, 2014), and Eq. 39 (Ho, 2015).
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t 1 1 = + 2 qt k 2 qe qe t
(30)
20
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(31)
t 1 t = + qt k 2 q e q e
(32)
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t 1 1 = + qt 2k 2 qe
t 1 1 = ( qe2 ) + t qt k2 qe
(33)
t 1 1 = + t 2 qt k2 − qe qe
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(34)
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t 1 1 = ( )t 2 qt (k2 qe ) qe t 1 t = k2 qe2 + qt 2 qe
t 1 1 = + 2 qt k2 qe qe
(36)
(37)
(38)
(39)
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t kt t = 22 + qt k2 qe qe
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1 1 1 = + 2 qt k2 qe qe
(35)
Second, based on the best fit of kinetic experimental data using the PSO model, many
416
authors have drawn controversial conclusions. For example, “the adsorption process is the
417
chemisorption, which involve valence forces through sharing electrons between adsorbate and
418
adsorbent”, “the best fit of experimental kinetic data in pseudo-second-order kinetics suggests the
419
chemisorption, which may involve valency forces through sharing of electrons between dye anion
420
and adsorbent”, and other similar conclusions. The problem with such conclusions has been
421
discussed by several researchers (Kumar, 2006a; Lima et al., 2015; Lima et al., 2016), who
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422
claimed that adsorption mechanisms cannot be directly assigned based on observing simple kinetic
423
experiments or by fitting kinetic models (i.e., the PFO and PSO models). Adsorption mechanisms can only be established by (1) using several analytical techniques
425
(i.e., FTIR, SEM, nitrogen adsorption-desorption isotherms, Raman spectroscopy, TGA/DTA,
426
DSC,
427
titration, and solution calorimetry), and (2) having a good sense of the chemical nature of the
428
adsorbate and adsorbent, adsorbent’s surface, and chemical or physical interactions between the
429
adsorbent and adsorbate (Volesky, 2007; Lima et al., 2015; Lima et al., 2016). The use of
430
analytical techniques together with adsorptive thermodynamic data (i.e., changes in enthalpy and
431
entropy) and activation and adsorption energies, are necessary to confirm whether the adsorption
432
of contaminants in aqueous solution is a chemical or physical process (Lima et al., 2015; Tran et
433
al., 2016).
Si and
13
C solid-state NMR, XRD, XPS, pHPZC, pHIEP, CHN element analysis, Boehm
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29
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424
Finally, in most cases, experimental data for adsorption kinetics are well fitted by the linear
435
form of the PSO equation. However, caution should be taken in drawing conclusions based on
436
fitting to the linear form of the PSO equation. For example, Figure 6 presents a plot of t/qt versus t.
437
Clearly, the R2 values for the linear form of the PSO equation are very high (R2 > 0.99); however,
438
the corresponding R2 values for the nonlinear form of the PSO equation are significantly lower (R2
439
= 0.53–0.68). This finding means that the adsorption process of methylene green 5 (MG5) onto
440
synthesized activated carbon and commercial activated carbon (porous materials) is not
441
adequately described by the PSO equation. In fact, Tran et al. (2017a) concluded that the process
442
of MG5 adsorption onto these porous materials involved π-π interactions and pore filling, and was
443
not related to chemical adsorption. Obviously, the nonlinear method can be applied to obtain
444
kinetic model parameters that are more accurate than those obtained using the linear method.
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Figure 6
445 446
5.5. Elovich equation
447
5.5.1. Derivation of the Elovich equation An empirical equation was firstly proposed by Roginsky and Zeldovich (1934) for the
449
adsorption of carbon monoxide onto manganese dioxide. However, this equation is now generally
450
known as the Elovich equation and has been extensively applied to chemisorption data
451
(McLintock, 1967). This equation can be expressed mathematically as follows:
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448
(40)
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dqt = α exp(− βqt ) dt 452
where qe and qt are the amounts of adsorbate uptake per mass of adsorbent at equilibrium and at
453
any time t (min), respectively; α (mg/g × min) is the initial rate constant because dqt/dt → α when
454
qt → 0; and β (mg/g) is the desorption constant during any one experiment.
become Eq. 41 (nonlinear). qt =
460
ln(1 + αβ t )
(41)
EP
linear form (Eq. 42) can be obtained: qt =
459
β
To simplify the Elovich equation, Chien and Clayton (1980) assumed αβt >> 1. Thus, a
457 458
1
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456
By applying the boundary conditions of qt = 0 at t = 0, the integrated form of Eq. 40 will
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455
1
β
ln(αβ ) +
1
β
ln(t )
(42)
and a plot of qt versus lnt should give a linear relationship with a slope of (1/β) and an
intercept of (1/β)ln(αβ).
23
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461
5.5.2. Incorrect expression of the Elovich equation Errors in the presentation of the nonlinear form of the Elovich model are common in the
463
literature. These incorrect equations (Eqs. 43–45) can be found in several previous papers (Ho and
464
McKay, 1998a; Lin and Wang, 2009; Alagumuthu et al., 2010; Ben Ali et al., 2016).
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462
qt = β ln(αβ ) + ln(t ) 1
β
ln(t )
(44)
SC
qt = β ln(αβ ) +
(43)
465 466 467
5.6. Intra-particle diffusion model
M AN U
qt = β ln(αβ ) + β ln(t )
(45)
The linearized transformation of the intra-particle diffusion model (Weber and Morris, 1963) is presented as follows: qt = k p t + C
(46)
where kp (mg/g × min) is the rate constant of the intra-particle diffusion model and C (mg/g) is a
469
constant associated with the thickness of the boundary layer, where a higher value of C
470
corresponds to a greater effect on the limiting boundary layer.
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468
Generally, although the PSO model can adequately describe adsorption kinetic
472
experimental data, this model does not reveal the adsorption mechanisms. Similarly, the Elovich
473
equation seems to describe various reaction mechanisms, such as bulk diffusion and surface
474
diffusion. In contrast, the intra-particle diffusion model can be useful for identifying the reaction
475
pathways and adsorption mechanisms and predicting the rate-controlling step. In a solid-liquid
476
sorption process, adsorbate transfer is often characterized by film diffusion (also known as
477
external diffusion), surface diffusion, and pore diffusion, or combined surface and pore diffusion.
478
In short, if a plot of qt against t0.5 is linear and passes through the origin, the adsorption is entirely 24
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479
governed by intra-particle diffusion. In contrast, if the intra-particle diffusion plot gives multiple
480
linear regions, then the adsorption process is controlled by a multistep mechanism. Four steps associated with transport processes during adsorption by porous adsorbents
482
were originally proposed in reference (Walter, 1984). The first stage is transport in the solution
483
phase (known as “bulk transport”; occurs quickly), which can occur instantaneously after the
484
adsorbent is transferred into the adsorbate solution; therefore, it does not control engineering
485
design. In most cases, this stage occurs too rapidly and its contribution is considered negligible.
486
The second stage is “film diffusion” (occurs slowly). In this stage, the adsorbate molecules are
487
transported from the bulk liquid phase to the adsorbent’s external surface through a hydrodynamic
488
boundary layer or film. The third stage involves diffusion of the adsorbate molecules from the
489
exterior of the adsorbent into the pores of the adsorbent, along pore-wall surfaces, or both (known
490
as “intraparticle diffusion”; occurs slowly). The last stage, adsorptive attachment, often occurs
491
very quickly; therefore, it is also not significant for design. These four steps are summarized in
492
Figure 7 (Weber and Smith, 1987).
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481
Figure 7
493
6. Adsorption isotherms
495
6.1. Adsorption equilibrium
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494
Milonjić (2009a) and Milonjić (2010) suggested that the amount of adsorbate adsorbed onto
497
an adsorbent depended on the equilibrium concentrations of metal ions, equilibrium solution pH,
498
and temperature. An adsorption isotherm should be given as the equilibrium adsorbed amounts
499
versus the equilibrium ion concentrations for a constant equilibrium solution pH and temperature.
500
Thus, environmental parameters in the sorption system (especially solution pH) must be carefully
501
controlled at the given value over the entire contact period until the sorption equilibrium is
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reached. These comments were in good agreement with the suggestion that metal-ion adsorption is
503
pH dependent (Volesky, 2003; Tien, 2007; Volesky, 2007; Tien, 2008). However, the pH effect
504
has invariably been examined in terms of the initial pH of the aqueous solution. Not a single case
505
has reported data demonstrating the changes in the solution pH during the course of an adsorption
506
experiment.
RI PT
502
In the scientific literature, adsorption equilibrium studies in batch experiments have been
508
conducted in different ways as follows: (1) solution pH values were not mentioned in the
509
manuscript, (2) initial pH values were neither measured nor adjusted and final pH values were
510
measured, (3) initial and final pH values were measured, (4) initial pH values were adjusted and
511
final pH values were not mentioned, (5) initial pH values were adjusted and final pH values were
512
measured, (6) initial and final pH values were adjusted, (7) pH was controlled several times during
513
the course of the reaction, (8) a constant pH was maintained throughout the equilibration time by
514
adding acidic or alkaline solutions, and (9) experiments were conducted at a constant pH using a
515
buffered solution (Smičiklas et al., 2009).
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507
Kumar (2006a) recommended that presenting a plot of qe versus Ce for the complete
517
adsorption isotherm in an adsorption study plays a key role in identifying the regions (e.g., Henry,
518
Freundlich, Langmuir, and BET) in which the experimental data relating to adsorption equilibrium
519
are actually located. In contrast, plots of the Freundlich, Langmuir, or other adsorption isotherm
520
models do not help to identify these regions. Figures 8a and 8b provide typical complete
521
adsorption isotherms that should be presented in the investigation of liquid-phase adsorption.
522
Kumar and Sivanesan (2006) also recommended that using equilibrium data covering the
523
complete isotherm was the best way to obtain the parameters in isotherm expressions; equilibrium
524
data with a partial isotherm was not sufficient, instead equilibrium data that covers the complete
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26
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525
isotherm was required. Furthermore, an inconsistent definition of the adsorption isotherm plot in the literature was
527
recognized by Li and Pan (2007); the plot of qe against Ce/Wo (with Wo being a liquid/solid ratio) is
528
invisible with the traditional definition of the complete adsorption isotherm (the plot of qe versus
529
Ce).
RI PT
526
Recently, Senthil Kumar et al. (2014) presented a plot of %removal versus C0 in an
531
adsorption equilibrium study instead of presenting the complete adsorption isotherm (Figure 8a).
532
However, Hai (2017) made a critical note that it is clear that at every initial concentration of
533
methylene blue (MB; 50, 100, 150, 200, 250 mg/L), the removal percentage of MB by sulfuric
534
acid-treated orange peel (STOP) at 30 °C was always overwhelmingly higher than the
535
corresponding values at 40, 50, and 60 °C. This result revealed that increasing the temperature
536
from 30 to 60 °C resulted in a decrease in the adsorption capacity (qe) of MB dye onto STOP
537
(Figure 8a). However, the maximum adsorption capacities of STOP from the Langmuir model
538
(Qomax) exhibited the following order: 60 °C (83.333 mg/g) > 50 °C (71.428 mg/g) > 40 °C (62.5
539
mg/g) > 30 °C (50 mg/g). This logic problem might be caused by the adsorption process of MB
540
onto STOP not reaching equilibrium at the different temperatures (see adsorption isotherms in
541
Figure 8a) owing to the low initial MB concentrations (50–250 mg/L) used at a high solid/liquid
542
ratio of 4.0 g/L (Hai, 2017). Therefore, in adsorption equilibrium studies, presenting plots of
543
%removal versus Co, %removal versus Ce, or qe versus Co should be avoided, and a plot of qe
544
versus Ce for the complete adsorption isotherm must be presented.
M AN U
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545
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530
Figure 8b provides a typical example of the comparison of adsorption performance under
546
the same operating conditions (i.e., temperature and solution pH). Clearly, “adsorbent B” exhibits
547
a higher affinity than “adsorbent A” at low initial adsorbate concentrations (Co) and low
27
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548
equilibrium adsorbate concentrations (Ce), whereas the opposite order (“adsorbent A” >
549
“adsorbent B”) was found at higher Co and Ce values (Volesky, 2007). It was recently identified that many researchers have made questionable conclusions when
551
studying the effects of agitation rate or shaking speed on the adsorption capacity (qe) or maximum
552
adsorption capacity (Qomax) of an adsorbent toward an adsorbate. For example, Chu et al. (2005)
553
concluded that the adsorption capacity of vitamin E onto silica varies as a function of the agitation
554
rate (120–180 rpm). The Qomax values exhibited the following order: 43.71 mg/g at 180 rpm >
555
24.20 mg/g at 160 rpm > 24.20 mg/g at 140 rpm > 17.62 mg/g at 120 rpm. However, Choong and
556
Chuah (2005) made a critical remark that the agitation rate only impacts on the speed at which a
557
system reaches equilibrium, but not on the equilibrium itself. This means that when the adsorption
558
process obtains a true equilibrium (sufficient contact time between adsorbent and adsorbate), the
559
Qomax values at different agitation rates will be insignificantly different. This is because the
560
decrease of the boundary layer resistance a higher agitation rate will facilitate the transport of the
561
adsorbate to the adsorbent.
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562
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550
Figure 8
Although adsorption isotherms can insignificantly contribute to elucidating adsorption
564
mechanisms, they are less helpful in this regard than data on adsorption kinetics and
565
thermodynamics (Volesky, 2003; Tien, 2007; Tien, 2008). However, collecting adsorption
566
isotherms is a useful strategy to both describe the relationship between the adsorbate concentration
567
in solution (liquid phase) and the adsorbent (solid phase) at a constant temperature and design
568
adsorption systems (Tran et al., 2016).
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569
A wide variety of models of adsorption isotherms have been applied in the literature. These
570
models can be classified as follows: (1) irreversible isotherms and one-parameter isotherms (i.e.,
28
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Henry isotherm); (2) two-parameter isotherms (i.e., Langmuir, Freundlich, Dubinin–
572
Radushkevich, Temkin, Flory–Huggins, and Hill); (3) three-parameter isotherms (i.e., Redlich–
573
Peterson, Sips, Toth, Koble–Corrigan, Khan, Fritz–Schluender, Vieth–Sladek, and Radke–
574
Prausnitz); and (4) more than three-parameter isotherms (i.e., Weber–van Vliet, Fritz–Schlunder,
575
and Baudu) (Kumar and Porkodi, 2006; Hamdaoui and Naffrechoux, 2007; Foo and Hameed,
576
2010). Of these, the Langmuir and Freundlich models are the most commonly used, followed by
577
the Dubinin–Radushkevich and Redlich–Peterson models, because of the usefulness of their
578
model parameters, their simplicity, and their easy interpretability.
579
6.2. Langmuir equation
580
6.2.1. Derivation of the Langmuir equation
M AN U
SC
RI PT
571
The theoretical Langmuir equation (Langmuir, 1918), which was originally applied to the
582
adsorption of gases on a solid surface, was developed using the following assumptions: (1) a fixed
583
number of accessible sites are available on the adsorbent surface and all active sites have the same
584
energy; (2) adsorption is reversible; (3) once an adsorbate occupies a site, no further adsorption
585
can occur on that site; and (4) there is no interaction between adsorbate species. The nonlinear
586
form of the Langmuir model is described in Eq. 47 and its four linearized forms are shown in Eqs.
587
48–51.
588
o Qmax + K L Ce 1 + K LCe
AC C
qe =
EP
TE D
581
(47)
Hanes–Woolf linearization of the Langmuir model (Type 1): Ce 1 1 = ( o )Ce + o qe Qmax Qmax K L
589
(48)
Lineweaver–Burk linearization of the Langmuir model (Type 2):
29
ACCEPTED MANUSCRIPT
1 1 1 1 =( o ) + o qe Qmax K L Ce Qmax Eadie–Hoffsiee linearization of the Langmuir model (Type 3): qe = ( 591
− 1 qe o ) + Qmax K L Ce
(50)
Scatchard linearization of the Langmuir model (Type 4): qe o = − K L qe + Qmax KL Ce
RI PT
590
(49)
SC
(51)
where Qomax (mg/g) is the maximum saturated monolayer adsorption capacity of an adsorbent, Ce
593
(mg/L) is the adsorbate concentration at equilibrium, qe (mg/g) is the amount of adsorbate uptake
594
at equilibrium, and KL (L/mg) is a constant related to the affinity between an adsorbent and
595
adsorbate. For a good adsorbent, a high theoretical adsorption capacity Qomax and a steep initial
596
sorption isotherm slope (i.e., high KL) are generally desirable (Kratochvil and Volesky, 1998;
597
Wang, 2009).
TE D
M AN U
592
The limitations of using the four linear forms of the Langmuir model have been
599
highlighted by Bolster and Hornberger (2007). The transformation of data for linearization can
600
result in modifications of error structure, introduction of error into the independent variable, and
601
alteration of the weight placed on each data point, which often leads to differences in the fitted
602
parameter values between linear and nonlinear versions of the Langmuir model. For the Type 1
603
linearization, because Ce and Ce/qe are not independent, the correlation between Ce and Ce/qe is
604
overestimated, i.e., this equation may provide good fits to data that do not conform to the
605
Langmuir model. For the Type 2 linearization, transformation leads to clustering of data points
606
near the origin and is extremely sensitive to variability at low values of qe (high values of 1/qe).
607
For the Type 3 linearization, the abscissa is not error free, and qe/Ce and qe are not independent. 30
AC C
EP
598
ACCEPTED MANUSCRIPT
Thus, the correlation between qe/Ce and qe is underestimated, i.e., this equation may provide poor
609
fits to data that do conform to the Langmuir model. Finally, the variables qe and qe/Ce are also
610
not independent in the Type 4 linearization. In this case, the correlation between qe and qe/ Ce is
611
underestimated, i.e., this equation may provide a poor fit to data that do conform to the Langmuir
612
model.
613
6.2.2. Derivation of the separation factor
RI PT
608
If the experimental data are adequately described by the Langmuir model, it is essential to
615
calculate the separation factor. Hall et al. (1966) originally proposed that the essential
616
characteristics of the Langmuir isotherm model can be expressed in terms of a dimensionless
617
constant called the separation factor or equilibrium parameter RL, which is defined as follows: RL =
M AN U
SC
614
1 1 + K LCo
(52)
where RL is a constant separation factor (dimensionless) of the solid-liquid adsorption system, KL
619
is the Langmuir equilibrium constant, and Co (mg/L) is the initial adsorbate concentration.
TE D
618
Notably, the isotherm shape can be predicted using the separation factor (RL) (Weber and
621
Chakravorti, 1974) and the Freundlich exponent n (Worch, 2012). Table 1 summarizes the various
622
isotherm shapes.
624 625
Table 1
AC C
623
EP
620
6.2.3. Mistakes concerning the Langmuir model and the separation factor Wan, et al. (2014) published a corrigendum because of a misapplication of the nonlinear
626
form of the Langmuir equation (Eq. 53). A similar mistake in presenting the nonlinear form of the
627
Langmuir equation (Eq. 54) was observed by Kumar and Porkodi, (2007b).
31
ACCEPTED MANUSCRIPT
(53)
Ce 1 1 = + o o qe K LQmax Qmax Ce
(54)
RI PT
Ce C K = oe + o L qe Qmax Qmax
Furthermore, an unexpected typographical error was made in reference (Egirani, 2004). As
629
a result, the sentence “a plot of Ce/qe versus Ce should indicate a straight line of slope 1/KLQomax
630
and an intercept of 1/Qomax” was corrected to “a plot of Ce/qe versus Ce should indicate a straight
631
line of slope 1/Qomax and an intercept of 1/ KLQomax” by Ho (2004a).
SC
628
The incorrect expression and inaccurate calculation of RL were recognized and discussed
633
by Kumar (2006a) and Kumar (2006b). First, the separation factor RL is not a Langmuir constant,
634
and is only employed for isotherms that obey the Langmuir model. Second, RL values will vary
635
with the initial adsorbate concentration, irrespective of the shape of the isotherm, and RL values at
636
different initial adsorbate concentrations cannot be calculated directly from the Langmuir
637
isotherm, but can be calculated from the Langmuir equilibrium constant KL. These
638
misunderstandings and mistakes are summarized in Table 2.
TE D
M AN U
632
Furthermore, a mistake related to the definition of RL compared with the original definition
639
was stated by Fu et al. (2007). The incorrect presentation is shown in Eq. 55.
641
1 o 1 + K LQmax Co
(55)
AC C
RL =
EP
640
Recently, Hai (2017) commented that “the authors’ conclusion about separation factor
642
(RL) was not valid. It is noted that there is no information or value of RL mentioned in the paper’s
643
results and discussion. It is impossible for the authors to conclude that the values of RL were found
644
to be between 0 and 1, indicating the favorable adsorption of MB dye onto STOP.”
645
Clearly, the separation factor is related to the Langmuir equation in the adsorption 32
ACCEPTED MANUSCRIPT
isotherm. Nevertheless, Goswami et al. (2016) recently described an incorrect relationship
647
between the separation factor and adsorption kinetic models (i.e., PFO, PSO, and intra-particle
648
diffusion) at different initial cadmium concentrations. This is a fundamental misunderstanding that
649
should be avoided.
651
6.3. Freundlich equation
652
6.3.1. Derivation of the Freundlich equation
SC
Table 2
650
RI PT
646
The Freundlich equation is one of the earliest empirical equations used to describe
654
equilibrium data and adsorption characteristics for a heterogeneous surface (Freundlich, 1906).
655
Unlike the Langmuir equation, the Freundlich isotherm can describe neither the (arithmetic)
656
linearity range at very low concentrations nor the saturation effect at very high concentrations.
657
Hence, the Freundlich isotherm does not describe the saturation behavior of an adsorbent (Wang,
658
2009). The nonlinear and linear forms of the Freundlich equation can be expressed as shown in
659
Eqs. 56 and 57, respectively.
qe = K F Cen
TE D
M AN U
653
log qe = n log Ce + log K F
(56)
EP
(57)
where qe (mg/g) is the amount of adsorbate uptake at equilibrium, Ce (mg/L) is the adsorbate
661
concentration at equilibrium, KF (mg/g)/(mg/L)n is the Freundlich constant, and n (dimensionless)
662
is the Freundlich intensity parameter, which indicates the magnitude of the adsorption driving
663
force or the surface heterogeneity.
AC C
660
33
ACCEPTED MANUSCRIPT
6.3.2. Mistakes concerning the Freundlich equation
665 666
Several investigators have identified an incorrect expression (Eq. 58) of the linear form of the Freundlich equation (Kumar and Porkodi, 2007b; Alagumuthu et al., 2010).
log qe =
1 + log K F n log Ce
RI PT
664
(58)
Furthermore, several discussions that are inconsistent with the original concepts of the
668
Freundlich theory have been identified in the literature (Lu, 2008; Hai, 2017). Hai (2017)
669
commented that the exponent n of the Freundlich equation must be dimensionless. Therefore, the
670
original authors incorrectly reported the units of the exponent n (g/L); and there is no validation for
671
the statement of the significance of the n value for the adsorption of MB dye onto STOP is as
672
follows: when n = 1 the adsorption is linear, when n < 1 the adsorption is a chemical process, and
673
when n > 1 the adsorption is a physical process. According to the Freundlich theory, the adsorption
674
isotherm becomes linear when n = 1, favorable when n < 1, and unfavorable when n > 1. Similarly,
675
Harsha et al. (2015) also made a basic mistake when they reported the units of the exponent n as
676
g/L.
TE D
M AN U
SC
667
Lu (2008) highlighted that in many cases KF is not the maximum adsorption capacity and
678
the KF value is only equal to the maximum adsorption capacity when n approaches infinity.
679
Although KF is not defined as the maximum adsorption capacity (Qomax), KF values and Qomax
680
values should be of the same order. Such a mistake has been discussed by Tran (2017), where the
681
reported KF values followed the order: 4.471 at 303 K > 3.439 at 313 and 323 K > 2.877 at 333 K,
682
while the Qomax values were 30.12 mg/g at 313 K > 21.367 mg/g at 323 K > 21.276 mg/g at 333 K
683
> 20.492 mg/g at 303 K. This mistake might be attributable to a miscalculation.
684
AC C
EP
677
Notably, Kumar (2006a) highlighted that values for the exponent n (Eq. 59) in the range of
34
ACCEPTED MANUSCRIPT
0–10 suggest favorable adsorption. If the experimental equilibrium data do not lie in the Henry
686
region, then the linear regression method will just check the hypothesis instead of verifying the
687
theory behind the Freundlich model; therefore, it is not possible in practice to obtain n > 10
688
(Kumar, 2006a). A corresponding error was also found in a published paper (Huang et al., 2014),
689
in which the n values reported for the removal of aniline and Cr(VI)/aniline + Cr(VI) by an
690
activated carbon/chitosan composite were 10.20 and 11.34, respectively.
RI PT
685
SC
qe = K F Ce1 / n 6.4. Redlich–Peterson equation
692
6.4.1. Derivation of the Redlich–Peterson equation
M AN U
691
(59)
A three-parameter Redlich–Peterson isotherm was proposed upon considering the
694
limitations of the Freundlich and Langmuir isotherms (Redlich and Peterson, 1959). This model
695
incorporates the features of the Freundlich and Langmuir models and might be applicable for
696
demonstrating adsorption equilibrium over a wide range of adsorbate concentrations. The
697
nonlinear form of this empirical model is given as follows:
K RPCe 1 + a RP Ceg
(60)
EP
qe =
TE D
693
where KRP (L/g) and aRP (mg/L)−g are the Redlich–Peterson constants and g (dimensionless) is an
699
exponent whose value must lie between 0 and 1.
700
AC C
698
Eq. 60 becomes a linear isotherm (Henry’s law equation) at low surface coverage (g = 0),
701
reduces to the Langmuir isotherm when g = 1, and transforms into the Freundlich isotherm when
702
KRP and aKP >> 1 and g = 1. Therefore, if the g value is outside the range of 0–1, the data is not
703
adequately explained by the Redlich–Person equation. Accurate calculation of g can be helpful in
704
expatiation of where the isotherm presentations, neither in the Freundlich or Langmuir (Kumar
35
ACCEPTED MANUSCRIPT
705
and Sivanesan, 2006).
706
6.4.2 Mistakes concerning the Redlich–Peterson equation A series of comments related to mistakes in calculating the exponent g have been reported
708
elsewhere (Inbaraj, 2006; Kumar and Porkodi, 2007a; Kumar et al., 2007; Kumar et al., 2007;
709
Kumar and Porkodi, 2008). These mistakes involved values of the exponent g that were outside the
710
range of 0–1 (Table 3). It is not easy to predict the parameters of the Redlich–Peterson equation
711
because there are three unknown parameters. Although a new linear form of the Redlich–Peterson
712
equation was published by Wu et al. (2010), the nonlinear form might be more appropriate for
713
accurately calculating the parameters of adsorption models with more than two unknown
714
parameters, such as the Redlich–Peterson model.
M AN U
SC
RI PT
707
Table 3
715
6.5. Dubinin–Radushkevich equation
717
6.5.1. Derivation of the Dubinin–Radushkevich equation
structure of an adsorbent (Dubinin and Radushkevich, 1947), and is expressed as follows:
qe = q DR e − K RDε
2
EP
719
The Dubinin–Radushkevich equation was developed to account for the effect of the porous
(61)
The linear form of the Dubinin–Radushkevich equation is:
AC C
718
TE D
716
ln q e = − K DR ε
ε = RT ln(1 +
2
+ ln q DR
(62)
1 ) Ce
(63)
By inserting Eq. 63 into Eq. 61, Eq. 64 can be obtained:
36
ACCEPTED MANUSCRIPT
2
2
2
ln q e = − K DR R T ln (1 +
1 ) + ln q DR Ce
(64)
The parameters qDR and KDR in Eq. 64 can be obtained as follows: (1) a plot of lnqe against
721
ln2(1 + 1/Ce) has a slope = −KDRR2T2 and an intercept = lnqRD, and the E value can be obtained
722
using Eq. 65, and (2) a plot of lnqe against R2T2ln2(1 + 1/Ce) has a slope = −KDR and an intercept =
723
lnqRD, and the E value can be obtained using Eq. 66. Notably, the E values obtained from Eqs. 65
724
and 66 are the same (Tran et al., 2016).
E=
1 1 = 2 K DR − 2slope
SC
1 RT = 2 K DR − 2 slope
M AN U
E=
RI PT
720
(65)
(66)
where qRD (mg/g) is the adsorption capacity, KRD (mol2/kJ2) is a constant related to the sorption
726
energy, ɛ is the Polanyi potential, E (kJ/mol) is the mean adsorption energy, R is the gas constant, T
727
is the temperature in Kelvin, and qe and Ce are obtained from Eq. 1.
728
6.5.2. Mistakes concerning the Dubinin–Radushkevich equation
731
equation (Cavas, 2008; Fu et al., 2008). These erroneous forms are shown in Eqs. 67–70.
EP
730
Some authors have highlighted erroneous expressions of the Dubinin–Radushkevich
Incorrect nonlinear form of the Dubinin–Radushkevich equation:
AC C
729
TE D
725
2
q e = q DR exp( − K DR ( RT (ln 1 + 1 / C e ) ) 732
Incorrect linear form of the Dubinin–Radushkevich equation:
ln q e = −2 K DR RT ln(1 + 733
(67)
1 ) + ln q DR Ce
(68)
Incorrect expressions for the Polanyi potential (ɛ):
37
ACCEPTED MANUSCRIPT
ε = RTe1/ C
(69)
1 ) Ce
(70)
e
RI PT
ε = RT ln(
Additionally, the magnitude of E may give useful information about the type of adsorption
735
process (physical or chemical) (Fu et al., 2008; Tran et al., 2016). Fu et al. (2008) commented that
736
the E values for the removal of phenolic compounds by organophilic bentonite can be categorized
737
as corresponding to ion exchange (E = 8–16 kJ/mol), whereas the original authors made an
738
inconsistent conclusion that the adsorption of two phenolic compounds could be regarded as
739
physical adsorption.
M AN U
SC
734
Recently, Tran (2017) made the following comment on the conclusions of the original
741
paper: “the obtained value of E in this work varies from 32.596 kJ/mol to 40.572 kJ/mol for studied
742
temperature which is higher than the adsorption energy values previously enumerated.” However,
743
these adsorption energy (E) values might not have been calculated correctly. Assuming the β
744
values at 303 K (β = 1.93 × 10−8 mol2/kJ2), 313 K (2.99 × 10−8), 323 K (2.00 × 10−8), and 333 K
745
(2.35 × 10−8) reported by these authors are correct, the recalculated adsorption energy (E) values
746
are 5090 kJ/mol at 303 K, 4089 kJ/mol at 313 K, 5000 kJ/mol at 323 K, and 4613 kJ/mol at 333 K.
747
Thus, the E values in this study ranged from 4089 to 5091 kJ/mol, which is impossible for a
748
heavy-metal biosorption process.
749
7. Adsorption thermodynamics
750
7.1. Principles of adsorption thermodynamics
AC C
EP
TE D
740
751
Thermodynamic studies are an indispensable component of predicting adsorption
752
mechanisms (e.g., physical and chemical). The key distinctions between physical and chemical
38
ACCEPTED MANUSCRIPT
753
adsorption were summarized in detail in a recent report (Tran et al., 2016). The thermodynamic
754
parameters can be computed according to the laws of thermodynamics using the following
755
equations: ∆G o = − RT ln K C
RI PT
756
(71)
The relationship between ∆G° and ∆H° and ∆S° is described as follows: ∆Go = ∆H 0 − T∆S 0
The well-known van’t Hoff equation is obtained by substituting Eq. 71 into Eq. 72 − ∆H o 1 ∆S o x + R T R
(73)
M AN U
ln KC =
SC
757
(72)
758
where R is the universal gas constant (8.3144 J/(mol × K)) and T is the absolute temperature in
759
Kelvin.
The Gibbs energy change (∆G°) is directly calculated from Eq. 71, whereas the enthalpy
761
change (∆H°) and entropy change (∆S°) are determined from the slope and intercept, respectively,
762
of a plot of lnKC versus 1/T (Eq. 73). The common units of ∆G°, the gas constant, and temperature
763
are J/mol, J/(mol × K), and K, respectively; therefore, the equilibrium constant KC in Eq. 73 must
764
be dimensionless (Milonjić, 2007; Milonjić, 2009b; Canzano et al., 2012; Dawood and Sen, 2012;
765
Zhou et al., 2012; Zhou and Zhou, 2014; Tran et al., 2016; Ghosal and Gupta, 2017; Hai, 2017;
766
Rahmani-Sani et al., 2017; Zhou, 2017).
EP
AC C
767
TE D
760
Eq. 72 describes the relationship of ∆G° with ∆H° and ∆S°, and it is useful for checking the
768
logic of calculated values for these thermodynamic parameters. Unfortunately, associated
769
mistakes have been found in the literature. Fu et al. (2008) substituted the values of ∆H° and ∆S°
770
into Eq. 72 to obtain ∆G°, but the obtained ∆G° values were significantly different from the ∆G°
771
values obtained using Eq. 71. Fu et al. (2008) highlighted that this mistake might result from
39
ACCEPTED MANUSCRIPT
772
incorrect application of the method for calculating the equilibrium constant. Clearly, accurate estimation of thermodynamic parameters is directly dependent on
774
accurate determination of the equilibrium constant between two phases (KC; dimensionless). In the
775
literature, the thermodynamic parameters can be calculated from KC values derived from
776
adsorption-isotherm constants (i.e., Langmuir, Freundlich, Frumkin, Flory–Huggins, and Henry)
777
or the partition coefficient (Liu, 2009; Doke and Khan, 2013; Tran et al., 2016). However, to
778
obtain an appropriate calculation method, several factors need to be considered thoroughly. First,
779
the equilibrium constant (KC) must be dimensionless. Second, the linear regression coefficient (R2)
780
of the van’t Hoff equation must be high. Third, the adsorbate in solution must have a high or low
781
concentration. In addition, the temperatures used for calculating the thermodynamic parameters
782
must have units of Kelvin (K), not degrees Celsius (°C). The incorrect use of temperature units led
783
to the publication of an erratum by Ho (2004a), with accurate recalculations.
M AN U
SC
RI PT
773
As the equilibrium constant KC can be derived using a number of approaches, considerable
785
variation in the thermodynamic parameters can be obtained; therefore, the most appropriate
786
approach should be determined. Here, we thoroughly discuss the derivation of the equilibrium
787
constant KC from adsorption isotherms (i.e., Langmuir, Freundlich, and Henry constants) and the
788
partition coefficient because of their popularity in the literature.
789
7.2. Equilibrium constant derived from the Langmuir constant (KL)
EP
AC C
790
TE D
784
The Langmuir equation was initially derived from a kinetic study and then subsequently
791
from a thermodynamic study. The derivation of the Langmuir equation from the thermodynamic
792
perspective can be described as follows (Crittenden et al., 2012; Tran et al., 2016). The
793
relationship between vacant surface sites on the surface of an adsorbent (Sv; mmol/m2), adsorbate
794
species in solution (A; mmol), and adsorbate species bound to surface sites (SA; mmol/m2) can be
40
ACCEPTED MANUSCRIPT
795
described by the following reaction:
SV + A ↔ SA
(74)
On the basis of the Langmuir expression, it is assumed that the reaction has a constant
797
Gibbs energy change (∆G°; J/mol) for all sites, so the thermodynamic equilibrium constant (KC;
798
dimensionless) can be expressed as:
RI PT
796
− ∆G o
⇔ KC = e
∆G = − RT ln K C
RT
(75)
SC
o
Another Langmuir assumption is that each site is capable of binding at most one adsorbate
800
molecule (monolayer). According to the equilibrium condition, the thermodynamic equilibrium
801
constant may be written as:
SA KC = =e SV [ A]
M AN U
799
− ∆G o
RT
(76)
where [A] is the concentration of adsorbate A in solution at equilibrium (mg/L), R is the universal
803
gas constant (8.314 J/mol × K), and T is absolute temperature K (273 + °C).
TE D
802
The critical problem with Eq. 76 is that there are two unknown parameters (i.e., SV and
805
[A]). However, this problem can be solved if the total sites available or monolayer coverage (ST;
806
mol/m2) are fixed:
807
SA + SA KC [ A]
AC C
ST = SV + SA =
EP
804
⇔
SA =
K C [ A]ST 1 + K C [ A]
(77)
The expression of SA in units of mmol/m2 is not useful in mass balance, and units of mass
808
of adsorbate adsorbed per unit mass of adsorbent (qe; mg/g) are much more useful. The mass
809
loading (qe) can be obtained in units of mg/g (Eq. 1) by multiplying both sides of Eq. 71 by the
810
surface area (SBET; m2/g) of the adsorbent and the molecular weight of the adsorbate (Mw; g/mol).
41
ACCEPTED MANUSCRIPT
811
Thus, Eq. 77 becomes:
K [ A]ST S BET M w SA.S BET .M w = C 1 + K C [ A]
⇔
o Qmax K L Ce qe = 1 + K L Ce
(78)
where qe (mg/g) = SA × SBET × Mw is described by Eq. 1; Ce (mg/L) = [A] is the concentration of
813
adsorbate in solution at equilibrium; Qomax (mg/g) = ST × SBET × Mw is the maximum monolayer
814
adsorptive capacity of the adsorbent when the surface sites are saturated with adsorbate; the
815
relationship between KL and KC is described in the following discussion.
SC
RI PT
812
However, the main problem is that the Langmuir constant KL is dimensional with common
817
units of L/mmol or L/mg, while the equilibrium constant KC is dimensionless (without units).
818
Thus, the direct application of KL (L/mmol or L/mg) in the calculation of thermodynamic
819
parameters produces incorrect results, as discussed by many authors (Milonjić, 2007; Milonjić,
820
2009b; Canzano et al., 2012; Dawood and Sen, 2012; Zhou et al., 2012; Zhou and Zhou, 2014;
821
Anastopoulos and Kyzas, 2016; Tran et al., 2016; Ghosal and Gupta, 2017; Hai, 2017,
822
Rahmani-Sani et al., 2017). To solve this unit problem, several methods have been recommended
823
(Milonjić, 2007; Zhou and Zhou, 2014; Tran et al., 2016). Depending on the units of KL, the
824
equilibrium constant KC can easily be obtained as a dimensionless constant.
EP
TE D
M AN U
816
When an adsorption study is conducted in aqueous solution and KL has units of L/mmol, KC
826
can be easily obtained as a dimensionless parameter by multiplying KL by 55.5 and then by 1,000
827
(Eq. 79). This method was originally proposed by Milonjić (2007) and then developed by Zhou
828
and Zhou (2014) and Tran et al. (2016). The values of the parameters ∆G°, ∆H°, and ∆S° can be
829
calculated using the following equations:
AC C
825
KC = 55.5×1,000× KL
(79)
42
ACCEPTED MANUSCRIPT
∆Go = −RT ln(55.5×1,000× KL ) ln(55 .5 × 1,000 × K L ) =
(80)
− ∆H o 1 ∆S o × + R T R
(81)
where the factor 55.5 is the number of moles of pure water per liter (1,000 g/L divided by 18
831
g/mol) and the term 55.5 × 1,000 × KL is dimensionless.
RI PT
830
In the case of KL with units expressed in L/mg, Milonjić (2007 and 2009b) stated that KL
833
could be obtained as a dimensionless parameter by multiplying KL by 106 (Eq. 82). However, Zhou
834
and Zhou (2014) recommended that KC could be obtained as a dimensionless parameter by
835
multiplying KL by the molecular weight of the adsorbate (Mw; g/mol), by 1000, and then by 55.5
836
(Eq. 85).
M AN U
SC
832
KC = 106 K L ∆G o = − RT ln(106 K L )
TE D
− ∆H o 1 ∆S o ln(10 K L ) = x + R T R 6
(82) (83) (84)
where the factor 106 is the solution density (assuming the density of pure water is 1.0 g/mL) and
838
the term 106 × K is dimensionless.
EP
837
K C = M w × 55.5 ×1,000 × K L
AC C
(85)
∆Go = −RT ln(Mw × 55.5×1,000× KL )
(86)
− ∆ H o 1 ∆S o ln( M w × 55.5 ×1,000 × K L ) = × + R T R
(87)
839
where the factor 55.5 is the number of moles of pure water per liter and the term Mw × 55.5 × 1,000
840
× KL is dimensionless.
43
ACCEPTED MANUSCRIPT
In a recent paper, Tran et al. (2016) applied Eqs. 79–87 to compare thermodynamic
842
parameters calculated from the Langmuir constants derived from four linear forms of the
843
Langmuir model. They concluded that (1) both the recommendations of Milonjić (2007 and
844
2009b) and Zhou and Zhou (2014) provide the same methods for calculating the thermodynamic
845
parameters, and (2) there is some deviation between these methods for the results from Types 1, 3,
846
and 4; only Type 2 produces identical results.
847
7.3. Equilibrium constant derived from the Freundlich constant (KF)
SC
RI PT
841
The Freundlich equation is consistent with the thermodynamics of heterogeneous
849
adsorption (Crittenden, et al., 2012). The Freundlich constant KF can be obtained as a
850
dimensionless value using Eq. 88 (Ghosal and Gupta, 2015; Tran et al., 2016).
M AN U
848
K ρ 106 (1− ) KC = F ( ) n 1000 ρ 1
K ρ 106 (1− ) ∆G o = − RT ln( F ( ) n ) 1000 ρ
K F ρ 10 6 (1− n ) − ∆ H o 1 ∆S o x + ( ) )= R T R 1000 ρ 1
ln(
(89)
(90)
where ρ is the density of pure water (assumed as ~1.0 g/mL).
EP
851
TE D
1
(88)
It is noted that the units of KF rely on the units used for the liquid-phase concentration (C)
853
and solid-phase concentration (q). Units of mg/L or mmol/L for C and mg/g or mmol/g for q are
854
used most frequently to demonstrate adsorption from water solutions. The differing units of KF can
855
be reciprocally converted using Eq. 91 (Worch, 2012).
AC C
852
K F = K F' ( M w )1−1 / n 856
(91)
where the units of the Freundlich constant KF are (mg/g)/(mg/L)1/n, with Co and Ce (mg/L) and qe
44
ACCEPTED MANUSCRIPT
857
(mg/g); the units of KF′ are (mmol/g)/(mmol/L)1/n, with Co and Ce (mmol/L) and qe (mmol/g); and
858
Mw is the molecular weight of the adsorbate. The exponent 1/n is not affected by the units of the
859
liquid-phase concentration (C) and solid-phase concentration (q) Based on a comparison of the thermodynamic parameters calculated from the Freundlich
861
constant (dimensionless) and Langmuir constant (dimensionless), Tran et al., (2016) concluded
862
that the signs and magnitudes of ∆G°, ∆H°, and ∆S° calculated from KF were consistent with those
863
calculated from KL. Of course, the experimental data in the adsorption isotherms must be fitted
864
well by the Langmuir and Freundlich models, and the R2 value of the van’t Hoff equation must be
865
higher than 0.90 (Tran et al., 2016). It is also evident that, to some extent, the application of KF to
866
estimate the thermodynamic parameters should be approached with caution.
867
7.4. Equilibrium constant derived from the partition coefficient (Kp)
M AN U
SC
RI PT
860
868
reported by Biggar and Cheung (1973). The equilibrium constant can be defined as follows:
Kp =
as γ s C s = ae γ eCe
TE D
869
Changes in the thermodynamic partition coefficient with changes in temperature were first
(92)
where as is the activity of the adsorbate adsorbed onto the adsorbent, ae is the activity of the
871
adsorbate in solution at equilibrium, γs is the activity coefficient of the adsorbate adsorbed onto the
872
adsorbent, γe is the activity coefficient of the adsorbate in solution at equilibrium, Cs is the
873
concentration of adsorbate adsorbed onto the adsorbent at equilibrium (mg/L), and Ce is the
874
concentration of adsorbate in solution at equilibrium (mg/L). Cs is defined by the mass balance of
875
adsorbate that disappears from the solution, which should appear on the adsorbent.
876 877
AC C
EP
870
When the concentration of adsorbate in the solution approaches zero, which results in Cs → 0 and Ce → 0, the activity of coefficient γ approaches unity, and Eq. 92 can be written as:
45
ACCEPTED MANUSCRIPT
Cs
Lim C Cs →0
e
=
as = Kp ae
(93)
Kp values can be obtained plotting ln(Cs/Ce) versus Cs and extrapolating Cs to zero. If a
879
straight line fits the data with a high regression coefficient (R2) and its intersection with the vertical
880
axis provides the value of Kp, the partition coefficient will be in unison with the equilibrium
881
constant. The ∆G° value can be directly calculated using Eq. 71, while the values of ∆H° and ∆S°
882
are determined from the slope and intercept, respectively, of Eq. 73.
SC
RI PT
878
This method has been widely applied in the literature. A summary of the applications of
884
this method can found in the critical review in reference (Doke and Khan, 2013). However,
885
incorrect applications of Biggar and Cheung’s definition have also been identified in the literature.
886
In a typical experiment, Senthil Kumar et al. (2014) made a mistake in the application of Kp during
887
calculation of the thermodynamic parameters for the adsorption of MB onto STOP (Table 4). Hai
888
(2017) highlighted that it is impossible to obtain an equilibrium constant, Gibbs energy change
889
(∆G°), enthalpy change (∆H°), and entropy change (∆S°) for the adsorption process at every initial
890
MB concentration, as shown in Table 4. Assuming that the experimental data reported by Senthil
891
Kuma et al. (2014) are correct, Hai (2017) recalculated the thermodynamic parameters based on
892
the method of Biggar and Cheung (1973), and the corrected thermodynamic parameters are also
893
listed in Table 4. Likewise, Lima et al. (2015) also determined the value of the adsorption
894
equilibrium constant (KC) from the value of the best fit nonlinear isotherm equilibrium model
895
instead of using the equilibrium constant (Kp) calculated from the initial and equilibrium
896
concentrations of the adsorbate.
AC C
EP
TE D
M AN U
883
897
Table 4
898
Importantly, according to the United States Environmental Protection Agency (USEPA,
46
ACCEPTED MANUSCRIPT
1999), the partition coefficient is only appropriate for calculating the thermodynamic parameters
900
if the initial adsorbate concentration is low. Analogous conclusions can be found in the literature
901
(Liu, 2009; Salvestrini et al., 2014; Lima et al., 2015; Tran et al., 2016; Hai, 2017). It has been
902
highlighted that the partition coefficient is only equal to the thermodynamic equilibrium constant
903
when the adsorbed concentrations in the solutions are very low. In this situation, the partition
904
coefficient can be used to calculate the thermodynamic parameters. Recently, Tran et al. (2016),
905
who compared the thermodynamic parameters calculated from the Langmuir constant and the
906
partition coefficient, concluded that although the signs of the calculated ∆G°, ∆H°, and ∆S°
907
parameters were the same, the partition coefficient might not be appropriate for calculating the
908
thermodynamic parameters owing to the low regression coefficient of the van’t Hoff equation (R2
909
= 0.53).
910
7.5. Equilibrium constant derived from the distribution coefficient (Kd)
M AN U
SC
RI PT
899
In 1987, Khan and Singh (1987) proposed a method for calculating thermodynamic
912
parameters (Eq. 94) based on the method of Biggar and Cheung (1973). The distribution
913
coefficient (Kd) can be defined as follows:
(94)
In this method, Kd values are obtained by plotting ln(qe/Ce) against Ce and extrapolating to
AC C
914
qe Ce
EP
Kd =
TE D
911
915
zero Ce. If a straight line fits the data with a high regression coefficient (R2), then its intersection
916
with the vertical axis provides the value of Kd. Fundamentally, Eq. 94 can be derived from the
917
Freundlich and Langmuir equations. If n = 1, the Freundlich equation (Eq. 56) will become
918
Henry’s equation for a linearized isotherm (Eq. 95), and the Freundlich constant (KF) will be equal
919
to the Henry constant (KH). For very low concentrations of adsorbate (KL and Ce << 1), the
47
ACCEPTED MANUSCRIPT
920
Langmuir equation (Eq. 47) will become Henry’s equation (Eq. 95), and the Henry constant (KH)
921
will become QomaxKL. The Henry constant (KH) is also referred to as the distribution coefficient
922
(Kd).
qe = K H Ce
RI PT
(95)
This method has been widely applied to calculating thermodynamic parameters in the
924
literature. Unfortunately, the units of Kd in Eq. 94 are L/g as Ce has units of mg/L and qe has units
925
of mg/g. Therefore, it is impossible to directly employ Kd as the equilibrium constant for the
926
calculation of ∆G°, ∆H°, and ∆S°. This problem associated with the units has been discussed by
927
several scientists (Patrickios and Yamasaki, 1997; Milonjić, 2007; Canzano et al., 2012; Dawood
928
and Sen, 2012; Tran et al., 2016; Zhou, 2017). Canzano, Iovino et al. (2012) suggested that the
929
partition coefficient Kd (L/g) could be converted to KC (dimensionless) by multiplying Kd by a
930
factor of 1,000, as originally proposed by Milonjić (2007 and 2009b).
M AN U
SC
923
Similar to the partition coefficient, the distribution coefficient may be appropriate for
932
estimating the thermodynamic parameters when the initial concentration of the adsorbate is low
933
(Salvestrini et al., 2014; Tran et al., 2016). Tran et al. (2016) concluded that the signs of ∆G°, ∆H°,
934
and ∆S° estimated from the distribution coefficient and the Langmuir constant are the same.
935
However, the units of Kd (L/g) are different from those of KL (L/mg), and the adsorption
936
equilibrium data do not fit Henry’s adsorption isotherm. As a result, application of the distribution
937
coefficient was not appropriate for calculating the thermodynamic parameters in this study; the
938
low regression coefficient of the van’t Hoff equation (R2 = 0.42) is further evidence of the
939
inappropriateness of this approach.
AC C
EP
TE D
931
940
In summary, to determine accurate thermodynamic parameters, several points should be
941
thoroughly considered. First, the equilibrium constant (KC) must be dimensionless. Second, if the 48
ACCEPTED MANUSCRIPT
concentrations of adsorbate used to obtain the adsorption isotherm are very low (diluted solutions),
943
the partition (Kp) or distribution coefficients (Kd) are appropriate for calculation of the
944
thermodynamic parameters; otherwise, the Langmuir (KL) or Freundlich (KF) constant models may
945
be more appropriate. Third, the plot of lnKC against 1/T corresponding to the van’t Hoff equation
946
must be linear with a high regression coefficient (R2). Additionally, it is necessary to consider
947
whether the adsorption process can reach equilibrium and consideration of the adsorption isotherm
948
shapes and the adsorption model fit are also recommended. Thus, presentation of the complete
949
adsorption isotherm (plot of qe versus Ce) is strongly recommended. Finally, the determined
950
thermodynamic parameters must have a logical relationship with the experimental data.
M AN U
SC
RI PT
942
Notably, numerous recent studies have reported methods of calculating thermodynamic
952
parameters from the partition coefficient (Kp) or distribution coefficient (Kd) that differed from the
953
traditional concepts defined in Sections 7.4 and 7.5, respectively. A typical mistake is present in
954
the work of Nekouei et al. (2016). They studied the adsorption thermodynamics at only one initial
955
adsorbate concentration and different temperatures instead of using a range of adsorbate
956
concentrations (i.e., from 100 mg/L to 1,000 mg/L) and different temperatures (i.e., 10 °C, 20 °C,
957
30 °C, and 50 °C). This mistake led to invalid conclusions regarding the adsorption
958
thermodynamics.
959
8. Others mistakes
960
8.1. Inconsistent data points in experimental data and model fitting
EP
AC C
961
TE D
951
Significant differences between the number of data points in an experiment and those used
962
for model fitting should be avoided. For example, Azizian (2008a) made the following critical
963
comments about the paper of Karadag et al. (2007): there were six experimental data points
964
regarding the adsorption kinetics (plots of qt versus t), but only five experimental data points were
49
ACCEPTED MANUSCRIPT
used for fitting of the experimental data to the PSO model (plot of t/qt versus t). This omission
966
resulted in inaccurate calculations and questionable conclusions. The R2 values of the PSO model
967
were very high (0.992–1.000), but the difference between the experimental (qe,exp) and calculated
968
(qe,cal) values was more than 100% (for example qe,exp = 6.720 mg/g and qe,cal = 15.526 mg/g).
969
Clearly, the qe values calculated from the experimental data and the model were significantly
970
different, but the authors (Karadag et al., 2007) concluded that “The pseudo-second-order kinetic
971
model agrees very well with the dynamic behavior for the adsorption of dyes RR239 and RB5 onto
972
CTAB-zeolite under several different dye concentrations, temperatures, and pH values”; the
973
validity of this conclusion is very questionable.
M AN U
SC
RI PT
965
Lima et al. (2015) observed a change in kinetic parameters when five experimental points
975
were deleted to achieve a good R2 value. They concluded that the strategy of deleting some data
976
points to improve the R2 value caused serious errors in the values of qe and k1 in the PFO equation
977
or k2 in the PSO equation.
TE D
974
Azizian (2008) pointed out that in reference (Karadag et al., 2007), a comparison was made
979
between the results of fitting four experimental equilibrium data points to the Langmuir model and
980
fitting five experimental equilibrium data points to the Freundlich model. Therefore, it is
981
impossible for the authors (Karadag et al., 2007) to conclude that “the Freundlich model exhibited
982
a slightly better fit than the Langmuir model.” To compare the fits of two different models, the
983
same experimental data (including the same number of experimental data points) should be used
984
(Azizian, 2008a). Likewise, Harsha et al. (2015) examined adsorption isotherms using seven
985
experimental data points. However, in the plots for calculating the Langmuir, Freundlich, and
986
Dubinin–Radushkevich models, only three experimental points were used. It is impossible to
AC C
EP
978
50
ACCEPTED MANUSCRIPT
987
obtain the Langmuir, Freundlich, and Dubinin–Radushkevich parameters from only three
988
experimental points. A similar mistake was found in reference (Goswami et al., 2016).
989
8.2. Oxidation state of chromium Many investigators (Aoyama, 2003; Park et al., 2006a; Park et al., 2006b; Park et al.,
991
2006c) have commented that mistakes in analyzing chromium species in aqueous solution have
992
resulted in the incorrect elucidation of hexavalent chromium adsorption, attributing Cr(VI)
993
removal from an aqueous solution to “anionic adsorption”. Generally, when Cr(VI) comes into
994
contact with organic substances or reducing agents, especially in an acidic medium, it is easily or
995
spontaneously reduced to Cr(III), as Cr(VI) has a high redox potential (above +1.3 V under
996
standard conditions). Therefore, there is a strong possibility that the mechanism of Cr(VI) removal
997
by biomaterials or biomaterial-based activated carbon is not “anionic adsorption” but
998
“adsorption-coupled reduction”. Various authors (Aoyama, 2003; Park et al., 2006a; Park et al.,
999
2006b; Park et al., 2006c) also suggested that in Cr(VI) adsorption studies, it is necessary to
1000
analyze both the Cr(VI) and total Cr in aqueous solution, as well as determining the oxidation state
1001
of chromium bound to the biomaterial or activated carbon.
TE D
M AN U
SC
RI PT
990
The authors (Aoyama, 2003; Park et al., 2006a; Park et al., 2006b; Park et al., 2006c)
1003
pointed out that in most papers, only Cr(VI) in aqueous solutions was analyzed by the standard
1004
colorimetrical method; the pink colored complex formed from between 1,5-diphenycarbazide and
1005
Cr(VI) in an acidic solution can be spectrophotometrically analyzed at 540 nm. Similarly, the total
1006
Cr in aqueous solutions has been analyzed using atomic absorption spectroscopy (AAS) or
1007
inductively coupled plasma-atomic emission spectroscopy (ICP-AES), which cannot distinguish
1008
Cr(VI) from the total Cr. Additionally, Aoyama (2003) underlined that the total Cr present in a
1009
solution can be determined by oxidizing any Cr(III) formed with KMnO4, followed by the same
AC C
EP
1002
51
ACCEPTED MANUSCRIPT
procedures described for the determination of Cr(VI). The adsorption density can be calculated
1011
from the difference between the initial concentration of Cr(VI) and the final concentration of total
1012
Cr. In contrast, the Cr(III) concentration is calculated from the difference between the final total Cr
1013
and final Cr(VI) concentrations.
RI PT
1010
Several techniques have been applied in the literature to ascertain the oxidation state of
1015
chromium on an adsorbent, such as X-ray photoelectron spectroscopy (XPS) and X-ray absorption
1016
spectroscopy (XAS). For example, Dambies et al. (2001) investigated the characterization of
1017
Cr(VI) interactions with chitosan using XPS. On the basis of their XPS data, they concluded that
1018
Cr(VI) was entirely reduced to Cr(III) on glutaraldehyde crosslinked beads, while only 60% of
1019
Cr(VI) was found in its reduced form on raw beads. Additionally, Cr(VI) binding and reduction to
1020
Cr(III) by agricultural byproducts of Avena monida (oat) biomass was characterized by
1021
Gardea-Torresdey et al. (2000). Their XAS studies further corroborated that, although Cr(VI)
1022
could bind to oat biomass, it was easily reduced to Cr(III) by positively charged functional groups,
1023
and Cr(III) was subsequently adsorbed by available carboxyl groups.
TE D
M AN U
SC
1014
A study on using fermentation waste for detoxification of Cr(VI) contaminated aqueous
1025
solutions was published by Park et al. (2008). In this study, the colorimetric method was used in
1026
combination with excess potassium permanganate to analyze both the Cr(VI) and total Cr in
1027
aqueous solution, and XPS was used to ascertain the oxidation state of the chromium bound on the
1028
biomass. Park et al. (2008) concluded that the mechanism of Cr(VI) removal by the fermentation
1029
waste involved reduction of Cr(VI) to Cr(III) (redox reaction). As a result, kinetic and equilibrium
1030
models based on the “reduction” mechanism were used to describe the behavior of Cr(VI) and total
1031
Cr in aqueous solution.
1032
AC C
EP
1024
Two main mechanisms for removal of Cr(VI) from aqueous solution by nonliving
52
ACCEPTED MANUSCRIPT
biomass were proposed by Park et al. (2005). In the first mechanism (direct reduction), Cr(VI)
1034
was directly reduced to Cr(III) in the aqueous phase by contact with electron-donor groups of the
1035
biomass, i.e., groups with lower reduction potentials than that of Cr(VI) (+1.3 V). However, the
1036
second mechanism comprised three steps: (1) binding of anionic Cr(VI) ion species to positively
1037
charged groups on the biomass surface, (2) reduction of Cr(VI) to Cr(III) by adjacent
1038
electron-donor groups, and (3) release of the Cr(III) ions into the aqueous phase, owing to
1039
electronic repulsion between the positively charged groups and the Cr(III) ions, or complexation
1040
of Cr(III) with adjacent groups capable of binding chromium. If there are a small number of
1041
electron-donor groups in the biomass or a low concentration of protons in the aqueous phase,
1042
chromium bound on the biomass can remain in the hexavalent state. Therefore, the extent to
1043
which mechanisms I and II operate depends on the nature of the biosorption system, including
1044
solution pH, temperature, functional groups on the biomass, and biomass and Cr(VI)
1045
concentrations (Park et al., 2006b; Park et al., 2006a). These two main mechanisms are
1046
summarized in Figure 9.
Figure 9
1047
8.3. Incorrect labels
EP
1048
TE D
M AN U
SC
RI PT
1033
Incorrect labeling of compounds should also be avoided. A publication entitled “Selenite
1050
adsorption and desorption in main Chinese soils with their characteristics and physicochemical
1051
properties” included such a mistake, as pointed out by Goldberg (2016). The purpose of this work
1052
was to study the adsorption of Se(IV) (selenite), not Se(VI) (selenate); however, the paper reported
1053
that the authors prepared Se solutions using Na2SeO4 (hexavalent Se(VI)). This mistake was
1054
explained by the incorrect labeling of Na2SeO3 as Na2SeO4 in the Materials and Methods section.
AC C
1049
53
ACCEPTED MANUSCRIPT
Similarly, the author of the paper entitled “Adsorption sequence of toxic inorganic anions
1056
on a soil” prepared solutions from Na2HAsO4·7H2O as As(V) species. However, they mislabeled
1057
Na2HAsO4·7H2O as NaAsO2, a trivalent As(III) species (Goldberg, 2009).
1058
8.4. BET specific surface area of an adsorbent
RI PT
1055
Using the Brunauer–Emmett–Teller (BET) surface area of pahokee peat (0.88 m2/g) and
1060
assuming that the atrazine molecule is a sphere with a radius (r) of 4.16 × 10−10 m, Borisover and
1061
Graber (1997) estimated the maximum adsorption capacity of pahokee peat for atrazine. First, the
1062
cross-section area (A) of atrazine can be obtained as 3.14 × (4.16 × 10−10)2 = 54.4 × 10−20 m2;
1063
subsequently, the surface covered by 1 mol of atrazine (MA) can be calculated as (54.4 × 10−20 m2)
1064
× (6.023 × 1023/mol) = 3.3 × 105 m2/mol. Second, the maximum possible concentration of atrazine
1065
on the surface area (Qomax,covered; maximum adsorption capacity) was obtained by dividing the BET
1066
surface area (0.88 m2/g) by the surface covered by 1 mol of atrazine (3.3 × 105 m2/mol) to give 2.7
1067
× 10−6 mol/g. Finally, Qomax,covered was converted into weight units using (2.7 × 10−6 mol/g) ×
1068
(215.7 g/mol) to give 582 µg/g. This value (582 µg/g) is substantially higher than the maximum
1069
adsorption capacity obtained from the Langmuir equation (161 µg/g). Although these calculations
1070
are correct, these inconsistent values might originate from a misunderstanding by the authors
1071
(Borisover and Graber, 1997) who state that “N2 BET measured external surface area”, and thus
1072
attributed the value of 582 µg/g to the maximal possible atrazine concentration on the external
1073
surface of pahokee peat.
M AN U
TE D
EP
AC C
1074
SC
1059
According to the 2011 guide for the accelerated surface area and porosimetry (ASAP)
1075
system, the definition of the BET specific surface area (m2/g) includes both the t-Plot external
1076
surface area (m2/g) and the t-Plot micropore area (m2/g). Table 5 gives a typical example of correct
1077
and incorrect use of the Micromeritics report (experimental data measured using a Micromeritics
54
ACCEPTED MANUSCRIPT
ASAP 2020 sorptometer at 77 K). Although there were no problems found in the N2
1079
adsorption/desorption isotherms, the report results for BET analysis of the prepared activated
1080
carbon in Table 5 contain discrepancies, as the BET specific surface area value is less than the
1081
external surface area. This error resulted from calculation of the specific surface area (SBET) in the
1082
range 0.38 < p/p0 < 0.57, instead of 0.05 < p/p0 < 0.3.
Table 5
1083
RI PT
1078
Recently, Ben Ali et al. (2016) used the “iodine number” to determine the surface area of a
1085
biosorbent without any treatment (pomegranate peel; PGP) and concluded that “the specific
1086
surface area obtained is equal to 598.78 m2/g. Iodine number is generally used as an
1087
approximation for surface area and microporosity of active carbons with good precision”. Tran
1088
(2017) commented that there are two serious misconceptions in this work that need to be
1089
discussed.
M AN U
SC
1084
First, the iodine number of activated carbon is often determined following the internal
1091
method, ASTM D4607-14 (D4607-14 2014). According to the ASTM, the iodine number (mg/g;
1092
amount of iodine adsorbed (mg) by 1.0 g of activated carbon) is a relative indicator of porosity in
1093
activated carbon. Iodine molecules (≈0.27 nm) can be adsorbed into the micropores (pore width >
1094
1 nm) of porous materials. However, the iodine number does not necessarily provide a measure of
1095
the ability of activated carbon to adsorb other species. Although the iodine number may be used to
1096
approximate the surface area for several types of activated carbon, it must be realized that the
1097
relationship between surface area and iodine number cannot be generalized, as it varies with
1098
changes in the raw carbon material, processing conditions, and pore volume distribution.
1099
Biosorbents that have not undergone any treatment have never been defined as porous materials;
1100
thus, the porosity of a biosorbent is negligible.
AC C
EP
TE D
1090
55
ACCEPTED MANUSCRIPT
Therefore, the iodine number cannot be applied for the determination of porosity for any
1102
biosorbent. Moreover, it is impossible to obtain the very high iodine number reported for PGP
1103
(602 mg/g). The high iodine number for PGP can be attributed to the high sulfur content (0.89%)
1104
and prolonged contact time (>30 s) (Tran, 2017). According to the ASTM (D4607-14 2014), after
1105
transferring activated carbon (g) into hydrochloric acid solution (5 wt%), the mixture should be
1106
boiled gently for 30 s to remove any sulfur that may interfere with the test results. Therefore, it is
1107
clear that the iodine number is greatly affected by high sulfur contents. Notably, the contact time
1108
between activated carbon and iodine solution (0.1 N) strongly impacts the determined iodine
1109
number. The contact time recommended by the ASTM was approximately 30 s, while the contact
1110
time used by Ben Ali et al. was approximately 4 min. Recently, Tran et al. (2017c) prepared
1111
activated carbons from golden shower using different chemical activation methods with K2CO3
1112
(GSAC, GSBAC, and GSHAC). Their results indicated that the iodine numbers (mg/g) of the
1113
prepared activated carbons at a contact time of 30 s were significantly lower than those at 5 min;
1114
GSAC (2,604 mg/g < 2,883 mg/g), GSBAC (1,568 mg/g < 2,296 mg/g), GSHAC (2,695 mg/g <
1115
4,842 mg/g).
TE D
M AN U
SC
RI PT
1101
Second, the textural properties of an adsorbent (i.e., specific surface area, total pore
1117
volume, and micropore volume) can be obtained from conventional analysis of nitrogen
1118
adsorption-desorption isotherms, which are measured at 77 K using a sorptometer (e.g.,
1119
Micromeritics ASAP 2020). The BET method is widely employed to compute specific surface
1120
area (SBET) (Marsh and Reinoso, 2006). Therefore, it is impossible to measure the surface area of
1121
an adsorbent using the iodine number method. This mistaken assumption will lead to incorrect
1122
result, such as the extremely high surface area of PGP (598.78 m2/g). The BET surface areas of
1123
various biosorbents are approximately 40 m2/g for yellow passion-fruit shell, 20 m2/g for orange
AC C
EP
1116
56
ACCEPTED MANUSCRIPT
peel, 8.17 m2/g for wheat straw, 8.13 m2/g for sargassum, 4.01 m2/g for Moringa oleifera lamarck
1125
seed powder, 1.31 m2/g Spirogyra species, 1.21 m2/g for waste pomace from an olive oil factory,
1126
0.76 m2/g for soy meal shells, 0.48 m2/g for rubber tree leaves, and 0.48 m2/g for rice bran (Farooq
1127
et al., 2010; Tran et al., 2016). Thus, the discussions and conclusions regarding the surface area of
1128
PGP made by Ben Ali et al. (2016) are not valid, as they are inconsistent with the ASTM
1129
definitions and fundamental understanding of the porosities of materials.
1130
8.5. Maximum absorption wavelength in dye adsorption studies
SC
RI PT
1124
A comment on the method of using the maximum absorption wavelength (λmax) to calculate
1132
Congo red (CR) solution concentrations was published by Zhou et al. (2011). They pointed out that
1133
CR is very sensitive to pH and changes from red to blue owing to a π-π* transition of the azo group
1134
following protonation (Figure 10a). At lower pH values, CR is protonated and cationic CR shows
1135
two tautomeric forms: ammonium rich variety and azonium variety. Therefore, the maximum
1136
absorption wavelength used to calculate the concentration of CR in solution is strongly dependent
1137
on the solution pH (both initial and final) (Figure 10b); for example, λmax was 576 nm at pH 2.18–
1138
3.16, 567 nm at pH 3.86, and 496 nm at pH ≥ 4.71.
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Figure 10
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1139
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1131
Tien (2007) and Tien (2008) highlighted that commercial dyes are often mixtures of active
1141
ingredients and filler materials are often not recognized. Therefore, the possibility that
1142
experiments may involve bi-solute adsorption is often not considered.
1143
8.6. Cπ-cation and π-π interactions
1144
8.6.1. Cπ-cation interactions
AC C
1140
1145
Recently, Morosanu et al. (2016) investigated the biosorption of lead ions onto rapeseed
1146
biomass that was used as a biosorbent without any treatments. On the basis of FTIR measurements
57
ACCEPTED MANUSCRIPT
before and after adsorption, they concluded that the disappearance of the peak at 1710 cm−1, which
1148
is characteristic of C=O stretching, indicated surface complexion through Cπ-cation interactions.
1149
Similarly, Medellin-Castillo et al. (2017) examined the biosorption of Pb2+ and Cd2+ onto a
1150
biosorbent derived from industrial chili seeds. They also found changes in the intensity of the
1151
absorbance peak at 1657 cm−1 in heavy-metal-loaded chili seeds, suggesting that the adsorption of
1152
Cd2+ and Pb2+ involved π-cation interactions between the aromatic rings of the lignin and the
1153
Cd2+ and Pb2+ cations in the solution.
SC
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1147
In general, Cπ-cation interactions are attributed to electrostatic interactions between the
1155
aromatic rings of basic carbonaceous materials (i.e., biochar, carbon foam, carbon nanotubes,
1156
activated carbon, and graphene) and metallic cations. For example, Tran et al. (2015) used
1157
orange-peel-derived biochar, which was produced through a carbonization process under
1158
limited-oxygen conditions (also known as pyrolysis) at a high temperature (>400 °C). Biochar is
1159
known as a carbon-enriched porous material, similar to activated carbon. Thus, biochar also
1160
possesses a graphitic structure (C=C bonds; π-electrons). As a result, Cπ-cation interactions played
1161
a primary role in the adsorption of heavy metals onto biochar. Analogous conclusions were
1162
reached by other scholars (Swiatkowski et al., 2004; Uchimiya et al., 2010; Rivera-Utrilla and
1163
Sánchez-Polo, 2011).
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The contribution of Cπ-cation interactions to the mechanism of heavy-metal adsorption
AC C
1164
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1154
1165
onto carbonaceous material cannot be denied. However, unlike biochar and activated carbon,
1166
biosorbents (commonly derived from lignocellulose materials) do not possess a graphitic
1167
structure. In addition, although hydorchar prepared through hydrothermal carbonization (i.e., 150–
1168
250 °C controlled temperature for 2–72 h at a specific pressure) exhibits an aromatic carbon
1169
network, its properties are similar to those of biosorbents (Tran et al., 2017c). Therefore, the
58
ACCEPTED MANUSCRIPT
1170
presence of Cπ-cation interactions in heavy-metal adsorption onto biosorbents and hydrochar is
1171
still controversial and needs to be further investigated. Bui and Choi (2010) considered the role of cation-π bonding between the protonated
1173
amino group of oxytetracycline (OTC) and the graphitic π electrons of multiwalled carbon
1174
nanotubes (MWCNTs). Essentially, the cation-π bonding is dominated by the electrostatic forces
1175
between the cation and the permanent quadrupole of the π-electron-rich aromatic structure and
1176
cation-induced polarization (Ji et al., 2009). Like π-π interactions, cation-π bonding would be
1177
suppressed with increasing pH. This is because at a higher pH, deprotonation of the charged amino
1178
group and protonation of the enol groups will be enhanced and so the electron-acceptor ability of
1179
the oxytetracycline molecule is weaker (Ji et al., 2009). Bui and Choi (2010) opined that
1180
Oleszczuk et al. (2010) ignored the important roles of Ca2+ in the solution; for example,
1181
Ca2+ possibly forms a complex with OTC in the solution or Ca2+ can act as a cation bridge between
1182
the negatively charged OTC and the negative charges of the MWCNTs. Therefore, Bui and Choi
1183
(2010) suggested that Ca2+ may simultaneously bind with the negatively charged OTC and interact
1184
either with the negative charges or the graphitic π electrons of the MWCNTs via cation-π bonding.
1185
As pH is increased, both MWCNTs and OTC become more negatively charged and, consequently,
1186
probably interact more strongly with Ca2+, leading to lower desorption of OTC. This hypothesis
1187
could be further verified by studying the desorption of OTC in the presence of NaCl, instead of
1188
CaCl2.
1189
8.6.2. π-π interactions
AC C
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SC
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1172
1190
π-π interactions (also known as π-π electron donor-acceptor interactions) between
1191
the π-electrons in a carbonaceous adsorbent and the π-electron in the aromatic ring of an adsorbate
1192
were initially proposed by Coughlin and Ezra (1968). In short, the addition of
59
ACCEPTED MANUSCRIPT
electron-withdrawing groups (i.e., oxygen-containing and nitrogen-containing functional groups)
1194
at the edges of the individual graphene layers within a carbonaceous solid causes a considerable
1195
drop in the π-electron density. Positive holes are consequently created in the conduction π-band of
1196
the individual graphene layers, and the interactions between the π-electrons of a carbonaceous
1197
adsorbent and the π-electrons of the adsorbate aromatic rings become weaker.
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1193
Recently, Tran et al. (2017b), and Tran et al. (2017d) investigated the mechanisms of
1199
methylene green 5 (MG5) adsorption by commercial activated charcoal, synthesized activated
1200
carbons, and prepared biochars. They proposed that the primary mechanisms in MG5 adsorption
1201
were π-π interactions and pore filling, while hydrogen bonding and n-π interactions were minor
1202
contributors (Figure 11). To identify the existence of π-π interactions, they used two pieces of
1203
experimental evidence. First, FTIR analysis showed that a peak corresponding to the skeletal
1204
vibration of aromatic C=C bonds decreased in intensity and upshifted after MG5
1205
adsorption. Secondly, oxygenation of the surface of the carbonaceous solids (i.e., biochar and
1206
activated carbon) through a hydrothermal process with acrylic acid resulted in a decrease in MG5
1207
adsorption and indicated the importance of π-π interactions to the adsorption process.
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1198
As discussed in Section 8.6.1, hydrochar also possesses an aromatic carbon network;
1209
therefore, π-π interactions might be expected between the π-electrons of the aromatic C=C bonds
1210
in hydrochar and the π-electrons of an adsorbate. However, a recent study (Tran et al., 2017e)
1211
demonstrated that oxygenation of a hydrochar surface through a hydrothermal process with acrylic
1212
acid contributed to increasing MG5 adsorption and indicated the negligible role of π-π interaction
1213
in the adsorption process. FTIR analysis demonstrated that the aromatic C=C peak did not
1214
significantly decrease in intensity or shift toward higher/lower wavenumbers after adsorption,
1215
which further confirms the insignificant contribution of π-π interactions. Electrostatic attraction
AC C
EP
1208
60
ACCEPTED MANUSCRIPT
played a major role in the adsorption mechanism, while hydrogen bonding and n-π interactions
1217
were minor contributors. The primary adsorption mechanisms of MG5 onto hydrochar were
1218
similar to those on biosorbents, but dissimilar to biochar and activated carbon (i.e., π-π interaction
1219
and pore filling). An identical result was obtained in the investigation of phenol, MG5, and acid
1220
read 1 adsorption onto a commercial glucose-derived spherical hydrochar functionalized with
1221
triethylenetetramine (Tran, et al., 2017a). Therefore, it can be concluded that the addition of
1222
oxygen- and nitrogen-containing functional groups (electron-withdrawing groups) on the surface
1223
of hydrochar does not cause a considerable drop in the π-electron density, but this process provides
1224
abundant adsorption sites on the hydrochar surface.
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1216
Jiang et al. (2009) and Chen et al. (2009) argued over the primary adsorption mechanisms
1226
of hydroxyl- and amino-substituted aromatics on carbon nanotubes and graphite (CNTs/graphite).
1227
Chen et al. (2009) proposed that π-π interactions played a major role in the adsorption mechanism.
1228
However, Jiang et al. (2009) remarked that the experiments of Chen et al. (2009) were
1229
insufficient to support the presence of π-π electron-donor−acceptor (EDA) interactions between
1230
hydroxyl-substituted aromatics and CNTs/graphite. According to Jiang et al. (2009), phenolic
1231
compounds were not appropriate candidates to assess the presence of π-π EDA interactions
1232
between π-electron-donating aromatics and CNTs because of the significant effects of oxygen.
1233
Therefore, the oxygen effect should be considered in more detail in order to gain in-depth insights
1234
into the adsorption mechanisms of environmentally relevant phenolic compounds onto
1235
carbonaceous materials.
AC C
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Figure 11
1236 1237
8.7. Other miscellaneous errors Azizian (2007) commented that the theoretical development of empirical PFO and PSO
1239
kinetic adsorption models using statistical rate theory (SRT) was first reported by Azizian (2004),
1240
not by Rudzinski and Plazinski (2007). Furthermore, the idea that the PFO model can only be
1241
derived theoretically at a nearly constant bulk concentration was proposed by Azizian (2004). In
1242
addition, the conclusion that the PFO and PSO models are simplified forms of a more general
1243
equation was also proposed by Azizian (2004), not Rudzinski and Plazinski (2007). Similarly,
1244
mistakes related to either no citation of the original paper or incorrect citation were pointed out by
1245
Azizian (2008b).
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SC
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1238
A series of mistakes related to incorrectly digitized data, typos, inaccurate calculations,
1247
incorrect use of conditional equilibrium constants, incorrect units, incorrect references, incorrect
1248
application of modeling procedures, and other miscellaneous errors have been highlighted by
1249
Gustafsson and Lumsdon (2014).
TE D
1246
The distinction between heat of adsorption, adsorption energy, and activation energy in
1251
adsorption was reported elsewhere (Inglezakis and Zorpas, 2012). The authors concluded that it is
1252
important to distinguish the differential enthalpy at zero coverage (∆Hdo) from the differential
1253
enthalpy or isosteric heat (∆Hd) and the standard heat of complete coverage or integral enthalpy
1254
(∆H°), which expresses the total heat generation for the adsorption and is related to the
1255
thermodynamic equilibrium constant.
AC C
1256
EP
1250
Li et al. (2010) pointed out that (1) although the cited documents were solid and sound in
1257
their scientific aspects, the reviewers seemed to fail to take full advantage of the intrinsically
1258
contained information; (2) there were some critical errors in the main text; and (3) the writing style
62
ACCEPTED MANUSCRIPT
1259
of the paper was misleading and, to some extent, lacked cautiousness. They focused on 11
1260
comments and concluded that the original paper’s conclusions were not optimistic. However, most
1261
of these comments were rejected by the original authors (Mohan and Pittman, 2011). Regarding the correct citation for determining pHPZC using the batch equilibration method,
1263
Milonjić (2009a) commented that this method was originally proposed by Milonjić et al. (1975).
1264
Furthermore, Milonjić (2009a) noted that using correct and updated citations were very important
1265
for researchers to find relevant information, pioneer ideas, and make progress in a particular
1266
subject. Additionally, from a scientific point of view, it is always necessary to give credit to the
1267
authors who first proposed a method or theoretical model. Recently, Tran et al. (2017b) applied the
1268
“drift method” to determine the pHPZC of commercial activated charcoal (CAC). The effects of
1269
various operation conditions (i.e., different degassing times with N2, background electrolytes,
1270
concentrations of an electrolyte, solid/liquid ratios, and contact times) on the pHPZC were
1271
investigated. The results demonstrated that the pHPZC (9.81 ± 0.07) of CAC was insignificantly
1272
dependent on the operation conditions.
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1262
Geckeis and Rabung (2004) pointed out that photon correlation spectroscopy (PCS) is a
1274
method for colloid size determination, not for zeta-potential analysis. Methods that have been
1275
correctly applied for zeta-potential analysis include electrophoretic light scattering and laser
1276
Doppler velocimetry (LDV), and the units for the measured zeta potentials are mV, not eV.
AC C
1277
EP
1273
Lee (2017) considered the potential effects of flow velocity on the concentration and
1278
distribution of triphenyltin chloride (TPT) on nano zinc oxide (nZnO). The author remarked that
1279
TPT was possibly re-suspended by the hydraulic flow that occurs during hydrant flushing in a
1280
reactor because TPT can be loosely deposited on the nZnO surface. As reported in the literature,
1281
the flow velocity in a wastewater treatment system is one of the factors affecting the removal
63
ACCEPTED MANUSCRIPT
efficiency for a tested pollutant. The distribution of TPT on nZnO might vary during the
1283
adsorption process according to the time of hydrant flushing; therefore, the process of TPT
1284
adsorption onto nZnO might be affected by the operating conditions of a reactor. However, the
1285
authors of the commented paper replied that the application of nZnO for the removal of TPT from
1286
dockyard wastewater was examined using a batch adsorption technique. As a result, the effects of
1287
flow velocity on the adsorption process conducted in the batch experiments were negligible
1288
compared to that in pilot studies and/or column experiments.
SC
RI PT
1282
Kamagaté et al. (2016) and Komárek et al. (2016) considered the influence of Si species
1290
originating from the partial dissolution of quartz on the competitive adsorption of Cd(II), Cr(VI),
1291
and Pb(II) onto nanomaghemite- and nanomaghemite-coated quartz. They recommended that to
1292
accurately assess the interfacial reaction mechanisms occurring at the Fe-oxide/water interface in
1293
the presence of Si-complex mineral assemblages or Fe-coated sand systems, more attention should
1294
be paid to the possible release of silicate from Si-bearing minerals and its subsequent adsorption on
1295
reactive phases.
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1289
A critical paper entitled “comments on “zirconium-carbon hybrid sorbent for removal of
1297
fluoride from water: oxalic acid mediated Zr(IV) assembly and adsorption mechanism”” was
1298
published by Zhao (2015). The authors of the original paper concluded that the fluoride adsorption
1299
occurs on the surface sites of ZrOx-AC (commercial activated carbon modified with Zr together
1300
with oxalic acid) with –OH displacement and/or interacts with the positive charge of zirconium to
1301
form –COOH groups in the oxalate acid; however, Zhao (2015) suggested that if the fluoride
1302
concentration is high enough, it would completely desorb the oxalate acid from the ZrOx-AC
1303
surface. According to the results of previous experiments, Zhao (2015) suggested that it is
AC C
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1296
64
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1304
necessary to further consider or add the exchangeable role of chloride and oxalic acid in the
1305
proposed fluoride-adsorption mechanism. Fan et al. (2007) additionally discussed the mechanisms of fluoride adsorption by calcined
1307
Mg-Al-CO3 layered double hydroxides (CLDH). Based on the experimental data published in the
1308
original paper and analysis of other literature results, they concluded that XRD measurements
1309
indicated that mixed Mg-Al oxides, as well as partially restored LDH, was present in
1310
fluoride-loaded CLDH after freeze-drying treatment. Furthermore, fluoride can be effectively
1311
adsorbed onto MgO, demonstrating that fluoride adsorption over the mixed oxide along with a
1312
memory effect accounts for the effective removal of fluoride by CLDH.
M AN U
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1306
An analytical article on the magnitude of estimated maximum surface-area-normalized
1314
adsorption capacities (Qmax*) for the adsorption of polycyclic aromatic hydrocarbons (PAHs) and
1315
polychlorobiphenyls (PCBs) on soot and soot-like carbon materials was published by Werner and
1316
Karapanagioti (2005). The original authors (van Noort et al., 2005) used the Langmuir isotherm to
1317
extrapolate Qmax* at the solubility limit from solid-water distribution coefficients (Ks) measured in
1318
the pg/L to ng/L range along with estimated Langmuir affinities for adsorption (b) on a
1319
carbonaceous surface. After comparison with estimated surface-area-normalized monolayer
1320
adsorption capacities (Qmono*) and with empirical sorption data from the literature, Werner and
1321
Karapanagioti (2005) concluded that the Langmuir isotherm cannot be used to extrapolate
1322
maximum sorption capacities (Qmax*) near the aqueous-sorbate saturation limit from distribution
1323
coefficients measured at extremely low aqueous-sorbate concentrations. Adsorption sites in
1324
carbon materials are not uniform and other processes, such as multilayer adsorption, condensation
1325
in capillary pores, and absorption into the polymeric matrix, may be relevant near the solubility
1326
limit.
AC C
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1313
65
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Müller et al. (2017) analyzed strong conflicts between the XPS and XRD data and their
1328
interpretation by the original author in a study on the synthesis of Yb doped CuFe2O4 nanoferrite
1329
adsorbents (i.e., CuYb0.5Fe1.5O4) and the application of such adsorbents in the removal of different
1330
pollutants (e.g. methyl orange, safranin, Cr3 +, and Pb2 +). After a polemical discussion, Müller et
1331
al. (2017) concluded that because any experimental study stands and falls on the reliability of the
1332
investigated specimen the lack of any significance therefore holds for this study as a whole.
RI PT
1327
Interestingly, a series of recommendations and suggestions were written by the editor of
1334
Carbon for improving manuscript quality and avoiding mistakes (Thrower, 2007; Thrower,
1335
2008b; Thrower, 2008a; Thrower, 2010; Thrower, 2011). The author focused on five main topics:
1336
titles and abstracts, introduction and references, experimental, results and discussion, and
1337
language.
1338
9. Nonlinear-optimization technique
M AN U
SC
1333
To calculate the parameters of kinetic and isotherm models accurately in both batch and
1340
column experiments, application of the nonlinear method instead of the linear method has been
1341
recommended by many researchers (Porter, 1985; Ho, 2004b; Ho et al., 2005; Bolster and
1342
Hornberger, 2007; Han et al., 2007; Kumar, 2007; El-Khaiary et al., 2010; Chowdhury and Das
1343
Saha, 2011; Lima et al., 2015; Tran et al., 2015; Tran et al., 2017d).
EP
Furthermore, to identify the best-fit model, calculation of the chi-squared (χ2, Eq. 96) value
AC C
1344
TE D
1339
1345
is recommended in addition to calculating the coefficient of determination (R2, Eq. 97) for the
1346
nonlinear method. In the chi-squared test, the squares of the differences between the experimental
1347
data and data calculated using the models are divided by the corresponding data obtained and then
1348
summed. If the data obtained using a model are similar to the experimental data, χ2 is close to zero.
1349
High χ2 values indicate high bias between the experiment and model. Therefore, analyzing the data
66
ACCEPTED MANUSCRIPT
set using the chi-squared test is necessary to confirm the best-fit isotherm for a given sorption
1351
system (Ho, 2004b; Ho et al., 2005; Chowdhury and Das Saha, 2011; Lima et al., 2015; Tran et al.,
1352
2015; Tran et al., 2017b; Tran et al., 2017d; Tran et al., 2017e).
χ =∑ 2
R
2
(qe,exp − qe,cal ) 2 qe,cal
∑(q =1 − ∑ (q
e, exp
− qe, mean)2
=
∑ (q ∑ (q
e, cal
-q
e, cal 2 e, mean
- qe,mean)2
) + ∑(qe, cal - qe,exp )2
(96)
(97)
SC
e,exp
− qe,cal )2
RI PT
1350
where qe,exp (mg/g) is the amount of adsorbate uptake at equilibrium obtained from Eq. 1, qe,cal
1354
(mg/g) is the amount of adsorbate uptake achieved from the model using the Solver add-in, and
1355
qe,mean (mg/g) is the mean of the qe,exp values.
M AN U
1353
Lima et al. (2015) confirmed that the use of nonlinear equilibrium and kinetic adsorption
1357
models gives values that are reliable and statistically relevant for modeling the isotherm and
1358
kinetics of adsorption. Moreover, they did not suggest using linearized equilibrium and kinetic
1359
adsorption models, even in the cases of the linearized Langmuir Type 1 and linearized PSO Type 1
1360
equations that provide R2 values close to unity. The linearization of equilibrium and kinetic
1361
adsorption models could make the parameters determined from these models meaningless.
EP
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1356
Owing to the wide application of the nonlinear method in the study of adsorption
1363
processes, we provide here a short introduction to the application of this method using the “Solver
1364
add-in” in Microsoft Office Excel (2013 version). First, it is necessary to load the Solver add-in in
1365
Microsoft Excel: File → Excel options → Add-ins (select Excel Add-ins in Manage box) → select
1366
the Solver Add-in check box. Second, all Ce and qe values obtained experimentally are considered
1367
as input data, and the qe values from the Langmuir equation are calculated based on two variables
1368
(Qomax and KL ≠ 0). Using the Solver Add-in (Figure 12), the Qomax, KL, and R2 values can be
AC C
1362
67
ACCEPTED MANUSCRIPT
1369
obtained. Notably, other programs (i.e., Origin) also provide similar results and can accurately
1370
calculate the parameters of kinetic and isotherm models.
1371
Figure 12 10. Conclusions
RI PT
1372
In scientific publications, the correct use of technical terms and accurate calculations are
1374
essential. According to the viewpoints discussed in this review, we put forward the following key
1375
conclusions and perspectives:
1378 1379 1380 1381 1382
Adsorption performance should be expressed as qe (mg/g), while the use of
the unit of %removal for qe should be avoided or used cautiously. ii.
M AN U
1377
i.
The use of accurate citations and correct mathematical expressions in
original works is also recommended. iii.
Measurements of adsorption kinetics should be started at an initial time of
less than 2 min and finish when the adsorption process reaches true equilibrium. iv.
TE D
1376
SC
1373
A complete adsorption isotherm (plotting qe versus Ce) should be presented
1383
when investigating liquid-phase adsorption to identify the regions in which the
1384
experimental data relating to adsorption equilibrium are actually located. v.
Differences between the number of data points in an experiment and those
EP
1385
used for model fitting (i.e., the pseudo-second-order or Langmuir models) should be
1387
avoided.
1388
AC C
1386
vi.
For adsorption thermodynamics, the equilibrium constant (KC) must be
1389
dimensionless. The optimal method for calculating thermodynamic parameters should
1390
be appropriately selected according to the data from the adsorption equilibrium
1391
experiment. Notably, it is impossible to calculate thermodynamic parameters from an
1392
experiment using one initial adsorbate concentration at different temperatures. 68
ACCEPTED MANUSCRIPT
1393
vii.
To accurately estimate the parameters of adsorption kinetic and isotherm
models, the nonlinear optimization technique should be applied to decrease the bias
1395
between the qe values calculated from the experimental data and those estimated from
1396
the models. The chi-squared (χ2) test should be used alongside the nonlinear
1397
determination coefficient (R2) to obtain the best-fit models for adsorption kinetics and
1398
isotherms.
1399
viii.
RI PT
1394
An in-depth understanding of the models applied to adsorption kinetics and
isotherms is necessary to avoid misapplication of these models, as well as inaccurate
1401
discussions, calculations, and conclusions. ix.
More attention should be paid to various common misunderstandings about
M AN U
1402
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1400
1403
fundamental adsorption and chemistry concepts. Understanding the unique properties
1404
of adsorbents and target adsorbates can help avoid mistakes made when explaining
1405
adsorption mechanisms.
Although the comments and recommendations of some authors are not always correct, their
1407
observations and suggestions should be acknowledged because of their great contributions in
1408
transferring scientific knowledge.
1409
Acknowledgements
1410
This current work was financially supported by Chung Yuan Christian University (CYCU) in
1411
Taiwan. The first author would like to thank CYCU for the Distinguished International Graduate
1412
Students (DIGS) scholarship to pursue his doctoral studies. The authors gratefully acknowledge
1413
the editor and anonymous reviewer for their invaluable insight and helpful suggestion.
1414
Reference
1415
Alagumuthu, G., V. Veeraputhiran and M. Rajan (2010). "Comments on “Fluoride removal from
1416
water using activated and MnO2-coated Tamarind Fruit (Tamarindus indica) shell:
1417
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Anastopoulos, I. and G. Z. Kyzas (2016). "Are the thermodynamic parameters correctly
1419
estimated in liquid-phase adsorption phenomena?" Journal of Molecular Liquids 218:
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174-185. Aoyama, M. (2003). "Comment on “Biosorption of chromium(VI) from aqueous solution by
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cone biomass of Pinus sylvestris”." Bioresource Technology 89(3): 317-318.
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Arica, M. Y. (2003). "In reaction to the comment by Dr. Y.-S. Ho on our publication “Affinity dye-ligand
composite
membrane
for
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adsorption lysozyme and kinetic properties, Biochemical Engineering Journal 13
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(2003) 35–45”." Biochemical Engineering Journal 15(1): 79-80.
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1424
Azizian, S. (2004). "Kinetic models of sorption: a theoretical analysis." Journal of Colloid and Interface Science 276(1): 47-52.
1428
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poly(hydroxyethylmethacrylate/chitosan
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Azizian, S. (2006). "A novel and simple method for finding the heterogeneity of adsorbents on
1430
the basis of adsorption kinetic data." Journal of Colloid and Interface Science 302(1):
1431
76-81.
Azizian, S. (2007). "Comment on “Kinetics of Solute Adsorption at Solid/Solution Interfaces: A
1433
Theoretical Development of the Empirical Pseudo-First and Pseudo-Second Order
1434
Kinetic Rate Equations, Based on Applying the Statistical Rate Theory of Interfacial
1435
Transport”." The Journal of Physical Chemistry B 111(1): 318-318.
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1432
Azizian, S. (2008a). "Comments on “Adsorption Equilibrium and Kinetics of Reactive Black 5
1437
and Reactive Red 239 in Aqueous Solution onto Surfactant-Modified Zeolite”
1438
(Karadag, D.; Turan, M.; Akgul, E.; Tok, S.; Faki, A. J. Chem. Eng. Data 2007, 52,
1439
1615−1620)." Journal of Chemical & Engineering Data 53(1): 322-323.
1441
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1440
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Azizian, S. (2008b). "Comments on “Biosorption isotherms, kinetics and thermodynamics” review." Separation and Purification Technology 63(2): 249-250.
1442
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Table captions Table 1. Relationship between isotherm parameters and isotherm shape
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Table 2. Mistakes in the presentation and calculation of the separation factor (RL) Table 3. Incorrect values of the exponent g in the Redlich–Peterson equation
Table 4. Comparison of incorrect and correct thermodynamic parameters for methylene blue
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adsorption onto sulfuric acid-treated orange peel
Table 5. A typical example of correct and incorrect use of a Micromeritics report (data not
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published)
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Table 1. Relationship between isotherm parameters and isotherm shape
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Freundlich exponent Separation factor Isotherm shapes Remarks n=0 RL = 0 Irreversible Horizontal n<1 RL < 1 Favorable Concave n=1 RL = 1 Linear Linear n>1 RL > 1 Unfavorable Convex Note: Information was adapted from Worch (2012). Copyright (2012), with permission from De Gruyter. RL and n were calculated from equations 52 and 56, respectively.
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Table 2. Mistakes in the presentation and calculation of the separation factor (RL)
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Typical examples Remakes Langmuir parameters The RL is not the Langmuir o Q max KL RL constant, so it is mistake for Orange peel 54.5 0.101 0.01–0.17 presentation. OP Biochar 115 0.019 0.08–0.57 Langmuir parameters The RL values must be calculated RL o Q max KL at different range of initial adsorbate concentration, so it is Orange peel 54.5 0.101 0.17 mistake for calculation. OP Biochar 115 0.019 0.57 Langmuir parameters RL Qomax KL Correction presentation and calculation. Orange peel 54.5 0.101 0.01–0.17 OP Biochar 115 0.019 0.08–0.57 Note: The data were modified from our previous publication (Tran, You et al. 2015).
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Table 3. Incorrect values of the exponent g in the Redlich–Peterson equation Adsorbate
Sawdust
Reactive black
1.10
(Inbaraj, 2006)
Sawdust
Reactive red
1.04
(Inbaraj, 2006)
Congo red
2.91
(Kumar and Porkodi, 2008)
Xad-4 resin
4-chlorophenol at 303 K
1.07
(Kumar and Porkodi, 2007)
Xad-4 resin
4-chlorophenol at 318 K
1.19
(Kumar and Porkodi, 2007)
2+
–0.35
(Vasanth Kumar et al., 2007)
2+
–1.23
(Kumar et al., 2007
Tectona grandis
Cu
Syzygium cumini
Pb
Activated carbon/ chitoshan composite Activated carbon/ chitoshan composite Activated carbon
Aniline/aniline + Cr(VI)
1.04
(Huang et al., 2014)
Cr(VI)/aniline + Cr(VI)
1.04
(Huang et al. 2014)
Cr(VI)
1.02
(Huang et al. 2014)
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/chitoshan composite
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xerogel
Reference
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Anilinepropylsilica
g
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Adsorbent
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Table 4. Comparison of incorrect and correct thermodynamic parameters for methylene blue adsorption onto sulfuric acid-treated orange peel Incorrect thermodynamic parameters reported by Senthil Kumar et al. (2014)
50 100 150 200 250
Temperature
30 °C –12.5 –10.1 –8.86 –8.03 –7.29
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40 °C 50 °C 60 °C –53.7 –137 –10.4 –8.87 –8.49 –37.4 –90.3 –9.15 –8.04 –7.46 –32.9 –79.4 –8.19 –7.27 –6.52 –27.5 –64.2 –7.54 –6.64 –6.19 –23.7 –54.4 –6.61 –6.17 –5.64 KC values 30 °C 40 °C 50 °C 60 °C 142 54.9 27.2 21.5 54.8 33.6 19.9 14.8 33.7 23.3 14.9 10.5 24.2 18.1 11.9 9.35 18.1 12.7 9.97 7.66 Correct thermodynamic parameters suggested by Hai (2017) ∆Go ∆Ho ∆So KC van't Hoff equation (kJ/mol) (kJ/mol) (J/mol) 5.25
40 °C
4.33
50 °C
3.54
60 °C
3.27
-4.18 -3.81 -3.40
EP
30 °C
13.65
-31.39 y = 1642 – 3.78 R2 = 0.978
-3.28
The unit of J/mol/K was expressed as the original paper; the correction unit might be kJ/mol.
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a
∆Go (kJ/mol)
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Co (mg/L)
∆So (J/mol/K)a
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∆Ho (kJ/mol)
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Co (mg/L)
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Table 5. A typical example of correct and incorrect use of a Micromeritics report Correct data
Prepared activated carbon
Prepared Biochar
BET surface area
613
536
Langmuir surface area
1684
Micropore area
NA
External surface area
698
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Incorrect data
660
348
188
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NA: The micropore area is not reported because either the micropore volume is negative or the calculation of external surface area is larger than the total surface area (BET surface area). The unit is m2/g. Data is not published.
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Figure captions Figure 1. Some basic terms used in adsorption science and technology
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Figure 2. Basic properties of an adsorbent determined by various common techniques Figure 3. Schematic illustration of a new classification system for metal biosorption mechanisms
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Figure 4. A typical example of difference between (a) point of zero charge and (b) zeta potential of glucose-derived spherical biochar prepared from 800 °C
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Figure 5. Effect of contact time on the adsorption process of (a) methyl violet onto granulated mesoporous carbon (GMC) and granular activated carbon (GAC); (b) methyl tert-butyl ether onto carbonaceous resin (Ambersorb 563); (c) ibuprofen (IBP), carbamazepine (CBZ), ofloxacin (OFX), bisphenol-A (BPA), diclofenac (DFN), mecoprop (MCP), pentachlorophenol (PCP), benzotriazol (BZT), and caffeine
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(CAF) onto activated carbon cloths (resin phenolic precursor); and (d) methyl blue onto graphene oxide
Figure 6. Fits of kinetic adsorption data to the linear pseudo-second-order equation (the study
EP
of methylene green 5 adsorption onto commercial activated carbon (CAC) and synthesized activated carbons prepared from golden shower through different
AC C
chemical activation methods (GSAC, GSBAC, GSHAC, and GSHBAC))
Figure 7. Transport processes during adsorption by a porous adsorbent Figure 8. (a) non-equilibrium adsorption isotherms of methylene blue onto sulfuric acid-treated orange peel (STOP) at various temperatures, and (b) comparison of adsorption isotherm curves; adsorbent B performs better (higher qe at q10) than adsorbent A at lower equilibrium concentrations (e.g., Ce = 10 mg/L)
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Figure 9. Proposed mechanisms for Cr(VI) biosorption by nonliving biomass Figure 10. (a) Chemical structure of Congo Red and (b) UV-vis spectra of Congo Red
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solutions at different solution pH values Figure 11. An example of a graphene layer and proposed mechanisms of methylene adsorption green 5 onto biochar, synthesized activated carbon, and commercial
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activated charcoal
Figure 12. A simple guide to the nonlinear method of calculating the Langmuir parameters
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(RSS: residual sum of squares, TSS: total sum of squares)
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Figure 1. Some basic terms used in adsorption science and technology
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Figure 2. Basic properties of an adsorbent determined by various common techniques
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Figure 3. Schematic illustration of a new classification system for metal (bio)sorption mechanisms
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(Adapted from Robalds et al., 2016. Copyright (2016), with permission from Elsevier)
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Figure 4. A typical example of difference between (a) point of zero charge and (b) zeta
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potential of glucose-derived spherical biochar prepared from 800 °C (Data unpublished)
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Figure 5. Effect of contact time on the adsorption process of (a) methyl violet onto granulated mesoporous carbon (GMC) and granular activated carbon (GAC) (Reprinted from Kim et al.
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2016. Copyright (2016), with permission from Elsevier); (b) methyl tert-butyl ether onto carbonaceous resin (Ambersorb 563) (Reprinted from Hung and Lin 2006. Copyright (2006), with permission from Elsevier); (c) ibuprofen (IBP), carbamazepine (CBZ), ofloxacin (OFX),
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bisphenol-A (BPA), diclofenac (DFN), mecoprop (MCP), pentachlorophenol (PCP), benzotriazol (BZT), and caffeine (CAF) onto activated carbon cloths (resin phenolic precursor) (Reprinted from Masson et al. 2016. Copyright (2016) with permission from Elsevier); and (d) methyl blue onto graphene oxide (Reprinted with permission from Sharma et al. 2013. Copyright (2013) American Chemical Society)
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Figure 6. Fits of kinetic adsorption data to the linear pseudo-second-order equation (the study of methylene green 5 adsorption onto commercial activated carbon (CAC) and synthesized
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activated carbons prepared from golden shower through different chemical activation methods (GSAC, GSBAC, GSHAC, and GSHBAC)) (Adapetd from Tran et al., 2017d.
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Copyright (2017), with permission from Elsevier)
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Figure 7. Transport processes during adsorption by a porous adsorbent (Adapted with
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permission from Weber and Smith, 1987. Copyright (1987) American Chemical Society)
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Figure 8. (a) non-equilibrium adsorption isotherms of methylene blue onto sulfuric acid-treated orange peel (STOP) at various temperatures (Adapted from Hai 2016. Copyright (2016) Taylor and Francis), and (b) comparison of adsorption isotherm curves: adsorbent B performs better (higher qe at q10) than adsorbent A at lower equilibrium concentrations (e.g., Ce = 10 mg/L) (Adapted from Volesky 2007. Copyright (2007), with permission from Elsevier)
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Figure 9. Proposed mechanisms for Cr(VI) biosorption by nonliving biomass
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(Adapted from Park et al., 2005. Copyright (2005), with permission from Elsevier).
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Figure 10. (a) Chemical structure of Congo Red and (b) UV-vis spectra of Congo Red solutions at different solution pH values (Adapted from Zhou et al., 2011. Copyright (2011), with permission from Elsevier)
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Figure 11. An example of a graphene layer and proposed mechanisms of methylene
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adsorption green 5 onto biochar, synthesized activated carbon, and commercial activated
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charcoal (Adapetd from Tran et al., 2017 b,d. Copyright (2017), with permission from Elsevier)
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Figure 12. A simple guide to the nonlinear method of calculating the Langmuir parameters (RSS:
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Highlights • This study summarizes common literature mistakes in the field of
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adsorption • Reiteration and propagation of such mistakes in future publications should be avoided.
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• Correct expression and citation of the models used in adsorption studies are provided
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further investigated
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• We also highlight some problems that need to be thoroughly discussed or