Solubility of trioctylmethylammonium chloride in supercritical carbon dioxide and the influence of co-solvents on the solubility behavior

Accepted Manuscript Title: Solubility of trioctylmethylammonium chloride in supercritical carbon dioxide and the influence of co-solvents on the solubility behavior Authors: K.C. Pitchaiah, Neha Lamba, N. Sivaraman, Giridhar Madras PII: DOI: Reference:

S0896-8446(18)30022-6 https://doi.org/10.1016/j.supflu.2018.04.002 SUPFLU 4242

To appear in:

J. of Supercritical Fluids

Received date: Revised date: Accepted date:

10-1-2018 14-3-2018 1-4-2018

Please cite this article as: K.C.Pitchaiah, Neha Lamba, N.Sivaraman, Giridhar Madras, Solubility of trioctylmethylammonium chloride in supercritical carbon dioxide and the influence of co-solvents on the solubility behavior, The Journal of Supercritical Fluids https://doi.org/10.1016/j.supflu.2018.04.002 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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Solubility of trioctylmethylammonium chloride in supercritical carbon dioxide and the influence of co-solvents on the solubility behavior

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K.C. Pitchaiah1, Neha Lamba2, N. Sivaraman1, and Giridhar Madras2

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Homi Bhabha National Institute (HBNI), Indira Gandhi Centre for Atomic Research, Kalpakkam-603102, India

of Chemical Engineering, Indian Institute of Science, Bangalore-560012, India

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2Department

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Graphical Abstract:

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T = 323 K, 4.2 mol% co-solvent

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  P  L   xL ln x2  ln x3 (k 1) ln   1  1  1  1 3 2 k1L3   L4 3  P* T  2 3 

450 300

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CC

5

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x2.10 / mol.mol-1

600



C SC

150

O2

ol an h et +m

CO 2 SC

+

l no pa o r n-p

SCCO2 + n-hexane

0 10

15

20 P / MPa

25

30

35

Solubility of trioctylmethylammonium chloride in SCCO2 with co-solvents

Corresponding author. Tel. +91-044-27480500-24166; Fax: +91-044-27480065 Email: [email protected] (Sivaraman)

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Research highlights: First report on solubility of trioctylmethylammonium chloride in supercritical CO2



Influence of co-solvent on the solubility behavior investigated



New models based on association theory developed for ternary solubilities



Five/six parameter models derived using van Laar/Wilson activity coefficients

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New models correlated solubilities with an average deviation of < 8%

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

ABSTRACT

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Solubility of trioctylmethylammonium chloride (TOMAC) in supercritical carbon dioxide

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(SCCO2) was measured at 313, 323 and 333 K with pressure ranging from 10 to 30 MPa.

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Solubilities (in mole fraction) ranged from 0.5 x 10-5 to 12.7 x 10-5 in the investigated region.

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Influence of co-solvents on the solubility of TOMAC was studied at 313 and 323 K. Among the

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four models employed for correlating solubility of TOMAC in neat SCCO2, association theory based on van Laar activity coefficient model resulted in average deviation of 2%, while use of other models resulted within 10%. Solubility data were found to be self-consistent based on the

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Mendez-Teja model. Two new models were developed for the ternary system (SCCO2+cosolvent+liquid solute) based upon association theory along with the Wilson and van Laar activity

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coefficient models. These models successfully correlated solubility of TOMAC in SCCO2+cosolvent with an average deviation of < 8%.

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Keywords: Supercritical carbon dioxide; TOMAC; Co-solvent; Semi-empirical model; Solubility

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Introduction The main objective of green chemistry is the development of eco-friendly processes for the synthesis of various chemical compounds [1-3]. One of the twelve principles of the green

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chemistry is to reduce the use of auxiliary substances (solvents, separation agents etc.) and

determine some alternative innocuous solvents [2]. Organic solvents pose major challenge to the

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green chemistry because their toxic, flammable, volatile and carcinogenic nature. Moreover, the

large amount of the organic solvents used for the synthesis and downstream processing leads to a colossal amount of waste generation [1]. This necessitates the development of eco-friendly

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solvents that can reduce the adverse effect on the environment. The most prevalent of these

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solvent systems includes ionic liquids, supercritical fluids or the use of solvent-less systems and

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fluorous techniques [4, 5].

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Ionic liquids (ILs) are organic salts that are composed of cations and anions with low

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melting points (<373 K) [6]. While the cations may be inorganic or organic, the anions are always inorganic. These ILs are non-volatile, less flammable, recyclable and can be classified as green solvents. ILs have unique properties such as good solvating power, miscibility and,

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chemical and thermal stability [6, 7]. The properties of ILs can be fine-tuned in a wide range by choosing the appropriate cations and anions. This has led to the concept of ILs being “designer

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solvents”. ILs are a greener and safer alternative to the conventional organic solvents. ILs find applications in various fields such as organic chemistry, electrochemical synthesis, solvents for

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organic and inorganic synthesis, liquid-liquid extraction, chromatography, catalysis and polymerization processes [8-10]. ILs have attracted considerable interest over the last few years and have already successfully been applied for the extraction of metal ions from aqueous solutions.

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Trioctylmethylammonium chloride (TOMAC) is a quaternary ammonium based room temperature ionic liquid (RTIL), which exists as stable cation-anion pairs over a wide range of pH. It acts as an anion exchanger such as protonated amines without any pH limitations. Further, TOMAC is a versatile cation source for the synthesis of a large number of new hydrophobic ILs

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[11]. TOMAC is commonly employed as a surfactant and a phase transfer catalyst in many chemical reactions. TOMAC has also been well studied as an extractant for the metal ion

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extraction and recovery from the aqueous solutions [12-17]. Liquid-liquid extraction of various

divalent metal ions from chloride solutions was studied using TOMAC[12]. Extraction of platinum group of metal from chloride solutions was examined using the quaternary based ILs

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[16]. Along with these applications, trioctylmethylammonium salts were also employed as

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ligands for the extraction of uranium from natural waters and chloride solutions [13, 17].

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Liquid-liquid extraction is currently one of the most widely used techniques for the

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separation and recovery of metals in many industrial fields. However, one of the major

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disadvantages of this method is the usage of large amount of volatile organic compounds. Supercritical fluid extraction (SFE) is now considered as an alternative to the conventional solvent extraction techniques with some advantages over the conventional solvent extraction

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techniques [18, 19]. SFE uses a supercritical fluid as a solvent for the extraction and separation of various compounds of interest from wide variety of solid/liquid matrices. Supercritical fluids

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(SCFs) have unique properties of liquid-like densities, gas like viscosities and diffusivities that can be tuned by changing the temperature and pressure of the fluid [20, 21]. Moreover, the

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supercritical fluid based techniques result in the minimum generation of secondary liquid waste. These properties of the SCFs enable them to be used as a green solvent for the separation or extraction processes for many industrial applications.

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Supercritical carbon dioxide (SCCO2) is widely employed for the extraction and recovery of variety of compounds from both the solid and liquid matrices [22, 23]. Several industrial processes are in operation for the decaffeination of coffee, extraction of hop constituents, oils from leaves, fruits, seeds and spices [20, 24]. For all of these applications, solubility of

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compounds in SCCO2 is a preliminary requirement for the successful design and optimization of the SFE process. Most of the organic compounds, with the exception of strongly polar

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substances, have appreciable solubility in SCCO2 and can be extracted using neat SCCO2. The solubility of polar compounds in SCCO2 can be enhanced by using a co-solvent or an entrainer [25-27]. However, in case of metal ions, direct extraction of metal ions using SCCO2 is not

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feasible. Nevertheless, when the metal ions are complexed with suitable organic ligands, the

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resulting metal-ligand complexes become quite soluble in SCCO2. Therefore, both the

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solubilities of ligand and that of the metal complex play a major role in designing a SFE process

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for the metal ions.

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Experimental determination of solubility of compounds in SCCO2 at different temperatures and pressures is tedious and time consuming. Thus, suitable model predictions for the solubility at any operating condition are required. Equation of state (EOS) based models and

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semi-empirical equations are commonly used for the correlation of solubilities of compounds in

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SCFs. Several semi-empirical models are reported in the literature to correlate the experimental solubilities of compounds in SCCO2 [28-35]. However, a few semi-empirical correlations are

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available in the literature to correlate the solubilities of liquid compounds in SCFs. Recently, several equations were reported for correlating the solubility data of the liquid solutes in SCCO2 using the solution and association theories coupled with the different activity coefficient models [36-38]. Along with these models, different semi-empirical models have also been reported in

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the literature to correlate the solubilities of solid solutes in SCCO2 in the presence of co-solvents [39-43] Despite the availability of models for correlating the solubilities of solid compounds in SCCO2 in the presence of co-solvents, models correlating the solubilities of liquid solutes are scare. Chrastil equation was modified by Gonzalez et al. [44] to correlate the solubility of

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insights into the nature of interactions between solute, solvent and co-solvent.

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compounds in SCCO2 in the presence of co-solvents. However, this model may not provide

SCFs and ILs, both are green solvents and each of them has its own set of remarkable properties. Combination of these two is a new and interesting topic that can be used in several

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applications [45]. Solubility of RTILs in SCCO2 and knowledge of RTILs-SCCO2 phase

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behavior is essential in designing and operating a SFE based separation process. Phase behavior

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of some RTILs-SCCO2 systems was studied. Majority of these studies report the solubilities of

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SCCO2 in RTILs [46-48]. The studies on the solubility of ILs in SCCO2 medium are limited [49, 50] . Therefore in the present study, the solubility of an IL, TOMAC in SCCO2 medium was

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examined. The data relating the solubility of TOMAC in SCCO2 medium is crucial towards the development of a SFE based process for the extraction of metal ions.

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Thus, the main objectives of the present study were three fold: (a) experimental determination of solubilities of TOMAC in SCCO2 (b) study the effect of various co-solvents on the solubilities of

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TOMAC in SCCO2 and (c) development of new models for the ternary system (SCCO2 + cosolvent + solute) to correlate the solubilities of TOMAC in the SCCO2 in the presence of co-

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solvents.

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2. Experimental 2.1 Materials Carbon dioxide gas with a purity of 99.9 % was used for the solubility measurements.

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Trioctylmethylammonium chloride (TOMAC), HPLC grade methanol, n-propanol and n-hexane were employed in the present study. All the other chemicals used in the present study were of

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analytical grade. Detailed information about the chemicals used in the present study has been summarized in Table 1. 2.2 Procedure

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2.2.1 Solubility measurements

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A dynamic flow saturation type apparatus was used to measure the solubility of TOMAC

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in SCCO2 with and without a co-solvent. The experimental set-up and procedure for solubility

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measurements has been described in detail in our previous studies [38, 51]. The experimental set-

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up consisted of a carbon dioxide cylinder, a high pressure reciprocating CO2 pump (JASCO-PU2080-CO2), HPLC pump (JASCO-PU-2080-PLUS) 10 mL heat exchanger, 50 mL twin high pressure equilibrium cells, 10 mL entrainer column, thermostat (JASCO-CO-156), and a back

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pressure regulator (JASCO-880-81-BP). Initially SCCO2 was continuously passed through the equilibrium cells pre-loaded with the TOMAC for a period of 48 h to remove the presence of any

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volatile impurities.

In a typical experiment, 30 and 25 g of TOMAC was loaded into the 50 mL equilibrium

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cells, 1 and 2 respectively. The outlet of the equilibrium cell 1 was connected to the inlet of the equilibrium cell 2. CO2 from the gas cylinder was passed through a silica gel bed to remove the traces of water and improve the purity of CO2 to 0.999 mass fraction. The purified gas was then liquefied using a Peltier element and delivered using a CO2 pump to the heat exchanger to attain

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the desired temperature, after which it flows into the equilibrium cells containing TOMAC. The exiting stream of CO2 from equilibrium cells was passed through an entrainer column to trap the entrained liquid solute. CO2 from the entrainer column reaches to the back pressure regulator and

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the liquid solute was trapped in a collection vessel using quartz wool [38]. In case of the co-solvent experiments, the co-solvent was delivered using a HPLC pump and

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passed through a T-joint to get it mixed into the CO2 stream. The resultant CO2 and the co-

solvent stream was fed to a 10 mL heat exchanger to ensure the desired temperature and a thorough mixing of CO2 and co-solvent, before entering into the high pressure twin equilibrium

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cells. At a fixed experimental temperature, the equilibrium cells pre-loaded with TOMAC were

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pressurized until the desired pressure is reached. CO2 and co-solvent mixed stream was allowed

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continuously to flow through the system at a constant flow rate and the concentration of

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TOMAC in the SCCO2 stream was monitored continuously. The criterion for the accurate measurement of solubility in SCCO2 is based on the fact that the exiting CO2 stream should be

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saturated with the solute. CO2 flow rate was optimized to ensure the complete saturation of solute with SCCO2 [38]. All the experiments in the present study were conducted with a flow rate of 0.1 - 0.2 mL/min. The flow rate of co-solvent was varied from 0.001 – 0.005 mL/min, for the

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required mol % of the co-solvent in a particular binary mixture of CO2 + co-solvent.

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In each experiment, a minimum of 30 mg of TOMAC was collected by varying the collection periods. The amount of TOMAC collected was determined gravimetrically using an

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analytical balance (Shimadzu, AUW220D). The uncertainty in the gravimetric determination was ~ 0.5 %. On the basis of total flow of SCCO2 and amount of TOMAC collected for unit time, the solubility of TOMAC was determined. All the experiments were repeated in triplicate and the uncertainty in the experimental measurements was found to be ± 5%.

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The solubility is expressed in terms of mole fraction (x2) as

x2 

na ( f  t   / M )  na

(1)

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In Eq. (1) na is the number of moles of TOMAC collected per unit time, f is the flow rate of CO2 in mL/min, t is the collection period in minutes, ρ represents the density of CO2, M is the

2.2.1 Preparation of SCCO2 + co-solvent binary mixture:

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molecular weight of CO2

Addition of co-solvent to the SCCO2 increases both the critical temperature and critical

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pressure of the resultant mixture. The operating temperature and pressure has to be chosen such

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that the mixture of CO2 + co-solvent should be in supercritical region. The critical loci of CO2 +

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methanol, CO2 + n-propanol and CO2 + n-hexane were reported in the literature [52-54]. All the

and pressure of the mixtures.

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experiments involving CO2 + co-solvent mixtures were conducted above the critical temperature

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The binary mixtures of CO2 + co-solvents were prepared by adjusting the flow rates of CO2 and co-solvent. X mol % of the co-solvent in a binary mixture of CO2 + co-solvent can be

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obtained using the formula

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  fCO   CO  MWC 2 X ( mol %)  1   2    fC  C  MWCO2

1

   x 100  

(2)

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Where, fCO2 and fC denotes the flow rates, MWCO2 and MWC represents the molecular weight and ρCO2 and ρC stands for the densities of the carbon dioxide and the co-solvent, respectively. The density of the CO2 was obtained from the NIST webbook.

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3. Models and correlations 3.1 Mendez-Santiago and Teja (MT) model Mendez-Santiago and Teja [31] developed an expression for correlating the solubilities of compounds in supercritical fluids based on the dilute solution theory. The developed expression

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can also be used for checking the internal consistency of the experimental data for the solubilities

temperature, pressure and the density of SCCO2 as follows,

T ln( Px 2 )  A1  B1   C1T

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of solutes in SCCO2. The derived model expresses the solubility of a solute as a function of

(3)

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In Eq. (3), T is the temperature (K), P is the pressure (MPa), ρ denotes the density (kg.m-3), x2

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represents the solubility of solute (mol.mol-1) in SCCO2. A1, B1 and C1 are the temperature

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independent constants which can be obtained through the regression of the experimental data.

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The plot between T ln (Px2)-C1T and ρ gives a single straight line for all the isotherms of SCCO2

3.2 Chrastil model

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justifying the internal consistency of the solubility data.

Chrastil [28] derived an equation for the solubility of solute in SCF, based on the

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association theory of assuming the formation of solvato complex between solute and SCF. The model is represented by

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ln S  k ln  

A2  B2 T

(4)

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In Eq. (4), S represents the solubility of solute in SCF in kg.m-3, k denotes the association number, representing the number of solvent molecules associated in the solvato complex, ρ is the density of SCF in kg.m-3, A2 is a constant and defined as ∆H/R, where ∆H is the sum of enthalpy

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of vaporization and solvation and R is the gas constant, B2 is a constant and is a function of association number (k) and molecular weights of solute and solvent. 3.3 Modified Chrastil model for solubility of TOMAC in SCCO2 with co-solvents Chrastil equation correlates the solubilities of solutes in pure SCCO2. Gonzalez et al. [44]

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modified the Chrastil equation to correlate the solubilities of solutes in SCCO2 in the presence of a co-solvent by considering the solute-co-solvent-solvent complex formation. The modified form

ln S  k ln    ln m 

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of Chrastil equation is given by

A3  B3 T

5 

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In Eq. (5), S is the solubility of solute in SCCO2 + co-solvent mixture (kg.m-3), k denotes the

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number of solvent molecules associated in the solvato complex, ρ is the density of SCF (kg.m-3),

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γ represent the association number of co-solvent, m is the concentration of co-solvent (kg.m-3).

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A3 is a constant and defined as ∆H/R, where ∆H is the sum of enthalpy of vaporization and

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solvation and R is the gas constant, B3 is a constant and is a function of k, γ and molecular weights of solute, solvent and co-solvent.

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3.4 New Models

The solubility of solutes in SCCO2 with co-solvents depends on the pressure, temperature,

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density and co-solvent composition. Empirical models have been developed in the literature for the solubility of solid solutes in SCCO2 modified with a co-solvent using association theory [39,

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40]. These equations were developed by assuming each solute molecule is associated with molecules of SCCO2 and co-solvent to form a solvato complex. Same concept was adopted for deriving the equations for the solubility of liquid solutes in SCCO2 modified with a co-solvent.

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The association theory assumes that each solute molecule (A2) is associated with each co-solvent molecule (A3) and κ molecules of SCCO2 (A1) to form a complex denoted by A2 A3 A1 ,

A2  A3  A1  A2 A3 A1 The equilibrium constant can be expressed in terms of fugacities,

(7)

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 fˆA A A   2 3 1 *   f A2 A3 A1    SCF Kf    fˆA   fˆA   fˆA   2  1  3  f A*   f A*   f A*   2  S  1  SCF  3  SCF

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(6)

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SCF represents the supercritical phase of carbon dioxide and S represents the pure solute (liquid)

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phase. f  is the reference fugacity of the components in their respective phases. The fugacities

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of the solute and the co-solvent are expressed in terms of activity coefficient to account for the

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interactions between molecules while the fugacities of other components are expressed in terms of fugacity coefficient,  SCF

 xi  i f i l

(8)

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fi

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Where, i = A2A3A1κ, A2 and A3. fˆ j  x jˆ j P

(9)

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Where, j =A1. f n   n P 

Where, n = A1, A2, A3 and A2A3A1κ.

(10)

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The solute in SCCO2 exists mainly in the associated form hence x A2 A3 A1  x 2 and x A3  x3 represents the mole fraction of the solute and co-solvent in SCCO2. The fugacity of the solute in liquid phase is given by the following expression fˆ2   2l x2l f 2l

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(11)

fugacity of pure solute in liquid phase, f 2l can be expressed as,

(12)

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 V ( P  P2vap )  f 2l  P2vapsat exp  2  RT  

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 2l and x2l are the activity coefficient and the mole fraction of solute in the liquid phase. The

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Similarly, the fugacity of co-solvent in SCF phase can be written as,

(13)

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fˆ3   3 x3 f 3



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The pure component (solvent) in SCF phase, f 3 can be expressed as,

 V3 P  P3vap f 3  P  exp   RT 

 

(14)

 

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vap 3 sat

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Substituting the equations (8) to (14) in equation (7)

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Kf 



  V P  P2vap  x2l  2l P2vapsat exp  2  RT     2 P    



 x2 2 f 231         231 P SCF    V P  P3vap  x3 3 P3vapsat exp  3     x ˆ P    RT   1 1     3 P   1 P       S 





        SCF

(15)

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Equation (15) can be further simplified by taking the logarithm on both the sides as follows,

   P sub  * ln  K f   ln  x 2   ln  231 *   (1  k ) ln P   ln  2    ln  2  P P 231    



  ln  P  

RT

vap 3





vap  V3 P  P3 2    ln  x1   ln( sat ) P   RT

 ˆ     ln  1 *   ln  2l x 2l  ln  x3   ln  2   ln  3*  3   1 



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

(16)

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



V 2 P  P2vap



P  and ˆi are assumed to be reference pressure and reference fugacity coefficient for a particular component. The multiplication of association number and the fugacity coefficient of the solvent

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in SCF phase can be related to the density of SCCO2 as [55]

(16a)

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k ln ˆ1  1k [2( x1B11  x2 B231k1 )  B]

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Where, B    yi y j Bij , Bij is the second virial coefficient (of the pair i-j) of the mixture in

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SCCO2 phase. For example, B231k1 represents the virial coefficient of the mixture of the solvato complex (A2A3A1κ) and the solvent (A1). P2vap and P3vap can be correlated to the temperature

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using Antoine equation,

B2 B and ln P3vap  A3  3 T T

(16b)

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ln P2vap  A2 

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A2, A3 and B2, B3 in Eq. (16b) are temperature independent constants. The equilibrium constant can be expressed in terms of heat of solvation as,

ln K f 

H s RT

 qs

(16c)

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ΔHs is the heat of solvation and qs is a constant. From the definition of compressibility factor,

PV1 RT

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The above equation can also be expressed in terms of molar density ( 1 ) as,

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Z

P  Z 1 RT

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On multiplying the above equation by V2 or V3 on both the sides,

(16d)

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PV2  PV3   Z 1 or Z 1 RT 2 RT 3

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PV2 PV3  Z V2 1 or  Z V3 1 , these can be further rewritten as, RT RT

Z is the compressibility factor that can be expressed using virial equation of state as

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Z  (1  B 1  C 12  D 13  ...) . It can be assumed that the solubility is not the function of higher

power of density i.e.,  B2 ,  B3 etc. Hence these powers in expression for Z have been neglected in

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the ln x2 expression in Eq. (16). The terms

P2vap V2 P vap V and 3 3 are ~ 10-6 to10 -4 and thus can be RT RT

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neglected compared to other terms in Eq. (16). As the solubility of solute in SCCO2 is very small, x1 is assumed to be nearly equal to 1. Thus, the activity coefficient of solute in SCF phase,

 2 can be assumed at infinite dilution. Therefore, Eq. (16) can be rewritten as

16

( B  B3 )  P  H s ln x2  ln x3  ( k  1) ln   qs  k 1 (2 x1B11  B)  ( A2  A3 )  2  T  P *  RT    * k * * P* 2  231 1 2 3     1  1   ln  3   *k  1  231  2 xl  l   2 2 2  2 3  sat k  

 

IP T

(17)

Eq. (17) is the final expression for the solubilities of liquids in supercritical fluids. In Eq. (17),

SC R

P  is assumed to be 1 atm. 1 ,  2 and 3 are the molar densities of solvent, solute and co-solvent, respectively.  2 and  3 can be expressed using different activity coefficient models. In this work,

 2 and  3 are expressed using Wilson (Case 1) and van Laar activity coefficient models (Case

N

U

2).

A

Case 1:

M

The activity coefficient of any component ‘k’ in a multi component mixture is given by the

TE D

following expression using the Wilson activity coefficient model [56] m  m  x ln  k   ln   x j  kj   1   m i ik j 1  j 1  x  j

(18)

ij

EP

j 1

 ij  ii  exp   Vi  RT 

Vj

(18a)

CC

Where,  ij 

A

Using the above formulation for activity coefficients along with the Eq. (17), a model with seven was obtained for correlating the solubilities in SCCO2 in the presence of a co-solvent as mentioned below Eq. (19). The detailed derivation is presented in the supplementary information (see electronic supplementary information Case 1, Section 4).

17

    P  W1  1 1 ln x2  ln x3  ( k  1) ln    x3  1  1   kW2 1        P *  T   2 3   2 3   

(19)

  1  W3  x3W4    2  2 W5   W6 RT 3  1 1TR 

H s R

 ( B2  B3 ) 

2  2 R

(19a)

SC R

W1 

IP T

Where,

W2  2B11  B

U

W3  13  11

N

W4  13  33

M

A

W5  12  22    *k * * P* 2  231 1  2 3  W6  A2  A3  qs   *k 2 l l     x   231k 2 2  sat  

(19c) (19d)

(19e)

(19f)

TE D

 

(19b)

Eq. (19) correlates the solubility of liquid solute in SCCO2 + co-solvent system in terms of co-

EP

solvent composition, temperature, pressure and density of supercritical fluid. k is the association

CC

number for SCF, W1 to W6 are the temperature independent parameters and 1 ,  2 and 3 are the molar densities of solvent, solute and co-solvent, respectively.

A

Case 2:

The activity coefficient for a solute (  2 ) in a ternary mixture using van Laar activity coefficient model can be written as [56],

18 2

2

A   A  A  A   A  x A23  32   x12 A21  12   x3 x1  32   12   A23  A21  A13  21    A21   A12    A23   A23   A21   ln  2  2  A32 A   x1 12   x2  x3 A23 A21   2 3

(20)

A13  2q1a13 , A31  2q3a13 and

q1 V1  q3 V3

(20c)

N

q2 V2  q3 V3

(20b)

A

A23  2q2 a23 , A32  2q3a23 and

(20a)

SC R

q1 V1  q2 V2

U

A12  2q1a12 , A21  2q2 a12 and

IP T

In Eq. (20),

M

Where, qi is the measure of size of component i and aij denotes the interaction energy between

TE D

the two components.

The expression for the solubility of liquid solute (x2) in SCCO2 in presence of a co-solvent can

EP

now be obtained using the above activity coefficient model and Eq. (17),

CC

  P  L1  1 1 1 x3 L2 ln x2  ln x3  ( k  1) ln     k 1L3   L4   3  P *  T   2 3 

A

Where,

(21)

19

L1 

H s R

(21a)

 ( B2  B3 )

(21b)

L3  2B11  B

(21c)

IP T

L2  4 q3 a13  2 q3  a23  a12  a13 

2 *   231k 1*k 2*3* P   L4  A2  A3  qs  2 l l   *  231k  sat x2 2   

 

SC R

(21d)

Eq. (21) represents the new five parameter model for the solubility of liquid solute in SCCO2 in

U

presence of co-solvents developed using association theory based on the van Laar activity

N

coefficient model.

TE D

4. Results and discussions

M

supplementary information Case 2, Section 4).

A

The detailed derivation is presented in the supplementary information (see electronic

4.1 Solubility of TOMAC in neat SCCO2 The reliability and validity of the experimental set-up was examined at different

EP

temperatures and pressure by measuring the solubilities of tributyl phosphate [57] and trioctyl amine [58] in SCCO2. These results have been provided in the supporting information (see

CC

electronic supplementary information Figure S1, S2). The solubility of TOMAC in neat SCCO2 was determined at 313, 323 and 333 K with pressure ranging from 10 to 30 MPa. The solubilities

A

varied from 0.5 x 10-5 to 12.7 x 10-5 in the investigated region as shown in Table 2. The solubility data at different temperatures and pressure fall on to a single straight line, indicating the consistency of experimental solubility data. The effect of temperature and pressure on the solubility of TOMAC in SCCO2 is depicted by Figure 1(a) and 2(a). The solubility of TOMAC

20

was found to be increasing with pressure across all the isotherms. At a constant temperature, the density of SCCO2 increases with pressure that improves the specific interactions between SCCO2 and TOMAC, enhancing the solvating power and thus leading to the higher solubility. It can be observed from the Figures 1(a) and 2(a) that the solubility decreased with increase in

IP T

temperature at isobaric conditions. Temperature simultaneously affects the solute vapor pressure, SCCO2 density and intermolecular interactions. There are two competing factors which

SC R

influences the solubilities of TOMAC: (a) vapor pressure of TOMAC and (b) SCCO2 density.

TOMAC is a high molecular weight compound and thus has a significantly low vapor pressure due to the presence of large hydrocarbon backbone in its molecular structure. Therefore, the

U

vapor pressure of the TOMAC in the temperature region of 313 to 333 K is insignificant and

N

hence making density of SCCO2 as the dominating factor. The decrease of SCCO2 density with

A

temperature reflected in the decrease of solubility with temperature. Thus, the retrograde

M

behavior of the solubility was observed in the present study.

TE D

The experimental solubilities of TOMAC in neat SCCO2 were correlated using the MT model (Eq. (3)) as shown Figure 1(a). The self-consistency of the experimental solubilities of TOMAC in neat SCCO2 was checked by plotting T ln (Px2)-C1T with ρ as shown in Figure 1(b). All the

EP

model parameters were evaluated by performing the multiple linear regressions using the experimental data and are presented in Table 6. The deviation of the experimentally measured

CC

solubilities from the solubilities obtained from the model was estimated by calculating the

A

average absolute relative deviation (AARD %),

100 N  x2,cal  x2,exp AARD%  i1  x N 2,exp 

   

(22)

21

x2,cal is the solubility calculated by the model, x2,exp is the experimental solubility and N is the number of data points. The solubilities of TOMAC in neat SCCO2 were successfully correlated using the MT model with an AARD of 8%. Chrastil equation, Eq. (4) was also used to correlate the solubilities of TOMAC in neat

IP T

SCCO2. The experimental solubilities were fitted using the Chrastil model as shown in Figure

2(a) and an AARD of 6% was obtained. The model parameters k, A2 and B2.were obtained using

SC R

the multiple linear regressions. The logarithm of solubility (kg/m3) was also plotted against the logarithm of density (kg/m3) of SCCO2 as presented in Figure 2(b). It was observed that the log-

U

log plot of solubility with density is linear for all the isotherms. The association number (k) for

N

TOMAC can be obtained from the slopes of these lines and it was found to be about 3 in the

A

investigated range of temperatures and pressures. The slopes of all the isotherms were similar.

M

However, the slope showed a small increase at a higher temperature indicating that the lower vapor pressure of TOMAC makes the solubility as density dependent.

TE D

The solubility of TOMAC in neat SCCO2 was also correlated using two activity coefficient based models, solution theory based Wilson activity coefficient model [36] and association theory based van Laar activity coefficient model [59]. The details of the models and

EP

the obtained results are described in the supporting information (see electronic supplementary information Section 2, Table S1, Figure S3). The solution theory based Wilson activity

CC

coefficient model correlated the solubility data with an AARD of 10%. However, the association

A

theory based van Laar activity coefficient model provided a better correlation of solubilities with an AARD of only 2%. 4.2 Solubility of TOMAC in SCCO2 in the presence of co-solvents

22

The solubility of TOMAC in neat SCCO2 was found to be low, varying from 0.5 x 10-5 to 12.7 x 10-5 mole/mole in the investigated region. The weak solvating power of SCCO2 for polar compounds and metal ions is a limitation for its applications to many supercritical fluid based techniques. It has been reported earlier that the presence of small amount of co-solvents

IP T

(generally polar compounds) considerably increases the solubility of compounds in SCCO2 [41, 42, 60, 61]. Thus, in the present study, one non-polar compound, n-hexane and two polar

SC R

compounds, methanol and n-propanol were employed as co-solvents along with the SCCO2 to

enhance the solubility of TOMAC in SCCO2. The influence of co-solvents on the solubility behavior of TOMAC in SCCO2 was examined at 313 and 323 K with pressure ranging from 10-

U

30 MPa. The solubility measurements were carried out with SCCO2 + co-solvent mixtures with

N

the co-solvent composition ranging from 1.05 to 4.20 mol %.

A

The experimental solubilities of TOMAC in the presence of co-solvents have been listed

M

in Tables 3, 4 & 5, respectively. The solubility of TOMAC in SCCO2 with n-hexane, n-propanol

TE D

and methanol as co-solvents are depicted by Figure 3, 4 & 5, respectively. It can be observed that the solubility of TOMAC increases with the pressure at a constant temperature irrespective of the nature of co-solvent. It is evident from the Figure 3 that the effect of n-hexane on the

EP

solubility of TOMAC in SCCO2 is not appreciable. The solubility of TOMAC in SCCO2 + nhexane mixture was found to be similar to that in neat SCCO2. Similar results were obtained by

CC

W Wu et al for the solubility of [bmim] [PF6]. The effect of n-hexane on the solubility [bmim] [PF6] was studied and the solubility enhancement was only marginal even at 29 mol % of n-

A

hexane in SCCO2 [49, 50]. n-hexane is a non-polar compound and it has weak interactions with the TOMAC. The solvating power of n-hexane is close to that of the SCCO2. Thus, the solvating

23

power of SCCO2 + n-hexane mixture was also close to that of n-hexane / SCCO2. Therefore, the presence of n-hexane in SCCO2 did not reflect any changes in the solubilities. Figures 4 and 5 represent the solubilities of TOMAC in SCCO2 in presence of npropanol and methanol, respectively. The solubility of TOMAC increases drastically in the

IP T

presence of both of these polar co-solvents. At 313 K, 30 MPa and 4.2 mol% of co-solvent, the solubilities of TOMAC in presence of n-propanol and methanol were found to be 490 x 10-5 and

SC R

633 x 10-5 mole/mole, respectively. Under similar experimental conditions, the corresponding solubility in the absence of co-solvent was only 12.7 x 10 -5 mole/mole. In case of methanol as a co-solvent, the solubility increased by 50 times. The effect of polar co-solvent on the solubility

U

of ionic liquids such as [bmim] [PF6] was studied by Wu et al., and the solubility of ionic liquids

N

in SCCO2 was found to be increased by 103 times in the presence of polar co-solvents [49, 50].

A

TOMAC is a polar compound with a large hydrocarbon chain [62]. The solubility

M

enhancement is mainly due to the strong interactions of the TOMAC with the polar co-solvent.

TE D

Polar co-solvents such as methanol and n-propanol are both hydrogen bond donors and acceptors and thus can associate through hydrogen bonding. Methanol and n-propanol can interact with TOMAC by forming a hydrogen bond with “N” present in the TOMAC molecule. Therefore,

EP

addition of polar compounds to the SCCO2 can enhance the interactions with TOMAC resulting in the higher solubilities. The solubilities of TOMAC in SCCO2 in the presence of three co-

CC

solvents at a 313 K and 30 MPa are depicted in Figure 6. It can be observed from the Figure 6 that the effect of co-solvent followed an order of n-hexane < n-propanol < methanol. The effect

A

of co-solvent follows the similar trend of their respective polarities. The dipole-moment increases in the order of n-hexane < n-propanol < methanol. As the dipole-moment of the cosolvent increases, the tendency of neutralization of the charge in the ionic liquid increases,

24

thereby increasing the solubility in SCCO2. Therefore, polarity of the co-solvent is one of the main factors that decide the solubility of TOMAC in modified SCCO2 medium. In order to quantify the effect of co-solvent on the solubility of TOMAC in SCCO2, solubility enhancement factor, I2, was defined as follows [26]

IP T

x 2 ,te r n a r y

(2 3)

x 2 ,b in a r y

SC R

I2 

In eq. (38) x2,ternary denotes the solubility of TOMAC in SCCO2 with co-solvents and x2,binary denotes the solubility of TOMAC in neat SCCO2. The solubility enhancement factor, I2 is always

U

greater than unity irrespective of temperature and pressure employed in the present study. The

N

solubility enhancement factor is dependent on the co-solvent composition and nature of the co-

A

solvent employed. The magnitudes of the solubility enhancement factor follow an order of

M

n-hexane < n-propanol < methanol. Methanol is more effective in increasing the solubility of

TE D

TOMAC in SCCO2 compared to n-hexane and n-propanol (Figure 6). The solubility enhancement factor varied close to unity for n-hexane regardless of temperature, pressure and co-solvent composition. In case of methanol and n-propanol, the solubility enhancement factor

EP

increased with pressure and composition of the co-solvent. The solubility enhancement factor for n-propanol varied from 3.4 to 38 with co-solvent composition ranging from 1.05 to 4.20 mol% at

CC

313 K and 30 MPa. Under similar experimental conditions, the solubility enhancement factor for

A

methanol varied from 3.8 to 50. The solubility data of TOMAC in SCCO2 with co-solvents: n-hexane, n-propanol and methanol at 313 K and 323 K were correlated using the modified Chrastil equation, Eq. (5) as depicted in Figure 3(a1, a2), 4(a1, a2) and 5(a1, a2), respectively. An AARD of 12% was obtained between

25

the experimental and calculated solubilities using the modified Chrastil equation. Model parameters were evaluated using the multiple linear regressions and are represented in Table 7. Two new model equations (Eq. (19) and (21)) were developed to correlate the solubility of liquid

IP T

solute in SCCO2 in the presence of co-solvents using association theory with Wilson and van Laar activity coefficient models, respectively. The new correlation, Eq. (19) was obtained using

SC R

the association theory coupled with the Wilson activity coefficient model and it is comprised of seven adjustable parameters. These parameters were obtained from the non-linear regressions performed using the experimental data by applying some constraints on the model parameters.

U

For example, k is the association number and it should be always positive. In (Eq. (19)), W1

N

values can be either positive or negative, this value depends on the heat of solvation, virial

W1

was

always

found

to

be

positive

from

the

regression

implying

M

of

A

coefficients and interaction parameters for solute, solvent and co-solvent interactions. The value

H s  (( B2  B3 ) R  2  2 ) . Unlike W1, W2 was always found to be negative through

TE D

regression. The value of W3 depends on the interaction parameters for solvent/co-solvent and solvent/solvent interactions. W4 accounts for the interactions between solvent/co-solvent and co-

EP

solvent/co-solvent systems, respectively. Similarly, W5 takes into account the interactions between solvent/solute and solute/solute interactions. The value of these three parameters: W3,

CC

W4 and W5 were always found to be positive for a non-polar co-solvent, n-hexane and these were negative for polar co-solvents, methanol and n-propanol (which aids solubility of solute in

A

SCCO2). This indicates that the interaction between solvent/co-solvent (λ13) also plays a major role in enhancing the solubility of solutes in SCCO2 in the presence of co-solvent. Further, the value of W6 can be positive or negative depending on the value of (A2 + A3) is greater or less

26 2  *  *k * * P   231k 1 2 3   than the value of qs  2 l l  . W6 was always found to be negative from the  *  231k  sat x2 2   

 

regressions.

IP T

It was also observed that the contribution from the W5 term (-λ12-λ22) in Eq. (19) was negligible and hence, it can be neglected. Thus, Eq. (19), the association model based on Wilson activity

SC R

coefficient model reduces to a simplified six parameter model,

(24)

A

N

U

     P  W1  1 1  2 ln x2  ln x3  ( k  1) ln      x3  1  1   kW 2 1     P *  T   2  3 1   2 3   1  W3  x3W4   W6 RT  3

M

Eq. (24) was employed to correlate the solubility of TOMAC in SCCO2 at 313 K and 323 K in the presence of different co-solvents as shown in Figure 3(b1, b2), 4(b1, b2) and 5(b1, b2),

TE D

respectively. The model parameters along with the AARD values are reported in Table 7. However, the deviation of the calculated solubilities using different models from the experimental data in presence of different co-solvents: n-hexane, n-propanol and n-methanol

EP

have been provided in the supporting information (see electronic supplementary information

CC

Table S2, S3, S4).

The second model equation (Eq. (21)), developed using the association theory with van Laar

A

activity coefficient model is comprised of five adjustable parameters to correlate the solubility of liquid solutes in SCCO2 in the presence of co-solvents.

  P  L1  1 1 1 x3 L2 ln x2  ln x3  ( k  1) ln     k 1L3   L4   3  P *  T   2 3 

(21)

27

Where k, L1 to L4 are temperature independent parameters and were obtained using the nonlinear curve fitting with a constraint on value of k being always positive. In (Eq. (21)), L1 values can be positive or negative depending on the values of heat of solvation and virial coefficients. L1 was always found to be positive from the regression, implying Hs  (B2  B3 )R . The

IP T

parameter, L2 values account for the interaction between solvent/co-solvent, solute/co-solvent

and solvent/solute. It can be positive or negative depending on the value of 3a13 is greater or less

SC R

than the value of (a23-a12). In case of methanol and n-propanol the value of L2 was found to be negative, suggesting that (a23-a12) > 3a 13. L3 term in Eq. (21) that comprises of the virial

U

coefficients is same as that of W2 in Eq. (19) and its value was also found to be negative. In Eq.

N

(21), the term L4 is equivalent to term W6 in Eq. (19) and the value of L4 was always found to be

A

negative. The values of L4 and W6 were also found to be comparable for all three co-solvents. L4

M

can be positive or negative depending on the whether the value of (A2 + A3) is greater or less 2  *  *k * * P     231k 1   2 3 than the value of qs  2 l l  . Eq. (21) was employed to correlate the solubilities  *  231k  sat x2 2   

TE D

 

of TOMAC in SCCO2 in presence of different co-solvents.

EP

The correlated results of solubilities based on the four parameters modified Chrastil model (Eq. (5)), five parameters association theory based van Laar activity coefficient model (Eq. (21)) and

CC

six parameters association theory based Wilson activity coefficient model (Eq. (24)) are shown

A

in Table 7 along with their respective AARD %. Modified Chrastil equation (Eq. (5)) correlated the solubilities with an AARD of around 12%. It was observed that the newly derived models (Eq. (21) and Eq. (24)) have successfully correlated the solubility of TOMAC in SCCO2 in presence of co-solvents with an AARD of within 8%, lesser than the modified Chrastil model.

28

The parameters in the Eq. (21) and Eq. (24) also provide some preliminary physical interpretation of interactions between solute, solvent and co-solvent molecules. Thus, the current models are first of its kind to correlate the liquid solute solubilities in SCCO2 in the presence of different co-solvents at 313 K and 323 K as shown in Figure 3(c1, c2), 4(c1, c2) and 5(c1, c2),

IP T

respectively. However, it is important to note that the three models used for correlating the solubilities in SCCO2 in the presence of co-solvents consist of different number of parameters (4,

SC R

5 and 6, respectively). Thus, it is crucial to account the effect of different number of parameters to comment on the superiority of a model. This effect of different relative deviations and the number of parameters from different models can be accounted by using the Akaike information

N

U

criteria (AIC) to obtain the best model for correlating the solubilities.

(25)

TE D

 ESS  AIC  n ln   2p  n 

M

fit and the model complexity. It is given by,

A

AIC penalizes for the addition of parameters and provides a bridge between the goodness of the

In Eq. (25), n and p denotes the number of data points and the number of parameters in model,

EP

respectively. ESS is the error sum of squares or the residual sum of squares obtained after regressing the experimental data using a particular model. However, the AIC is used for a large

CC

sample size when (n / p > 40) and thus is not accurate for the small sample size. Hence, the Eq. (25) was corrected for the small sample size and is named as corrected Akaike information

A

criterion (AICC) [59, 63],

AICc  AIC 

2 p ( p  1) n  p 1

(26)

29

The model providing the minimum value of AICc among the compared models is the best model. Thus, Eq. (26) was used to compare the three models used in the present study to correlate the solubilities of TOMAC in SCCO2 with different co-solvents. The AICc values obtained for each model for different compositions of co-solvents have been provided in Table 7. This can be

IP T

observed from the AICc results in Table 7 that the four parameters modified Chrastil model (Eq.

(5)) is always better than the other two models (Eq. (21) and Eq. (24)) for correlating the

SC R

solubilities in SCCO2 with co-solvents for lower concentration of co-solvents (1.05 mol %).

Similarly, the newly developed five parameters association theory based van Laar activity coefficient model (Eq. (21)) is always better than the other two models (Eq. (5) and Eq. (24)) for

U

correlating the solubilities in SCCO2 with co-solvents for higher concentration of co-solvents

N

(4.20 mol %). However, for the intermediate concentration of co-solvents (2.10 mol %), both of

M

A

these models (Eq. (5) and Eq. (21)) can be used to correlate the experimental solubility data. 5. Conclusions

TE D

The solubility of trioctylmethylammonium chloride (TOMAC) in supercritical carbon dioxide (SCCO2) was determined using a flow saturation technique. The solubilities were measured at 313, 323 and 333 K with pressure ranging from 10-30 MPa. The solubilities were found to be

EP

low in the investigated regions. Thus, the solubilities of the compound were studied in the

CC

presence of co-solvents such as methanol, n-propanol and n-hexane to obtain the enhanced solubilities in SCCO2. The solubility behavior of TOMAC in SCCO2 containing co-solvent was

A

also investigated as a function of co-solvent composition. The solubility of TOMAC in SCCO2 did not show appreciable change in presence of non-polar co-solvent, hexane. However, it was increased significantly in the presence of polar co-solvents, methanol and n-propanol.

30

Solubility data of TOMAC in neat SCCO2 was correlated using Mendez-Teja and Chrastil models. Two new models were developed to correlate the solubilities of TOMAC in SCCO2 in presence of co-solvents, using association theory based on Wilson and van Laar activity coefficient models. The solubilities of TOMAC in SCCO2 with co-solvents were correlated using

IP T

the modified Chrastil and newly developed models, respectively. A lower AARD of less than 8%

was obtained using the new models having 5 and 6 parameters in comparison to the existing 4

SC R

parameters model. The penalty for the increased number of parameters in a model was accounted by the AICc values for the best model to be used. It was observed that AICc value was minimum for modified Charstil model for lower concentrations (1.05 mol %) of co-solvents whereas, it

U

was found to be minimum for association theory based van Laar activity coefficient model for

N

higher concentrations (4.20 mol %). Thus, both of these models can be used appropriately for

A

correlating the solubilities of polar RTILs in SCCO2 with co-solvents. Our endeavors include the

M

designing extraction of actinides using SCCO2 containing ligands e.g. TOMAC. The solubility

TE D

data on SCCO2 containing TOMAC is an important component in connection with the above

A

CC

EP

work.

31

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IP T

[2] P.T. Anastas, T.C. Williamson, Green chemistry: frontiers in benign chemical syntheses and processes, Oxford University Press, USA, 1998.

SC R

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TE D

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EP

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CC

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A

[10] P. Wasserscheid, W. Keim, Ionic liquids—new “solutions” for transition metal catalysis, Angew. Chem. Int. Ed., 39 (2000) 3772-3789. [11] J.-P. Mikkola, P. Virtanen, R. Sjöholm, Aliquat 336®—a versatile and affordable cation source for an entirely new family of hydrophobic ionic liquids, Green Chem., 8 (2006) 250-255.

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[12] T. Sato, T. Shimomura, S. Murakami, T. Maeda, T. Nakamura, Liquid-liquid extraction of divalent manganese, cobalt, copper, zinc and cadmium from aqueous chloride solutions by tricaprylmethylammonium chloride, Hydrometallurgy, 12 (1984) 245-254. [13] T. Sato, T. Nakamura, M. Kuwahara, Diluent effect on the extraction of uranium (VI) from

IP T

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SC R

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TE D

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[27] J. Jin, C. Zhong, Z. Zhang, Y. Li, Solubilities of benzoic acid in supercritical CO 2 with

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mixed cosolvent, Fluid Phase Equilib., 226 (2004) 9-13. [28] J. Chrastil, Solubility of Solids and Liquids in Supercritical Gases, J. Phys. Chem., 86 (1982) 3016-3021.

EP

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[31] J. Méndez-Santiago, A.S. Teja, The solubility of solids in supercritical fluids, Fluid Phase Equilib., 158 (1999) 501-510.

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[36] R.C. Narayan, J.V. Dev, G. Madras, Experimental determination and theoretical correlation

N

for the solubilities of dicarboxylic acid esters in supercritical carbon dioxide, J. Supercrit. Fluids,

A

101 (2015) 87-94.

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[37] N. Lamba, R.C. Narayan, J. Raval, J. Modak, G. Madras, Experimental solubilities of two

TE D

lipid derivatives in supercritical carbon dioxide and new correlations based on activity coefficient models, RSC Adv., 6 (2016) 17772-17781. [38] K.C. Pitchaiah, N. Sivaraman, N. Lamba, G. Madras, Experimental determination and

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model correlation for the solubilities of trialkyl phosphates in supercritical carbon dioxide, RSC Adv., 6 (2016) 51286-51295.

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[40] S.N. Reddy, G. Madras, A new semi-empirical model for correlating the solubilities of solids in supercritical carbon dioxide with cosolvents, Fluid Phase Equilib., 310 (2011) 207-212.

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[44] J.C. González, M.R. Vieytes, A.M. Botana, J.M. Vieites, L.M. Botana, Modified mass action law-based model to correlate the solubility of solids and liquids in entrained supercritical carbon dioxide, J. Chromatogr. A, 910 (2001) 119-125.

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[45] S. Keskin, D. Kayrak-Talay, U. Akman, Ö. Hortaçsu, A review of ionic liquids towards

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supercritical fluid applications, J. Supercrit. Fluids, 43 (2007) 150-180.

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systems, J. Phys. Chem. B, 105 (2001) 2437-2444.

TE D

[47] J.L. Anthony, E.J. Maginn, J.F. Brennecke, Solubilities and thermodynamic properties of gases in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate, J. Phys. Chem. B, 106 (2002) 7315-7320.

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[48] S.N. Aki, B.R. Mellein, E.M. Saurer, J.F. Brennecke, High-pressure phase behavior of carbon dioxide with imidazolium-based ionic liquids, J. Phys. Chem. B, 108 (2004) 20355-

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20365.

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A

temperature ionic liquid in supercritical CO 2 with and without organic compounds, Chem. Commun., (2003) 1412-1413.

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[50] W. Wu, W. Li, B. Han, T. Jiang, D. Shen, Z. Zhang, D. Sun, B. Wang, Effect of organic cosolvents on the solubility of ionic liquids in supercritical CO2, J. Chem. Eng. Data, 49 (2004) 1597-1601. [51] K. Pitchaiah, N. Sivaraman, M. Joseph, P. Mohapatra, G. Madras, Solubility of tri-iso-amyl

IP T

phosphate in supercritical carbon dioxide and its application to selective extraction of uranium, Sep. Sci. Technol., 52 (2017) 2224-2237.

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containing carbon dioxide at high pressures: methanol-carbon dioxide, n-hexane-carbon dioxide, and benzene-carbon dioxide systems, J. Chem. Eng. Data, 21 (1976) 53-55.

U

[53] K. Suzuki, H. Sue, M. Itou, R.L. Smith, H. Inomata, K. Arai, S. Saito, Isothermal vapor-

N

liquid equilibrium data for binary systems at high pressures: carbon dioxide-methanol, carbon

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dioxide-ethanol, carbon dioxide-1-propanol, methane-ethanol, methane-1-propanol, ethane-

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ethanol, and ethane-1-propanol systems, J. Chem. Eng. Data, 35 (1990) 63-66.

TE D

[54] M.V. da Silva, D. Barbosa, High pressure vapor–liquid equilibrium data for the systems carbon dioxide/2-methyl-1-propanol and carbon dioxide/3-methyl-1-butanol at 288.2, 303.2 and 313.2 K, Fluid Phase Equilib., 198 (2002) 229-237.

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[55] C. Jiang, Q. Pan, Z. Pan, Solubility behavior of solids and liquids in compressed gases, J. Supercrit. Fluids, 12 (1998) 1-9.

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[56] S.I. Sandler, in: Chemical, biochemical, and engineering thermodynamics, Wiley , India, 2006, 477-478.

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[57] Y. Meguro, S. Iso, T. Sasaki, Z. Yoshida, Solubility of organophosphorus metal extractants in supercritical carbon dioxide, Anal. Chem., 70 (1998) 774-779.

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[58] H.S. Ghaziaskar, M. Kaboudvand, Solubility of trioctylamine in supercritical carbon dioxide, J. Supercrit. Fluids, 44 (2008) 148-154. [59] N. Lamba, R.C. Narayan, J. Modak, G. Madras, Solubilities of 10-undecenoic acid and geraniol in supercritical carbon dioxide, J. Supercrit. Fluids, 107 (2016) 384-391.

IP T

[60] Y. Koga, Y. Iwai, Y. Hata, M. Yamamoto, Y. Arai, Influence of cosolvent on solubilities of

fatty acids and higher alcohols in supercritical carbon dioxide, Fluid Phase Equilib., 125 (1996)

SC R

115-128.

[61] E. Sahle-Demessie, U. Pillai, S. Junsophonsri, K. Levien, Solubility of organic biocides in supercritical CO2 and CO2+ cosolvent mixtures, J. Chem. Eng. Data, 48 (2003) 541-547.

U

[62] S.N. Aki, J.F. Brennecke, A. Samanta, How polar are room-temperature ionic liquids?,

N

Chem. Commun., (2001) 413-414.

A

[63] P. Kletting, G. Glatting, Model selection for time-activity curves: the corrected Akaike

A

CC

EP

TE D

M

information criterion and the F-test, Zeitschrift für medizinische Physik, 19 (2009) 200-206.

38

Table 1. Specifications of the chemicals used in the present study Source

Purity (%)

CAS number

Carbon dioxide

Sri Krishna Industrial Gases, Chennai, India

99.9

124-38-9

Trioctylmethylammonium chloride

TCI, Japan

99

5137-55-3

Methanol

SD Fine Chem Ltd; Mumbai, India

99.8

67-56-1

n-propanol

Merck, India

> 99

n-hexane

SD Fine Chem Ltd; Mumbai, India

99

SC R

U N

A M TE D EP CC A

IP T

Chemical Name

71-23-8

110-54-3

39

Table 2. Experimental solubilities of TOMAC in SCCO2 at temperature (T) and pressure (P) Density values taken from http://webbook.nist.gov/chemistry/fluid/

10.3

651.49

6.1

15

781.32

8.9

20

840.61

25

880.15

30

910.47

10.3

423.74

15

701.08

Solubility (mol/mol) x2 x 105 1.4

10.5 12.1 12.7

A

M

323

834.89

9.5

30

871.03

10.2

10.3

309.89

0.6

15

605.6

3.6

20

724.63

5.2

25

787.28

6.6

30

830.33

7.6

TE D EP CC

5.3 7.9

25

A

1.8

785.16

20

333

N

U

313

8.3

Density * (kg/m3) 320.54

P (MPa)

IP T

T (K)

SC R

*

Standard uncertainties (u) are u(T) = 0.1 K, u(P) = 0.1 MPa and relative uncertainty (ur), ur(x2) = 0.1

40

Table 3. Solubilities of TOMAC in SCCO2 in presence of n-hexane as a co-solvent

P (MPa)

Neat SCCO2

1.05 mol % 2.10 mol % 4.20 mol % n-hexane n-hexane n-hexane

10

6.1

5.8

7.8

15

8.9

8.9

11.4

20

10.5

10.5

13.5

25

12.1

11.2

30

12.7

11.9

10

1.8

1.8

15

5.3

20

7.9

25

9.5

30

10.2

14.0 14.6

15.3

15.3

U

14.6

4.4

4.9

7.1

8.0

7.0

9.6

10.5

8.6

12.1

12.9

10.2

13.6

13.6

N

2.7

A

TE D

M

323

12.5

SC R

313

9.5

IP T

T (K)

Solubility (mol/mol) x 2 x 105

A

CC

EP

Standard uncertainties (u) are u(T) = 0.1 K, u(P) = 0.1 MPa and relative uncertainty (ur), ur(x2) = 0.05

41

Table 4. Solubilities of TOMAC in SCCO2 in presence of n-propanol as a co-solvent

P (MPa)

Neat SCCO2

1.05 mol % 2.10 mol % 4.20 mol % n-propanol n-propanol n-propanol

10

6.1

8.7

22.7

15

8.9

18.7

53.4

20

10.5

26.2

87.4

25

12.1

37.0

30

12.7

43.3

10

1.8

2.0

15

5.3

20

7.9

25

9.5

30

10.2

428.8

127.2

490.1

U

111.9

10.7

31.2

115.7

21.0

61.2

227.0

28.4

94.7

360.5

34.0

118.7

439.6

N

14.6

A

TE D

331.4

5.5

M

323

231.2

SC R

313

109.1

IP T

T (K)

Solubility (mol/mol) x2 x 105

A

CC

EP

Standard uncertainties (u) are u(T) = 0.1 K, u(P) = 0.1 MPa and relative uncertainty (ur), ur(x2) = 0.05

42

Table 5. Solubilities of TOMAC in SCCO2 in presence of methanol as a co-solvent

10.5

27.3

15

8.9

25.0

71.3

20

10.5

33.2

104.9

25

12.1

43.0

30

12.7

49.2

10

1.8

2.6

15

5.3

20

7.9

25

9.5

30

10.2

100.0 311.0 435.6

SC R

6.1

556.8

169.5

632.8

U

146.2

6.4

18.2

13.4

35.6

142.4

22.7

70.0

279.2

32.7

103.3

420.3

40.7

127.2

515.3

N

TE D

323

10

A

313

Neat SCCO2

IP T

P (MPa)

M

T (K)

Solubility (mol/mol) x 2 x 105 1.05 mol % 2.10 mol % 4.20 mol % methanol methanol methanol

A

CC

EP

Standard uncertainties (u) are u(T) = 0.1 K, u(P) = 0.1 MPa and relative uncertainty (ur), ur(x2) = 0.05

43

Table 6. Regression analysis and model parameters from different correlations for solubilities of TOMAC in neat SCCO2

MT model (Eq. (3))

k A2 B2 R2 AARD (%)

A

CC

EP

TE D

M

A

N

U

Chrastil model (Eq. (4))

Values

IP T

Model Parameter A1 B1 C1 R2 AARD (%)

-2173 ± 40 2.2 ± 0.1 -5 ± 0.1 0.992 8.0

SC R

Model

3.3 ± 0.1 2069 ± 40 -29 ± 0.8 0.996 6.0

44

Table 7. Regression analysis and model comparison for solubilities of TOMAC in SCCO2 with different co-solvents

Model Parameters

n-hexane as a co-solvent

Parameter Values n-propanol as a co-solvent

methanol as a co-solvent

Modified Chrastil model (Eq. (5))

k γ A3 B3 R2 AARD (%) Co-solvent (mol %) AICc

2.9 ± 0.1 0.45 ± 0.01 1703 ± 40 -20 ± 1 0.968 12.0 1.05 2.10 4.20

5.1 ± 0.1 1.7 ± 0.1 -145 ± 10 -26± 2 0.992 12.0 1.05 2.10 4.20

5.1 ± 0.1 1.7 ± 0.04 255 ± 10 -26 ± 2 0.991 12.0 1.05 2.10 4.20

A

SC R

U

-198.7 -196.5 -171.3 -125.9 -206.8 -169.9 -123.0

N

1.2 127 ± 6 -2.2 x 10-4 ± 5 x 10-6 -1251 ± 100 -51154 ± 3000 -9.7 ± 0.1 0.995 7.0 1.05 2.10 4.20

M

A

1.2 1713 ± 6 -4.5 x 10-4 ± 5 x 10 -6 2188 ± 100 40114 ± 1474 -13.7 ± 0.2 0.996 8.0 1.05 2.10 4.20

TE D

k L1 L2 L3 L4 R2 AARD (%) Co-solvent (mol %) AICc

CC

Association model based on van Laar activity coefficient model (Eq. (21))

k W1 W2 W3 W4 W6 R2 AARD (%) Co-solvent (mol %) AICc

-213.1

-207.2

-199.4

-199.1

1.1 1684 ± 50 12 ± 0.5 -4 x 10-4 ± 5 x 10-6 -13 ± 0.2 0.966 7.0 1.05 2.10 4.20

EP

Association model based on Wilson activity coefficient model (Eq. (24))

-215.1

-211.2

-211.4

IP T

Model

-211.7

1.2 598 ± 22 -2 x 10 -4 ±1 x 10 -6 -1130 ± 45 -90426 ± 3600 -11 ± 0.1 0.997 6.0 1.05 2.10 4.20

-186.5 -150.2 -113.6 -170.7 -157.7 -114.3 1.2 1298 ± 20 -24 ± 1 -2.5 x 10-4 ± 5 x 10-6 -13 ± 0.2 0.993 8.0 1.05 2.10 4.20

1.1 385 ± 10 -45 ± 2 -2.3 x 10-4 ± 2 x 10-6 -10 ± 0.2 0.997 5.0 1.05 2.10 4.20

-190.8 -158.8 -126.7 -190.0 -171.0 -132.1

45

16 14 -1 5 x2.10 / mol.mol

12 10

IP T

8 6 4 2 0 5

10

15

20

25

30

0

N A

-600 -900

-1500 -1800

300

TE D

150

M

T ln (Px2) - C1T

-300

-1200

35

U

P / MPa

SC R

(a)

450

600

(b) 750

900

kg.m-3

Figure 1. (a) Variation of solubilities of TOMAC in neat SCCO2 with pressure at different

EP

temperatures; ■, 313 K; ●, 323 K; ▲, 333 K (b) variation of solubility of TOMAC in neat SCCO2 with density as represented by Eq. (3). Solid lines represent the model predictions based

A

CC

on the MT model (Eq. (3)).

46

1.5

0.9

IP T

S / kg.m-3

1.2

0.6

(a)

0.0 5

10

15

20

25

30

35

U

P / MPa

N

1 0

A

-1 -2 -3

M

ln S

SC R

0.3

-4

TE D

-5 5.4

5.7

(b)

6.0

6.3

6.6

6.9

7.2

ln 

EP

Figure 2. (a) Variation of solubilities of TOMAC in neat SCCO2 with pressure at different temperatures; ■, 313 K; ●, 323 K; ▲, 333 K; (b) variation of solubility of TOMAC in neat

CC

SCCO2 with density as represented by Eq. (4). Solid lines represent the model predictions based

A

on the Chrastil model (Eq.(4))

47 2.0

2.0

1.6

1.6

1.2

S / kg.m-3

S / kg.m-3

2.4

1.2 0.8

0.8 0.4

0.4

10

15

20

25

(a2)

0.0

30

10

35

15

P / MPa 30

15

15

10

5

5 0

10

15

20

25

30

N

(b1)

U

10

35

10

35

15

(b2) 20

25

30

35

P / MPa

A

P / MPa

30

SC R

5 x2.10 / mol.mol-1

20

25

M

30 25

15 10 5 0

TE D

20

20 5 x2.10 / mol.mol-1

5

x2.10 / mol.mol-1

20

0

5

25

25

25

x2.10 / mol.mol-1

20 P / MPa

IP T

(a1) 0.0

15 10 5 0

(c1)

15

20

EP

10

30

35

(c2)

10

15

20

25

30

35

P / MPa

CC

P / MPa

25

Figure 3. Solubilities of TOMAC at (a1, b1, c1) 313 K and (a2, b2, c2) 323 K in the presence of

A

n-hexane as a co-solvent; ■, 1.05 mol % n-hexane; ●, 2.10 mol % n-hexane; ▲, 4.20 mol % nhexane. The solid lines are model predictions based of (a1, a2) modified Chrastil equation (Eq. (5)); (b1, b2) association theory based Wilson activity coefficient model (Eq. (24)); (c1, c2) association theory based van Laar activity coefficient model (Eq. (21)).

48

100

100

10 S / kg.m-3

1

1 0.1

0.1 (a1) 15

20 25 P / MPa

30

10

x2.10 / mol.mol-1

N 1

25

30

35

M

P / MPa

15

20

10

25

30

35

(b2)

15

20 25 P / MPa

30

35

100

10

(c1)

1

10

5

10

EP

5

100

30

1000

x2.10 / mol.mol-1

TE D

1000 x2.10 / mol.mol-1

A

(b1)

20

25

10

5

10

15

20

U

100

100

5

x2.10 / mol.mol-1

1000

10

15

P / MPa

1000

1

(a2)

0.01 35

SC R

10

IP T

S / kg.m-3

10

(c2) 35

1

10

15

20 P / MPa

25

30

35

CC

P / MPa

Figure 4. Solubilities of TOMAC at (a1, b1, c1) 313 K and (a2, b2, c2) 323 K in the presence of

A

n-propanol as a co-solvent; ■, 1.05 mol % n- propanol; ●, 2.10 mol % n- propanol; ▲, 4.20 mol % n- propanol. The solid lines are model predictions of (a1, a2) modified Chrastil equation (Eq. (5)); (b1, b2) association theory based Wilson activity coefficient model (Eq. (24)); (c1, c2) association theory based van Laar activity coefficient model (Eq. (21)).

49

100

100

1

0.1 15

20

25

30

0.1 (a2)

0.01

(a1)

10

1

10

35

15

P / MPa

5 x2.10 / mol.mol-1

100

10

1

25

30

10

35

M TE D

1000

5

100

10

EP

(c1)

10

15

20

P / MPa

15

25

30

35

30

35

(b2)

20

25

30

35

P / MPa

A

P / MPa

x2.10 / mol.mol-1

N

(b1)

20

10

U

100

1000 5 x2.10 / mol.mol-1

5 x2.10 / mol.mol-1

1000

15

25

SC R

1000

10

20 P / MPa

IP T

S / kg.m-3

S / kg.m-3

10

10

100

10

(c2)

1 10

15

20

25

30

35

P / MPa

CC

Figure 5. Solubility of TOMAC at (a1, b1, c1) 313 K and (a2, b2, c2) 323 K in the presence of methanol as a co-solvent; ■, 1.05 mol % methanol; ●, 2.10 mol % methanol; ▲, 4.20 mol %

A

methanol. The solid lines are model predictions of (a1, a2) modified Chrastil equation (Eq. (5)); (b1, b2) association theory based Wilson activity coefficient model (Eq. (24)); (c1, c2) association theory based van Laar activity coefficient model (Eq. (21)).

50

IP T

x2.10 / mol.mol

-1

1000

SC R

5

100

10 1

2 3 X / mol%

4

5

U

0

N

Figure 6. Effect of co-solvent concentration on the solubilities of TOMAC in SCCO2 with co-

A

CC

EP

TE D

M

A

solvents, ■, n-hexane; ●, n-propanol; ▲, methanol; at T = 313 K and P = 30 MPa.