Comparison of silver and palladium nanoparticles loaded on activated carbon for efficient removal of Methylene blue: Kinetic and isotherm study of removal process

Powder Technology 228 (2012) 18–25

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Comparison of silver and palladium nanoparticles loaded on activated carbon for efficient removal of Methylene blue: Kinetic and isotherm study of removal process Mehrorang Ghaedi a,⁎, Sh. Heidarpour b, Syamak Nasiri Kokhdan c, Reza Sahraie d, Ali Daneshfar d, Behnaz Brazesh a a

Chemistry Department, Yasouj University, Yasouj 75918–74831, Iran Department of Chemistry, Payame Noor University, 19395–9697 Tehran, Iran Young Researchers Club, Yasooj Branch, Islamic Azad University, Yasooj, Iran d Department of Chemistry, Ilam University, Ilam, Iran b c

a r t i c l e

i n f o

Article history: Received 23 December 2011 Received in revised form 29 March 2012 Accepted 14 April 2012 Available online 2 May 2012 Keywords: Adsorption Methylene blue Silver nanoparticle loaded on activated carbon (Ag NPs-AC) Palladium nano particle loaded on activated carbon (Pd NPs-AC) Kinetic and thermodynamics of adsorption

a b s t r a c t The objective of this study was to assess and compare the usability of silver and palladium nanoparticles loaded on activated carbon (Ag NPs-AC and/or Pd NPs-AC) for the removal of Methylene blue (MB) molecules from aqueous solutions. Following the optimization of the effect of variables (batch method) including pH, contact time, initial dye concentration and Ag NPs-AC and Pd NPs-AC amounts on MB removal method the kinetic and isotherm studies have been carried out. Based on difference in MB contents (using a UV–vis spectrophotometer) before and after MB adsorption the removal percentage was calculated. The sorption processes followed the pseudo-second-order in addition to intraparticle diffusion kinetic models with good correlation coefficient. The equilibrium experimental data well fitted to the Langmuir models with maximum adsorption capacity of 71.4 and 75.4 mg/g for Ag NPs-AC and Pd NPs-AC, respectively. The obtained results showed that both adsorbents due to their high MB adsorption capacity in short equilibrium times are good alternative as low-cost sorbent in wastewater treatments. © 2012 Published by Elsevier B.V.

1. Introduction Dyes and pigments are widely applied in the textiles, paper, plastics, leather, food and cosmetic industry to color products. Organic dyes appear in many industrial effluents. Most commercial dyes due to their chemical stability and difficulty in decomposition [1] cause serious environmental and health problems such as mutagenic and carcinogenic effects [2]. Such colored effluents reduce the sunlight penetration to the aquatic environment and significantly hinder photosynthetic processes. On the other hand, dyes by reducing oxygen levels in water lead to suffocation of aquatic flora and fauna [3,4]. Many dyes and pigments have toxic, carcinogenic, mutagenic and teratogenic effects on aquatic and human life. Due to dye stability in the presence of light and heat, biodegradation and oxidizing agents in addition to their resistance to aerobic digestion [5], the treatment of wastewater is a difficult task. There is no single process capable for wastewater treatment because of complicated matrices of the matrix [6]. Practically, combination of different water treatment processes is required to efficiently obtain a desired water quality with low cost. Liquid-phase adsorption as the most popular pollutant

⁎ Corresponding author. Tel./fax: +98 741 2223048. E-mail address: [email protected] (M. Ghaedi). 0032-5910/$ – see front matter © 2012 Published by Elsevier B.V. doi:10.1016/j.powtec.2012.04.030

removal procedure generally produces a high-quality treated effluent [7–9]. The adsorption is an excellent alternative selection especially using inexpensive and high adsorption capacity adsorbent without requiring any additional pre-treatment step before application. Adsorption is superior to other wastewater treatment techniques in terms of its initial cost, flexibility and simplicity of design, ease of operation and insensitivity to toxic pollutants [10–12]. Due to unique properties of nanoparticles especially metal based nanoparticles in terms of high ordered structure, high mechanical and thermal strength, high number of vacant reactive surface sites metallic or semi-metallic behavior and high surface area, recently they are widely applied for removal of various toxic materials [13]. Methylene blue (MB) (Fig. 1) (3,7-bis(Dimethylamino)-phenothiazin5-ium chloride) as the selected model compound (thiazine cationic dye) is commonly used for coloring paper, temporary hair colorant, dyeing cottons, wools and so on. Although MB is not considered to be a very toxic dye, it can reveal very harmful effects on living things such as difficulties in breathing, vomiting, diarrhea and nausea [14]. The present work aims to study a convenient and economic method for MB removal from water by adsorption on Ag NPs-AC and/or Pd NPs-AC as new and high capacity adsorbents. Batch studies were carried out involving process parameters such as initial dye concentration, pH, contact time and dosage of adsorbents. Equilibrium and kinetic analyses were conducted to determine the factors that control the rate of adsorption and to

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3. Results and discussion 3.1. Characterization of adsorbent 3.1.1. Structural properties and amount of Ag NPs-AC Fig. 2A shows the UV–vis absorption spectra obtained at different time intervals after mixing AgNO3 aqueous solution with soluble starch aqueous solution at 50 °C. Fig. 1. Chemical structure of Methylen blue.

investigate their influence and to find out the possibility of using this material for dye removal [15–24]. 2. Experimental studies 2.1. Instruments and reagents All chemicals including NaOH, HCl, KCl, Methylene blue (MB) and activated carbon (AC) with the highest purity available are purchased from Merck, Dermasdat, Germany. An accurately weighted amount of MB was dissolved in deionized water to prepare 200 mg/L as stock solution, while the working solution was prepared by diluting this solution. The MB concentration evaluation was carried out using Jusco UV–visible spectrophotometer model V-570 at a wavelength of 431 nm while the pH/ion meter model-686 (Metrohm, Switzerland, Swiss), thermometer Metrohm was used for measurement of pH adjustment. Absorption measurements were carried out on a Perkin Elmer Lambda 25 spectrophotometer using a quartz cell with an optical path of 1 cm. X-ray diffraction (XRD) pattern was collected with an automated Philips X'Pert X-ray diffractometer with Cu Kα radiation (40 kV and 30 mA) for 2θ values over 10–80°. For XRD analyses, solid samples of the Ag nanoparticles were separated from the aqueous suspension by centrifugation at 4000 g with ethanol as an antisolvent and then dried overnight in an oven at 80 °C. The shape and surface morphology of the Ag nanoparticles were investigated by field emission scanning electron microscope (FE-SEM, Hitachi S4160) under an acceleration voltage of 15 kV. Ag NPs-AC and Pd NPs-AC according to our pervious publication [20]. 2.2. Batch adsorption experiments The effect of variables such as pH, amount of adsorbent, contact time, initial dye concentration and temperature on the adsorptive removal of MB was investigated. In all experiments, 50.0 mL of MB in a 100.0 mL Erlenmeyer flasks was agitated on stirrer at 350.0 rpm at fixed control temperature. The obtained experimental data at various times, temperatures and concentrations were fitted to different models to calculate and the kinetics and isotherm parameters of adsorption process at optimum values of all variables were investigated. The pH was adjusted by addition of dilute aqueous solutions of HCl and/or NaOH (1.0 M and 0.1 M). The removal percentage of MB was calculated using the following relationship %MB removal ¼ ððCo –Ct Þ=Co Þ  100

ð1Þ

where Co (mg/L) and Ct (mg/L) are the dye concentration at initial and after time t respectively and the equilibrium adsorption capacity of MB was calculated according to following equation: qe ¼ ðCo −Ce ÞV=W

ð2Þ

where C0 (mg/L) and Ce (mg/L) are the initial and equilibrium dye concentrations in solution, respectively, V the volume of the solution (L) and W is the mass (g) of the adsorbent.

Fig. 2. A: Temporal evolution of UV–visible absorption spectra after addition of AgNO3 solution into soluble starch solution at 50 °C. B: X-ray diffraction pattern of the starch-stabilized Ag nanoparticles. C: FESEM image of the Ag nanoparticles loaded onto activated carbon.

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X-ray diffraction (XRD) pattern of silver nanoparticle powder (Fig. 2B) shows peaks at 2θ angles of 38.17, 44.21, 64.32, and 77.12 that correspond to the [111], [200], [220], and [311] crystal planes that belong to cubic lattice structure [20,25,26] that according to the Debye–Scherrer equation [27] shows that Ag nanoparticles size was around 55 nm. The FESEM image of the Ag NPs (Fig. 2C) shows semi-spherical shape and uniform size distribution of Ag NPs in the range of 15–80 nm. 3.1.2. Structural properties of Pd NPs-AC Fig. 3A(a) shows UV–vis spectrum of aqueous solution of Na2PdCl4 in deionized water showing two strong ligand-to-metal charge-

transfer bands at 245 nm and 290 nm which belong to the hydrolysis product of PdCl3(H2O) −. Following chemical reduction their intensity diminished and show featureless inter-band transition to higher energy which corresponds to zerovalent Pd nanoparticles (absorption toward higher (Fig. 3A(b)) [20,28]. The solution color changes to dark brown after reduction with ascorbic acids due to formation of Pd nanoparticle suspension that was stable for several months [29]. The FESEM images of the activated carbon surface and the Pd nanoparticles deposited on activated carbon (Fig. 3B (a, b)) show the homogeneous and relatively smooth surface of AC, while Pd nanoparticle loaded AC (Pd NPs-AC) surface is highly disperse in the surface without any aggregation and approximately uniform in size

Fig. 3. A: UV–vis absorbance spectra of (a) aqueous Na2PdCl4 solution and (b) Pd nanoparticles suspension. B: (a) Typical TEM image of the starch-stabilized Pd nanoparticles and (b) the electron diffraction (ED) pattern of the Pd nanoparticles. C: FESEM images of (a) the activated carbon and (b) the Pd nanoparticles deposited on activated carbon.

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A 0.4 100 0.2 80 0

pHf-pHi

%R

0 60 40 20 0

2

4

6

8

10

6

8

10

-0.2 -0.4 -0.6

2

3

4

5

6

7

8

-0.8

9

pH

-1

pH

B 1.5

100 1

pHf-pHi

%R

80 60 40 20 0

0.5

0 0

2

4

-0.5

2

4

6

8

10

-1

pH -1.5

pH Fig. 4. A: Effect of system pH on adsorption of MB (7 mg/L) onto Ag NPs-AC (0.02 g) at 25 °C, B: effect of system pH on adsorption of MB (5 mg/L) onto Pd NPs-AC (0.02 g) at 25 °C.

distribution (in the range of 20–60 nm) that has good agreement with the obtained diameter by TEM image. A typical TEM image of the Pd nanoparticles (Fig. 3C(a)) shows narrow particle size distribution (25–90 nm range) that clarifies the exact crystal structure of the Pd nanoparticles, that confirms by ED pattern that the proposed sorbent has an ED pattern (Fig. 3C(b)). Based on cubic structure with the nanocrystalline nature. The rings in electron diffraction pattern can be assigned to the [111], [200], [220], [311], and [222] crystal planes of a face-centered-cubic (fcc) lattice structure [30].

the sample was filtered and the final pH again was measured. Similar procedure was carried out for Pd-NP-AC. The value of pHZPC can be determined from the curve that cuts the pH0 line of the plot Δ pH versus pH0 (Fig. 4A, B). It was found at pH 2.5 and 7.5 for Ag-NPs-AC and Pd-NPsAC. Therefore at low pH due to electrostatic repulsion and at high pH via attraction force the removal percentage significantly increased. At low pH, due to protonation of the functional group of AC both adsorbents have positive charge and via electrostatic repulsion, the removal percentage significantly decreased. In the case of increasing pH adsorbents gets neutral charge and via electrostatic attraction and hydrogen bonding the removal percentage will be increased.

3.2. Effect of pH 3.3. Effect of adsorbent dosage Solution pH affects both aqueous chemistry and surface binding sites of the adsorbents. The effect of initial pH on the removal percentage of MB in the pH range of 2 to 8 at room temperature (at 7 mg/L of MB for Ag NPs-AC and 5 mg/L of MB for Pd NPs-AC) using 0.02 g of both adsorbents at contact time of 15 min was investigated and respective results are presented in (Fig. 4A,B). It was observed that maximum MB removal is obtained at pH of 6.0, 7.0 using Ag NPs-AC and Pd NPs-AC, respectively. As it can be seen in part b of Fig. 4A,B both adsorbents have pHZCP around 7 that has good agreement with experimental result corresponding to the investigation of pH effect. At optimum pH dye adsorbs on both adsorbents via electrostatic attraction. The zero point charge (pHZPC) [31] for the adsorbents was determined by introducing 0.02 g of AgNP-AC into six 100 mL Erlenmeyer flasks containing 0.1 M potassium nitrate solution. Initial pH values of the six solutions were adjusted to 2–7 by addition of few drops of nitric acid or potassium hydroxide. The solution mixtures were allowed to equilibrate in an isothermal shaker (25±1 °C) for 24 h and following centrifugation

The size and amount of adsorbent significantly influence the amount of MB adsorption.By increasing the amount of adsorbents the surface area and adsorption capacity of each adsorbent significantly increased. It was found that by increasing the amount of adsorbents till 0.02 g and by increasing the surface area and reactive sites (silver and palladium atoms) the removal percentage increased rapidly and further addition has not significantly affected the MB removal percentage. Therefore, 0.02 g of both adsorbents was selected for subsequent work (Fig. 5 (A,B)). 3.4. Effect of initial dye concentration on adsorption of MB The influence of MB initial concentration in the range of 2–20 mg/L on its removal percentage and actual amount of adsorbed dye was investigated and results are shown in Fig. 6A, B. At higher concentration of MB despite the actual amount of adsorbed MB, the removal

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A

100

95

90

80

90

%R

Removal (%)

100

85 0.01

70 0.015

0.02

0.025

0.03

Amount of Ag-NP-AC (g)

60

100 50

Removal (%)

90

0

5

80

10

15

20

Dye Initial C(mgL- ) 1

70

B

60

100

50 40 0.005

0.01

0.015

0.02

0.025

90

0.03

Amount of Pd-NP-AC (g) 80

%R

Fig. 5. Effect of amount of Ag NPs-AC on adsorption of MB (7 mg/L) at 25 °C and effect of Pd NPs-AC on adsorption of MB (5 mg/L) at 25 °C.

70

percentage probability due to saturation of adsorbents surface significantly decreases. The high adsorption capacity and fast adsorption procedure may be attributed to high tendency of the soft atom of adsorbents to soft atom of MB through ion–dipole interaction or hydrogen bonding of MB molecule with various functional groups of AC.

60

50

0

5

3.5. Effect of contact time The MB removal percentage onto Pd NPs-AC and Ag NPs-AC at various contact times at 7 and 5 mg/L was investigated to evaluate the required equilibrium time. Short equilibrium time indicates high surface area adsorbent, and its suitability for fast and quantitative removal of dye. It was found that the adsorption rate is rapid at the initial stages (probably due to high ratio of vacant site to adsorbate molecule) and the system reach equilibrium about 9.5 min. The rapid adsorption at the initial contact time can be attributed to the availability of the reactive site of adsorbent, while at higher time due to the slow pore diffusion or saturation of adsorbent the removal rate do not change significantly. As it is obvious, more than 80% of MB removal was achieved in 7.5 min and thereafter the adsorption rate is slow so that up 98% of MB removal occurs at 9.5 min. It seems that at lower time due to high concentration gradient of MB its removal rate is high and sharp.

15

20

25

Fig. 6. Effect initial dye concentration on MB removal at room temperature A: Ag NPsAC, B: Pd NPs-AC.

A plot 1/qe versus 1/Ce should represent a line with slope of 1/Ka Qm and 1/Qm intercept of 1/Qm and respective data are presented in Table 1. The high correlation (R2 > 0.99) coefficient shows that Langmuir isotherms are applicable for the interpretation of MB adsorption onto Ag NPs-AC and Pd NPs-AC over the whole concentration range studies and maximum adsorption capacity of 71.43 mg/g for Ag NPs-AC and 75.4 mg/g for Pd NPs-AC. The difference can be attributed to higher tendency of Pd atom for dye removal. The Freundlich isotherm can be expressed in the linear form as follows [33]: Logqe ¼ logKF þ 1=nlogCe

3.6. Adsorption isotherms Studies of the adsorption isotherms for every adsorption process are necessary to attain some information about the nature of interaction of MB with adsorbents and to evaluate the applicability and efficiency of any new proposed adsorbent [31]. The experimental equilibrium data was fitted to three important and conventional isotherm models like Langmuir, Freundlich and Tempkin isotherms. In the Langmuir isotherm [32] the intermolecular forces decrease rapidly with distance and the predicted monolayer coverage of the adsorbate on the outer surface of the adsorbent is represented in linear form as follows:

1=qe ¼ ð1=Ka Qm Ce þ 1=Qm Þ

10

Dye initial C (mg L-1)

ð3Þ

ð4Þ

where KF ((mg/g)/(mg/L)1/n) and n are isotherm constants that indicate the capacity and intensity of the adsorption, respectively. The 1/n factor also indicates heterogeneity factor. The values of KF and n were obtained from the intercept and slope of the line obtained by plotting log qe versus log Ce and their values are given in Table 1. Furthermore, the low correlation coefficient shows the poor agreement of the experimental data of Freundlich isotherm with the experimental data. A high value of n is indicative of good adsorption over the entire studied concentration range, while small n is indicative of good adsorption at high concentrations but much less fitting experimental data at lower concentrations. A higher value of kF indicates a higher capacity of adsorbents. The Freundlich constants calculated from the linear equations were summarized in Table 1.

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Table 1 Isotherm constant parameters and correlation coefficients calculated for various adsorption MB onto (A): Ag NPs-AC and (B): Pd NPs-AC adsorbents. Model

Condition for applicability

Linear equation

Langmuir

Monolayer adsorption or homogeneous surface

Ce/qe = (1/KaQm) + Ce/Qm

Freundlich

Multi-layer adsorption or non-uniform distribution

log qe = log KF + (1/n) log Ce

Tempkin

Uniform distribution or heterogeneous surface

qe = B1 Ln KT + B1 Ln Ce

Tempkin isotherm model [34] was presented in linear from as follow: qe ¼ BT ln AT þ BT ln Ce

ð5Þ

The adsorption data were analyzed according to the linear form of the Tempkin isotherm. (R 2 ranged from 0.843 to 0.886). A (L/mg) is the equilibrium binding constant corresponding to the maximum binding energy, b (J/mol) is Tempkin isotherm constant and constant B (dimensionless) is related to the heat of adsorption. The values of the Tempkin constants (A and B) and the correlation coefficient are also of this model listed in Table 1 and are higher than the Freundlich value but lower than the Langmuir value. Therefore, the Tempkin isotherm represents a better fit of experimental data than the Freundlich isotherm but the Langmuir isotherm provides the best correlation for the experimental data. This result is expected since MB as a cationic dye tends to adsorb on the adsorbent as monolayer. The multilayer adsorption similarly, Tempkin isotherm follows from an assumption that the heat of adsorption drops linearly with increasing surface coverage. The Freundlich and Tempkin equations fit the experimental data better at low concentrations [35–37]. 3.7. Adsorption kinetics The respective experimental data at various stirring times corresponding to change in removal percentage was fitted to different kinetic models including first-order, second-order, Elovich and intraparticle diffusion models and the requirement and properties of each model are presented in Table 2. In the first‐order kinetic model [38], the value of the rate constant (k1) was obtained from slope of line obtained by plotting log (qe − q)

Table 2 Kinetic parameters for the adsorption of MB onto (A): Ag NPs-AC and (B): Pd NPs-AC adsorbent. Model

Linear equation

First-order kinetic

log(qe − qt) = log(qe)(k1/2.303) t

Second-order kinetic

(t/qt) = 1/k2qe2 + 1/qe (t)

Intraparticle diffusion

qt = kidt1/2 + C

Elovich

qt = 1/β ln (αβ) + 1/β ln(t)

Experimental data

Parameter and unit and their criterion

Parameters value of A

B

k1 × 10- 3 qe (calc) R2 k2 × 10- 4 qe (calc) R2 Kdiff C R2 Β Α R2 qe (exp)

2.303 21.77 0.981 1.598 34.5 0.993 0.740 7.254 0.973 0.147 0.5122 0.982 29.38

2.104 20.843 0.901 1.267 33.2 0.985 0.602 7.212 0.894 0.105 0.3687 0.879

Parameter and unit and their criterion

Parameters value of A

B

Qm (mg/g) Ka (L/mg) R2 1/n KF (L/mg) R2 B1 KT × 10+ 5 (L/mg) R2

71.43 0.056 0.992 0.077 0.029 0.909 2.176 11.84 0.886

75.4 0.062 0.987 0.063 0.030 0.867 2.012 10.49 0.843

versus t (Table 2). In spite of relatively low correlation coefficient of this model and its inappropriateness for analyzing initial stage kinetic data it fails to analyze the experimental data of the entire adsorption process. The low value of R 2 and the too close position of the experimental qe value to the theoretical qe value show inapplicability of this model [39] for interpretation of experimental data. Therefore, the experimental data was fitted to the second‐order rate constant. The second-order model [40] is represented in the linear from as follows: 2

t=q ¼ 1=k2 qe þ 1=qe ðt Þ

ð6Þ

Plotting of t/q versus t shows the linear relation that the value of K2 was calculated from its slope (Table 2). The high correlation coefficients of this model (R 2 ≥ 0.99) over whole adsorption stage in addition to the closeness of theoretical and experimental qe values show the applicability of this model for analyzing experimental data. The Elovich equation in linear form can be represented as [41,42]: qt ¼ 1=β lnð˛α βÞ þ 1=β lnðt Þ

ð7Þ

Plot of qt versus ln (t) leads to a linear that the Elovich parameters can be achieved from its slope and intercept respective recent is presented in (Table 2). Involvement of intraparticle diffusion model [43–45] on the evaluation of kinetic process as the sole mechanism was investigated according to equation qt ¼ kdif t

0:5

þC

ð8Þ

The value of qt was plotted versus t 0.5 MB and the results are shown in Table 2. A value of C as intercept of respective lines is proportional to the thickness of the boundary layer (Table 2). The values of Kdiff and C were calculated from the slope and intercept of the plot of qt versus t 1/2. C value is related to the thickness of the boundary layer and Kdiff is the intraparticle diffusion rate constant (mg/(g.min 1/2)) (Table 2). The plot found to give two lines part with values of t 1/2 and the rate constant Kdiff value was directly evaluated from the slope of the second regression line. The first one of these lines represents surface adsorption at the beginning of the reaction and the second one is the intraparticle diffusion at the end of the reaction [36,37]. 4. Conclusions The new adsorbents (Ag NPs-AC and Pd NPs-AC) have been synthesized and characterized with SEM, XRD and UV–vis. These new adsorbents have been applied for removal of MB in batch sorption and the influence of parameters such as initial MB concentration, time, pH and amount of adsorbents on MB removal was investigated. Analysis of experimental data Langmuir, Freundlich and Tempkin isotherms

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show that the equilibrium data were best fitted and described by the Langmuir model. The kinetics process is can be successfully fitted to second-order kinetic models with involvement of intraparticle diffusion model. 1) Adsorption of MB onto Ag NPs-AC and Pd NPs-AC follows Langmuir model and kinetic of adsorption process follow second other kinetic model. 2) The Ag NPs-AC is applicable for quantities removal of MB at 10 min with adsorption capacity of 34.5 mg/g. 3) The Pd NPs-AC has removal percentage of more than 95% of MB removal at 9.5 min with adsorption capacity of 33.2 mg/g.

Nomenclature Initial dye concentration (mg/L) Co t Time (min) Dye concentration (mg/L) at time t Ct Equilibrium adsorption capacity (mg/g) qe Dye concentration (mg/L) at equilibrium Ce V Volume of solution (L) W Weight of adsorbent (g) Rate constant of pseudo-first‐order adsorption (L/min) k1 Second-order rate constant of adsorption (g /mg. min) k2 h Second-order rate constants (mg/g. min) α Initial adsorption rate (mg/g. min) β De-sorption constant (g/mg) C Intercept of intraparticle diffusion (related to the thickness of the boundary layer) Rate constant of intraparticle diffusion (mg/g. min) Kdiff Maximum adsorption capacity reflected a complete Qm monolayer (mg/g) in Langmuir isotherm model; Langmuir constant or adsorption equilibrium constant (L/mg) Ka Isotherm constant indicate the capacity parameter (mg/g) KF related to the intensity of the adsorption n Isotherm constant indicate the empirical parameter (g/L) related to the intensity of the adsorption T Absolute temperature in Kelvin R Universal gas constant (8.314 J/K. mol) Related to the heat of adsorption (B1 = RT/b) BT Constant related to the heat of adsorption bT Equilibrium binding constant AT K Constant related to the adsorption energy at the D–R isotherm (mol 2 /(kJ 2)) Theoretical saturation capacity at the D–R isotherm, Qm ε Polanyi potential at the D–R isotherm (E) Mean free energy of adsorption Experimental data of the equilibrium capacity (mg/g) qe, exp Equilibrium capacity obtained by calculating from the qe, calc isotherm model (mg/g). Correlation coefficient R2

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