Comparison of Optimized Isotherm Models and Error Functions for

Article pubs.acs.org/jced

Comparison of Optimized Isotherm Models and Error Functions for Carbon Dioxide Adsorption on Activated Carbon Joanna Sreńscek-Nazzal, Urszula Narkiewicz, Antoni W. Morawski, Rafał J. Wróbel, and Beata Michalkiewicz* Institute of Chemical and Environment Engineering, West Pomeranian University of Technology, Szczecin, ul. Pulaskiego 10, 70-322 Szczecin, Poland S Supporting Information *

ABSTRACT: The adsorption of CO2 on commercial activated carbon WG12 and WG12 modified by ZnCl2 and KOH was investigated using a high pressure Sievert’s apparatus. The experimental data were analyzed using Langmuir, Freundlich, Sips, Toth, Unilan, Ftitz−Schlunder, and Redlich−Peterson equations. An error analysis was performed to examine the effect of using different error criteria for the isotherm parameters determination. Five error analysis methods were used: the sum of the squares of errors, the hybrid fractional error function, the average relative error, the Marquardt’s percent standard deviation, and the sum of the absolute errors. The Sips isotherm provided the best quality of fitting for all the experimental data. Error function analysis found that sum of the squares of the errors and hybrid fractional error function provided the best overall results.

1. INTRODUCTION In recent years, carbon dioxide has become the focus of many researchers attention. The atmospheric emission of anthropogenic carbon dioxide caused by burning fossil fuels is one of the main origins of climate change, namely global warming.1,2 In response to this problem there have been many studies of carbon dioxide capture and storage (CCS) or utilization. Absorption, adsorption, and chemical conversion are crucial steps of CCS.3−5 The current commercial operations for CO2 capture using a chemical absorption method with basic liquid amine species as the sorbent is expensive and energy intensive.6 CO2 capture based on an adsorption principle is considered to be more convenient, less expensive, and more energy-efficient. Various types of solid adsorbents have been considered, especially zeolites,7 carbons,8 and metal−organic frameworks.9 Porous carbons have played an important role in CO2 sorption and separation for a long time due to their specific features such as an environmentally friendly nature, low cost, high porous structure, high surface area, and thermal and chemical stability. The adsorption capacity and the performance of the activated carbon adsorption system are predicted from equilibrium sorption isotherms. The analysis of equilibrium of adsorption provides fundamental physicochemical data for evaluating the applicability of sorbent for the uptake of gas. Adsorption equilibrium is described by several types of adsorption isotherm. Usually the equations with two or three parameters are applied10−12 although the equations with four, and even with five parameters are available.13 The parameters of isotherm models express the surface properties and affinity of the adsorbent. The accurate mathematical description of the © 2015 American Chemical Society

equilibrium isotherm is essential to the design of adsorption systems. The two-parameter models can be linearized. Linear regression was used to determine the fitted isotherm. The least-squares method was widely applied to determine the best line fitting to the obtained data. The correlation coefficient R or the coefficient of determination R2 was used to test the goodness of fit of the model.14,15 The simple linear analysis is not possible for a three-parameter, or more, isotherm. The trialand-error optimization method applicable to computer operations was developed for a three-parameter isotherm.16 Linear regression is the most commonly used method, nevertheless it was shown that depending on the way the isotherm equation was linearized, the isotherm parameters and error distributions were different.17 Transformations of nonlinear equations to linear forms alter their error structure and can violate the error variance and normality assumptions of standard least-squares.18,19 The linearization method is an inappropriate technique for determining isotherm parameter values.20,21 The linear regression is most frequently used because of its simplicity, but a nonlinear method has been suggested as a better way to obtain the equilibrium isotherm parameters.17,21 Nonlinear regression gives a more complex and mathematically rigorous method for determining parameter values.22 Nowadays the nonlinear optimization has been found to be the best way to select the most fitted equation.23−25 Nonlinear Received: March 29, 2015 Accepted: October 19, 2015 Published: October 27, 2015 3148

DOI: 10.1021/acs.jced.5b00294 J. Chem. Eng. Data 2015, 60, 3148−3158

Journal of Chemical & Engineering Data

Article

(SBET) was measured by means of the SBET (Brunauer− Emmett−Teller) equation. The total pore volume (Vp) was calculated on the basis of the amount of nitrogen adsorbed at the highest relative pressure. Micropore volume (Vmic) was estimated by Density Functional Theory method. Micrographs were obtained using an ultrahigh resolution field emission scanning electron microscope (UHR FE-SEM Hitachi SU8020) equipped with Secondary Electron (SE) detectors, four quadrant photo-diode backscattered electron detector (PD-BSE). For SEM investigations, samples were mounted on an aluminum stub using a carbon conductive adhesive tape. The X-ray photoelectron spectroscopy measurements were performed in a commercial multipurpose (XPS, LEED, UPS, AES) UHV surface analysis system (PREVAC), which is operating at a base pressure in the low 10−10 mbar range. The UHV system consists of two main chambers. The preparation chamber gives the possibility of cleaning and control of the surface composition by Auger spectroscopy (AES) and lowenergy electron diffraction (LEED). The analysis chamber is equipped with nonmonochromatic X-ray photoelectron spectroscopy (XPS) and kinetic electron energy analyzer (SES 2002; Scienta). Calibration of the spectrometer was performed using Ag 3d5/2 transition. The sample in the form of fine powder was thoroughly degassed prior to measurement so that during XPS measurements the vacuum was in the low 10−9 mbar range. X-ray photoelectron spectroscopy was performed using Al Kα (1486.6 eV) radiation. Charging effects were observed and the correction of the binding energy scale was performed using the C 1s peak at 284.6 eV; however, in case of the Wg12-ZnCl2 sample differential charging was observed which is not possible to correct. 2.3. Measurements of CO2 Adsorption. High pressure CO2 adsorption studies were performed at a temperature of 40 °C and pressure up to 40 using an Intelligent Manometric Instrument (IMI) produced by Hiden Isochema. The method of the measurement is known as Sieverts’ method or the manometric method. This is a stepwise technique using two cells (dosing cell and sample cell containing the sample) separated by a valve. In the beginning the system is evacuated. The valve is closed, and gas is introduced to the dosing cell. After temperature equilibration, the valve is opened and the gas is shared with the sample cell. The difference between the calculated amount of gas before and after the valve is opened is the amount adsorbed by the sample. After temperature equilibration, the valve is closed, the data measurement is taken, and the reference volume is filled with a new amount of gas for the next step. This process continues with the total quantity of gas absorbed determined from the sum of the uptake for each step. About 0.3 g was loaded on a manometric adsorption analyzer with a dossing cell of 4.8635 ± 0.0027 cm3 and a sample cell of 4.9888 ± 0.0002 cm3. The carbons were outgassed for 16 h at 250 °C to 10−5 Torr. The skeletal volumes were estimated by helium pycnometry before the CO2 adsorption. Pure CO2 (4.8) was supplied from a gas cylinder (Messer Polska Sp. z o. o.). The real-time analysis used least-squares regression of two relaxation models in order to extrapolate a value of the asymptote and assessed the time-scale of interaction. This method was used to actively adjust the total time for which data was collected for each isotherm point. Equilibration relaxation kinetics were monitored using a computer algorithm with calculations carried out in real time with equilibrium uptake

regression involves a minimization (or maximization) of the difference between experimental measurements and the mathematical model. The sum of the squares of the errors (SSE) is the most widely used error function.26 The others error functions such as the sum of the absolute errors (SAE), the average relative error (ARE), the hybrid fractional error function (HYBRID), and Marquardt’s percent standard deviation (MPSD) can be also applied to predict the best isotherm. The error functions mentioned here above have been used recently for liquid−solid adsorption systems.27−30 No detailed studies were available so far comparing the accuracy of error functions in predicting the optimum isotherm and also the values of isotherm parameters for CO2− solid adsorption system. Carbon dioxide adsorption using activated carbon modified by ammonia31,32 and amines33,34 is well-known. The enhancement of CO2 adsorption over activated carbon impregnated by KOH was described as well.35 Studies of commercial activated carbon WG12 modified by KOH and ZnCl2 are presented here. It is necessary to emphasize that contrary to the adsorption studies presented by Guolt et al.,34 KOH and ZnCl2 were washed out after the modification route and were not present in resulting materials. The aim of the present research was to investigate the effect of the isotherm type and the method used to derive its parameters on the predictions by the parameters within the models. The two two-parameter and five three-parameter isotherms and five error functions were used to discuss this issue. To the best of our knowledge, such a detailed critical analysis of the adsorption of CO2 on solid adsorbents has not been presented up to now. The enhancement of the CO2 adsorption on commercial activated carbons modified using KOH and ZnCl2 (but not impregnated) was not described as well.

2. MATERIALS AND METHODS 2.1. Adsorbent Preparation. A commercial activated carbon WG12, kindly supplied by Gryfskand Sp. z o. o. Hajnówka, Poland, was used as a starting material. The WG12 samples were treated with KOH (Sigma-Alrdrich) and ZnCl2 (Sigma Alrdich). The mass ratio of WG12/KOH was equal to 1:1. The mass ratio of WG12/ZnCl2 was equal to 1:0.5. The soaking time was 3 h. The obtained mixtures were dried at 200 °C during 10 h and heated at 800 °C, for 1 h under a flow of N2. The resulting carbonaceous materials were repeatedly washed with water, then with a 5 M solution of HCl, and finally with water again until the filtrate reached a neutral pH and became free of chloride ions. Finally these samples were dried again. The obtained carbonaceous materials were denoted as WG12_KOH and WG12_ZnCl2, respectively. 2.2. Characterization of Activated Carbons. Qualitative elemental analysis of the activated carbons was performed by an energy-dispersive X-ray fluorescence spectrometer. (EDXRF), Epsilon3, PANalytical. XRD patterns of the carbons were recorded using PANalytical X-ray Empyrean diffractometer with Cu Kα radiation. The angular speed was 0.033°/s with 0.02° step. Spectra were analyzed using X’Pert HighStore diffraction software. Textural characterization of the activated carbons was made using nitrogen sorption experiments carried out using volumetric gas sorption instrument Quadrasorb ovo, Quantachrome Instruments. Before analysis, samples were outgassed at 250 °C and 1·10−6 bar for 16 h. The specific surface area 3149



Article

where UmT is the constant reflecting maximum adsorption capacity, aT is the Toth constant, and nT is the heterogeneity factor, 0 < nT ≤ 1, For a homogeneous surface nT = 1 and the Toth equation reduces to the Langmuir equation. 3.1.5. Unilan Isotherm. Unilane equations45 assume a heterogeneous surface and approximately continuous energy distribution of site yields.

value determined when 99.9% of the predicted value was achieved. Typical equilibration times were < 40 min. The accuracy of the temperature was better than 0.1 K. Amounts adsorbed were calculated by computer software on the basis of the volume of CO2 dosed using the volume of the three-parameter Redlich−Kwong−Soave cubic equation of state.36 The repeatability of the isotherm points averaged ± 0.7 %. Detailed information can also be found elsewhere.36−39

U=

3. THEORETICAL BASIS OR THEORETICAL CALCULATIONS Many different equations for the mathematical description of adsorption isotherms are known and described in the literature. The equations define the absolute amount of adsorbed gas (U) dependent on the pressure (p). 3.1. The Adsorption Isotherm Equations. 3.1.1. Langmuir Isotherm. The Langmuir40 theory assumes monolayer coverage of adsorbate over a homogeneous adsorbent surface (i.e., all sites are equal, resulting in equal adsorption energies). Once an adsorbate molecule occupies a site, no further adsorption can take place at that site. The sorbent has a finite capacity for the adsorbate. The Langmuir equation41 is applicable to homogeneous sorption where the sorption of each molecule has equal sorption activation energy. U ap U = mL L 1 + aLp (1)

U=

U=

(3)

where UmS is a constant reflecting maximum adsorption capacity, aS is the Sips constant, and nS is the heterogeneity factor. The difference between the Sips and the Langmuir equation is the heterogeneity factor nS, usually lower than 1. The smaller is the value of this parameter, the more heterogeneous is the adsorbent surface. If nS is equal to 1, the Sips equation is reduced to the Langmuir equation and the surface is homogeneous. 3.1.4. Toth Isotherm. Toth isotherm44 is another kind modification of a Langmuir isotherm applicable for heterogeneous adsorption. Most sites have an adsorption energy lower than the maximum. The Toth equation assumes asymmetrical quasi-Gaussian distribution of site energies. U=

UmFSaFSp 1 + UmFSpnFS

(7)

n

SSE =

∑ (qcal − qexp)i2

(8)

i=1

The major drawback is that the magnitude of the errors, thereby the square of the errors increases as the pressure gets higher. Isotherm parameters provide a better fit toward the adsorption obtained at the higher values of pressure. 3.2.2. The Hybrid Fractional Error Function. The hybrid fractional error function (HYBRID) improves the fit at low pressure values, comparing to SSE:48

UmTa Tp (1 + (a Tp)nT )1/ nT

(6)

where UmFS is a constant reflecting maximum adsorption capacity, aFS is the Fritz−Schlunder constant, and nFS is the Fritz−Schlunder model exponent. 3.2. The Error Functions. The standard goodness of linear fit is measured by calculating the Pearson correlation coefficient R. The R describes strength and direction of linear relationships between two numerical variables but does not reflect nonlinear relationships. Even if the nonlinear association is quite strong, R can be equal to zero or be much smaller than 1. To evaluate the fit of the isotherms described above to the experimental data, five different error functions, appropriate to nonlinear models were chosen. The parameters of the isotherms were determined by minimizing the error functions across the CO2 pressure range. The solver add-in with Microsoft’s spreadsheet Excel was used for calculations. 3.2.1. The Sum of the Squares of the Errors. The sum of the squares of the errors (SSE) is the most common used error function:

(2)

UmSaSpnS 1 + a S · p nS

UmRPaRPp (1 + aRPp)nRP

where UmRP is a constant reflecting maximum adsorption capacity, aRP is the Radke−Prausnitz constant, and nRP is the Radke−Prausnitz model exponent. 3.1.7. Fritz−Schlunder Isotherm. The Fritz−Schlunder isotherm model47 can be described as follows:

where KL is the Freundlich constant and nF is the heterogeneity factor. 3.1.3. Sips (Langmuir−Freundlich) Isotherm. The Sips isotherm43 is a combination of the Langmuir and Freundlich isotherms. Sips introduced a finite adsorption limit UmS to the Freundlich equation.

U=

(5)

where UmU is a constant reflecting maximum adsorption capacity, aU is the Unilan constant, and s is the constant dependent on the difference between the minimum and maximum adsorption energy 3.1.6. Radke−Prausnitz Isotherm. The Radke−Prausnitz equation46 is given by

where U is the amount of an adsorbate on the surface in equilibrium, UmL is the constant reflecting theoretical monolayer capacity, and aL is the affinity constant or Langmuir constant related to the apparent energy of sorption 3.1.2. Freundlich Isotherm. The Freundlich isotherm42 is an empirical equation describing an adsorption on heterogeneous surfaces. U = KLpnF

UmU ⎛ 1 + aUpe s ⎞ ln⎜ −s ⎟ 2s ⎝ 1 + aUpe ⎠

HYBRID = (4) 3150

100 n−p

n

⎡ (q

∑ ⎢⎢ i=1

⎣

cal

− qexp)2 ⎤ ⎥ ⎥ qexp ⎦i

(9)



Article

Each sum of the squares of the error values is divided by the experimental adsorption values. The equation includes the number of freedom degrees of the system, for example, the number of experimental points minus the number of parameters of the equation. 3.2.3. The Average Relative Error Function. The average relative error (ARE) is a function49 minimizing the fractional error distribution across the entire range of independent variables: ARE =

100 n

n

∑ i=1

Table 1. Chemical Composition of Activated Carbons Determined by EDXRFa

qcal − qexp qexp

i

(10)

The number of experimental points is included as a divisor. 3.2.4. The Marquardt’s Percent Standard Deviation. The Marquardt’s percent standard deviation (MPSD)50 is expressed as 1 MPSD = 100 n−p

⎛ q − q ⎞2 cal exp ⎟ ∑ ⎜⎜ qexp ⎟⎠ i=1 ⎝ i

element wt/%

WG12

WG12_ZnCl2

WG12_KOH

Al Ca Cl Cu Fe K Mg Na P S Si Zn

1.31 2.66 1.05 0.05 2.38 2.08 0.10 0.70 0.11 1.65 5.12 0.00

1.61 0.97 4.87 0.02 1.43 0.63 0.19 0.00 0.04 1.62 3.08 4.54

0.00 0.03 1.04 0.00 0.16 0.39 0.00 0.00 0.00 0.09 2.41 0.00

a

Standard uncertainty u is u(concentration) = 0.01 wt % (0.95 level of confidence).

n

(11)

and is similar to a geometric mean error distribution modified by the number of degrees of freedom of the system. This function is very popular in adsorption field studies.51 3.2.5. The Sum of the Absolute Errors Function. The sum of the absolute errors (SAE)52 is similar to the SSE. n

SAE =

∑ |qcal − qexp|i i=1

(12)

Thus, the same disadvantage as for SSE, namely better fit at high pressure, is observed. 3.3. Optimization of Error Functions. The choice of error function can affect the derived isotherm parameters. The optimum parameters are difficult to identify because a different set of isotherm parameters can be obtained depending on the error function.53 The meaningful comparison between the parameter sets can be made by so-called “sum of the normalized errors” (SNE) described by Porter et al.54 Briefly, to calculate SNE, the values of the errors obtained for each error function for each set of isotherm constants were divided by the maximum errors for that error function.

Figure 1. EDS analysis of the activated carbons.

corresponding to the kalsilite, KAlSiO4, were identified. At the spectra of WG12_ZnCl2, peaks of kalsilite were not observed but new distinguished signals were detected. These signals can be assigned to Znl‑xFexAl2O4 spinels57 but also to hercynite, Fe2+Al2O4.58 At the XRD patterns of WG12_KOH only characteristic signals from carbon were observed. These findings were consistent with EDXRF and EDS results. FE-SEM images were taken to observe the surface topography of the activated carbons (Figure 3). The surface of the raw material (WG12) was fairly smooth, with few cracks. The picture of materials after chemical treatment show that the activation stage produced extensive external surfaces with cavities and pores. FE-SEM observations were consistent with nitrogen sorption results (Table 2). The nitrogen sorption method was adopted to investigate the textural characteristics of activated carbons. The chemical treatment of WG12 increased BET specific surface area, micropore volume, and total pore volume of the produced adsorbents. The changes were more significant when KOH was used. This was attributed to KAlSiO4 dissolving in KOH solution and the reaction of carbon with KOH at high temperature. Development of new micro- and mezopores and enlargement of micro- and mezopores took place. Figure 4 presents the survey spectrum of all samples. The zinc-treated sample was measured in a wider range in order to visualize Zn 2p transition. The main signals were C 1s and O

4. RESULTS Table 1 shows chemical composition of activated carbon WG12 before and after modifications determined by EDXRF. WG12 contained alumina, calcium, chlorine, iron, calcium, sulfur, silicon, sodium, and traces of copper, magnesium, phosphorus. Most of the elements were partially eliminated during activation with ZnCl2. However, zinc and chlorine content increased. After KOH treatment Al, Cu, Mg, Na were completely eliminated and Ca, Fe, K, S nearly eliminated. These results were confirmed by EDS examinations of the samples (Figure 1) Figure 2 shows X-ray diffraction patterns of the activated carbon. All the samples showed three signals (002), (100), and (110), which indicated a partially graphitic structure of the activated carbon.55 These signals were very broad and the peaks (004), (101), and (006), typical for high graphitized carbons,56 were not observed. The degree of graphitization of all activated carbon was not high. At the XRD patterns of WG12, the signals 3151



Article

Figure 2. XRD patterns of activated carbons, vertical lines correspond to KAlSiO4, JCPDS 11-0579 (WG12) and Znl‑xFexAl2O4, JCPDS 82-1583 (WG12_ZnCl2).

Figure 3. FE-SEM micrographs of activated carbons.

Table 2. Textural Properties of Activated Carbons and pHa SBET activated carbon WG12 WG12_ZnCl2 WG12_ KOH

2. −1

m g

1186 1374 1800

Vp 3. −1

cm g

0.572 0.674 0.893

Vmic 3. −1

cm g

0.420 0.484 0.734

dHe g·cm−3

pH

2.16 2.21 2.31

10.11 6.80 6.87

a Standard uncertainties u are u(SBET) = 1 m2.g−1, u(Vp) = 0.001 cm3.g−1, u(Vmic) = 0.001 cm3.g−1, u(dHe) = 0.01 g·cm−3, u(pH) = 0.01 (0.95 level of confidence).

1s. However, there were visible additional small signals marked on the spectra. The elemental surface concentration is given in Table 3. The spectrum of C 1s signal is presented in Figure 5. There is a visible main peak at about 284.6 eV and the long tail. The tail consists of different bonds of carbon with other elements such as oxygen in different groups such as a carboxyl or ketone group. The spectra of all samples looks similar;

Figure 4. XPS survey spectrum. The main transitions are denoted on the spectrum. 3152



Article

Table 3. Elemental Surface Concentration on the Basis of XPS Studiesa atom/%

WG12

WG12_ZnCl2

Al Ca Cl Cu Fe K Mg Na P S Si Zn C O

0.36

2.4

0.32

0.25

WG12_KOH

1.8

0.78 89.7 7

1.79 1.13 82.3 12.08

2.3

Figure 6. XPS K 2s transition. Samples WG12_KOH and WG12_ZnCl2 contain potassium below the detection level.

87.9 9.8

a Standard uncertainty u is u(concentration) = 0.01 wt % (0.95 level of confidence).

Figure 7. XPS Zn 2p doublet. Splitting of the individual transitions is not a chemical shift but results from differential charging of the sample. Figure 5. XPS C1 s signal for three ACs. The main peak corresponds to elemental carbon and the broad shoulder on the left is attributed to carbon bound with different groups containing oxygen like COOH, CO, etc.

compound. One can conclude from the amount of Al that the oxygen comprised in this compound is about 5 atom %. The total oxygen in the WG12_ZnCl2 sample is about 12 atom % compared to 7.2 atom % and 9.8 atom % for WG12 and WG12_KOH, respectively. This allows the possibility to understand the O 1s signals presented in Figure 8. Signal O

therefore, one can conclude that during preparation the surface of carbon does not undergo chemical changes. Figure 6 presents K 2s signal. Only the WG12 sample contains potassium above detection level. One can conclude that during preparation, in the samples WG12_KOH and WG12_ZnCl2 the potassium from the surface was washed out. Figure 7 shows the Zn 2p1/2 and Zn 2p3/2 signal observed in the WG12_ZnCl2 sample. The signal is too broad to be explained with only a chemical shift. If one deconvolutes the 2p3/2 transition with two components then their positions will be 1022.5 and 1026.55 eV. Literature review gives 1022.5 eV, 1023.1 eV, and 1022.0 eV for ZnO, ZnCl2, and Zn4Si2O7(OH2)·2H2O, respectively.59−61 Therefore, the component with position 1026.55 eV cannot be explained by chemical shift. It is the result of charging of the poorly conducting grains of material. XRD analysis suggests that this is the Znl‑xFexAl2O4 phase, and one can expect a chemical position of the 2p3/2 signal similar to that for ZnO. Moreover the surface concentration of chlorine is too small to support the ZnCl2 form of zinc in the sample. One should also note that the ratio of Zn/Al is about 1:2, that is, the same as that in the suggested

Figure 8. XPS O 1s transition. Very broad signal in the case of the WG12_ZnCl2 sample results from differential charging. 3153



Article

Langmuir isotherm does not provide a good model for carbon dioxide adsorption on WG12 and modified WG12 activated carbons. As indicated by the SNE, the parameter set that produces the best overall Langmuir fit are SSE for both WG12 and WG12_ZnCl2 and HYBRID for WG12_KOH. The theoretical Langmuir isotherms and experimental data are illustrated in Supporting Information Figure S1. The Freundlich isotherm constants and error functions obtained for WG12, WG12_ZnCl2, and WG12_KOH are presented in Table 5. The parameter sets of all the error

1s in the WG12_ZnCl2 sample can be divided into a signal similar to that for WG12 (about 7 atom %) and a signal originating from Znl‑xFexAl2O4 compound which is charged because of its insulating properties (about 5 atom %). Position of the O 1s signal in the case of sample WG12_KOH is 532.6 eV. Oxygen gives transitions at 530.4 eV and 531.8 eV for ZnO62,63 and A2O3, respectively.61 Similarly like it was in case of Zn 2p3/2 transition it is expected that the Znl‑xFexAl2O4 phase is charged and it influences the O 1s signal. It is worth noting that the peak originating from sample WG12 is asymmetric compared to sample WG12_KOH. One can conclude that the shoulder at lower values of binding energies corresponds to potassium bound with oxygen. The sets of CO2 adsorption isotherm parameters and error functions including SNE are presented in Tables 4−10. A comparison of the SNE was undertaken and thereby the isotherm constants which would provide the closest fit to the measured data were found.

Table 5. Freundlich Isotherm Constants with Error Analysisa SSE

Table 4. Langmuir Isotherm Constants with Error Analysisa SSE UmL aL SSE HYBRID ARE MPSD SAE SNE

8.524 0.186 0.8249 1.1560 1.3279 5.0166 0.9218 0.3654

UmL aL SSE HYBRID ARE MPSD SAE SNE

12.974 0.110 0.8564 1.3872 2.6650 4.8425 0.9223 0.7898

UmL aL SSE HYBRID ARE MPSD SAE SNE

15.685 0.110 2.0054 3.1106 5.6415 10.0549 2.2028 1.4855

HYBRID

ARE

WG12 8.193 8.256 0.223 0.229 3.6048 17.1565 2.9168 14.9745 3.0358 14.7127 5.7443 16.6684 3.2507 15.8881 0.7049 2.9750 WG12_ZnCl2 12.320 11.829 0.132 0.154 2.6701 13.6782 1.7994 10.0381 2.4479 9.0806 3.5896 9.5681 2.4165 12.8803 0.8582 3.4703 WG12_KOH 14.749 14.061 0.138 0.164 4.4994 15.5772 3.0225 11.3994 3.9839 10.3321 5.8640 10.8991 4.0899 14.6354 1.2534 3.4927

MPSD

SAE

7.302 0.317 29.5918 26.4162 25.8135 23.9220 28.2914 5.0000

8.530 0.196 3.7321 4.2206 4.1913 8.4012 3.5271 0.9241

11.227 0.171 20.8267 15.4856 12.5752 12.0920 19.7563 5.0000

12.992 0.112 3.9417 4.3802 5.7287 7.5953 3.8706 1.7517

13.267 0.185 23.3730 17.3841 14.3542 13.8072 22.1292 5.0000

15.752 0.113 6.1134 6.5656 8.3156 10.8507 5.9789 2.2746

KF nF SSE HYBRID ARE MPSD SAE SNE

1.780 0.411 2.7120 4.0360 7.7284 12.8306 3.3199 1.1889


1.872 0.488 3.8816 6.6607 14.6281 24.5605 5.1379 1.8394


2.289 0.485 4.4808 7.6599 16.1854 27.8967 5.6883 2.1528

HYBRID

ARE

WG12 1.494 1.359 0.469 0.512 9.7943 32.9828 5.0010 18.1370 7.0068 15.3000 11.2127 16.5183 7.3683 26.2601 1.2629 2.8643 WG12_ZnCl2 1.482 1.291 0.562 0.618 15.6551 40.1045 6.9218 20.4114 10.3777 17.3201 16.3607 18.9117 9.5235 28.1406 1.5541 2.8140 WG12_KOH 1.871 1.653 0.549 0.598 14.5055 32.1987 6.8494 17.5468 9.9489 15.3510 15.3317 16.3905 9.7394 24.2128 1.6167 2.7626

MPSD

SAE

1.253 0.547 74.2938 37.5759 23.3935 19.4478 60.4659 5.0000

1.649 0.425 6.9267 7.1913 9.5584 12.3556 6.4126 1.4346

1.178 0.656 87.2362 42.5959 26.2525 22.9592 63.1905 4.9348

1.650 0.517 8.4571 9.1212 13.0636 16.8164 7.8087 1.6170

1.549 0.629 67.1046 34.0428 21.5462 19.4599 51.8099 4.6976

2.083 0.506 9.0834 10.0143 14.0928 18.0299 8.4093 1.8922

a

Standard uncertainties of all constants are equal to 0.001, uncertainties of all errors are equal to 0.0001 (0.95 level of confidence).

functions are significantly different from each other. The SNE values are the highest of all the isotherm models. On the basis of SNE, the SEE for WG12 and HYBRID for both WG12_ZnCl2 and WG12_KOH produced the best Freundlich fit. However, the best Freundlich fit cannot be acceptable. Figure S2 confirms that the Freundlich equation cannot be used for modeling the carbon dioxide adsorption on WG12 activated carbons. Table 6 present the Sips isotherm constants determined by nonlinear regression and error functions. The three constants UmS, aS, and nS are similar across the range of error functions. The SNE for all adsorbents were the lowest of the all the models. The Sips equation gives a reasonable approximation to the optimum parameter set. The SNE indicate that the SSE parameter set produces the best overall fit for both WG12 and WG12_ZnCl 2 , whereas HYBRID is more suitable for WG12_KOH. The Sips isotherm equations is recommended

a


The numbers in bold type in Tables 4−10 indicate the minimum SNE for the each isotherm and each activated carbon. The numbers underlined indicate the lowest SNE value from all the isotherm and the optimum parameters set for each activated carbon. The Langmuir isotherm constants for WG12, WG12_ZnCl2, and WG12_KOH estimated by nonlinear regression using different error functions are depicted in Table 4. The values of constants UmL and aL are quite similar but the magnitude of the error values is high, especially for the modified WG12. The 3154



Article

Table 6. Sips Isotherm Constants with Error Analysisa SSE UmS aS nS SSE HYBRID ARE MPSD SAE SNE

10.305 0.177 0.763 0.0591 0.0973 0.1795 0.1601 0.0785 0.2249

UmS aS nS SSE HYBRID ARE MPSD SAE SNE

15.745 0.108 0.812 0.0029 0.0060 0.0032 0.2617 0.0031 0.0509

UmS aS nS SSE HYBRID ARE MPSD SAE SNE

20.485 0.104 0.768 0.0101 0.0292 0.0693 0.3042 0.0110 0.1519

HYBRID

ARE

WG12 11.054 11.485 0.166 0.158 0.717 0.697 0.2242 4.3563 0.1109 2.2323 0.1601 1.4820 0.1386 1.5497 0.1827 3.6612 0.2413 3.2958 WG12_ZnCl2 15.490 15.695 0.109 0.108 0.822 0.815 0.0650 1.9038 0.0586 2.0673 0.0626 1.8646 0.2526 3.3599 0.0659 1.9159 0.0790 1.6070 WG12_KOH 19.697 19.284 0.108 0.111 0.787 0.796 0.0889 2.2723 0.0521 1.7197 0.0653 1.6097 0.1891 1.8172 0.0951 2.3107 0.1334 2.2414

MPSD

SAE

11.620 0.157 0.696 8.7052 3.2006 2.0224 1.8199 7.1285 5.0000

11.620 0.157 0.696 1.0018 1.1570 1.3012 1.3524 0.9935 2.0025

14.040 0.123 0.868 8.2318 7.3010 8.0199 5.3412 8.2931 5.0000

15.778 0.108 0.812 0.1770 0.3064 0.1866 1.8132 0.1729 0.4471

18.065 0.119 0.823 6.6848 4.3524 3.7219 2.4631 6.8756 5.0000

20.458 0.105 0.767 0.3773 0.6313 0.8981 1.8514 0.3466 1.2449

The Toth isotherm parameters and error functions for pristine and modified activated carbon are presented in Table 7. Table 7. Toth Isotherm Constants with Error Analysisa SSE

a


UmT aT nT SSE HYBRID ARE MPSD SAE SNE

11.667 0.262 0.567 0.1326 0.2921 0.7999 1.1408 0.1415 0.3923


18.693 0.127 0.590 0.0275 0.0560 0.0632 0.1013 0.0292 0.0627


26.495 0.134 0.507 0.0175 0.0390 0.0547 0.1486 0.0175 0.1707

HYBRID

ARE

WG12 16.436 24.298 0.331 0.383 0.406 0.312 0.7865 8.5442 0.4352 5.6865 0.7606 4.0226 0.9902 3.7216 0.8065 8.5596 0.4367 2.7360 WG12_ZnCl2 20.863 20.969 0.128 0.126 0.533 0.533 0.1372 2.8132 0.0885 2.3019 0.0943 2.3018 0.1012 2.2658 0.1339 2.7456 0.1134 2.5732 WG12_KOH 29.455 29.680 0.136 0.138 0.466 0.461 0.0795 2.1855 0.0431 1.3839 0.0510 1.2422 0.0839 0.8782 0.0784 2.1673 0.1478 2.9536

MPSD

SAE

44.938 0.408 0.241 18.9091 11.5970 7.2963 4.6932 19.0439 5.0000

11.667 0.261 0.565 1.5198 2.0673 2.6083 3.4551 1.4886 1.4305

22.536 0.127 0.503 6.0131 4.2154 4.3913 3.9713 5.9106 5.0000

18.668 0.128 0.589 0.6730 0.9287 0.9431 1.1690 0.6487 0.9511

34.541 0.131 0.422 4.4381 2.2563 1.8532 1.0899 4.4009 4.8502

26.493 0.134 0.506 0.5384 0.7688 0.7961 1.2820 0.5345 2.0131

a


for analysis of the experimental data. The same can be concluded on the basis of Figure 9. The experimental adsorption isotherm fit very well with Sips equation model regardless the error function.

The values of the parameters for modified WG12 do not vary significantly across the range of error methods but shows deviation over a wide range for WG12. Although, the SNE values for both WG12_ZnCl2 and WG12_KOH are very low, the SNE of the Sips isotherm are lower. On the basis of SNE one can conclude that the closest fits are produced by SSE and HYBRID. From Figure S3 it is evident that the Toth equation can be used for modified WG12 but not for pristine activated carbon. Table 8 present the Unilan isotherm constants and error functions. The values of the parameters vary across the range of error methods and the values of aU show significant deviation over a wide range. Based on the sum of normalized errors, the SSE parameter set produces the best overall fit for all the WG12 activated carbons. Although the experimental adsorption isotherm fitted quite well with Unilan equation model, the MPSD is not recommended as an error function (Figure S4). The Fritz−Schlunder and Radke−Prausnitz isotherms constants and error analyses are presented in Tables 9 and 10, respectively. The Fritz−Schlunder and Radke−Prausnitz isotherms parameters of all the error methods are significantly different from each other. The differences for Fritz−Schlunder are higher than for Radke−Prausnitz. It is interesting to note

Figure 9. Experimental data for WG12 (□), WG12_ZnCl2 (○), WG12_KOH (△), and Sips isotherms obtained by SSE (gray ···), HYBRID (black ···), ARE (black −−−), MPSD (−·−·−), SAE (gray −−−). 3155



Article

Table 8. Unilan Isotherm Constants with Error Analysisa SSE UmU aU s SSE HYBRID ARE MPSD SAE SNE

10.500 0.099 2.267 0.3198 0.3426 0.4631 2.8028 0.4350 0.2257

UmU aU s SSE HYBRID ARE MPSD SAE SNE

18.844 0.039 2.582 0.0767 0.1034 0.1791 0.8100 0.0940 0.1596

UmU aU s SSE HYBRID ARE MPSD SAE SNE

26.300 0.025 3.117 0.1560 0.2231 0.4850 2.2539 0.1583 0.3576

HYBRID

ARE

WG12 12.519 11.421 0.056 0.076 3.094 2.807 1.3417 10.7926 1.0963 9.9755 1.1595 9.9575 3.2656 12.2627 1.2358 10.2720 0.4014 2.5651 WG12_ZnCl2 33.499 31.876 0.004 0.005 4.945 4.810 0.4463 5.5912 0.3444 4.7904 0.4302 4.6052 0.8307 5.2707 0.3635 4.9782 0.2822 2.8419 WG12_KOH 43.126 26.340 0.003 0.024 5.394 3.320 0.7705 6.6798 0.5648 5.6710 0.7772 5.6505 1.5982 6.4533 0.7303 6.4641 0.4358 2.8876

MPSD

SAE

17.999 0.008 5.508 23.1541 20.8829 20.4598 18.2983 22.1188 5.0000

15.961 0.022 3.959 1.7813 2.0980 2.1345 6.4574 2.0741 0.7284

30.500 0.005 4.883 10.9624 9.0365 7.9321 7.4350 9.7182 5.0000

25.515 0.014 3.717 1.1032 1.2437 1.4612 3.4521 1.1517 1.0053

39.459 0.003 5.488 13.0625 10.7491 9.5337 8.6144 12.7542 5.0000

26.373 0.024 3.132 1.5286 1.8907 2.4754 5.5366 1.4608 1.3098

Table 9. Fritz-Schlunder Isotherm Constants with Error Analysisa SSE

HYBRID

ARE

MPSD

SAE

4.403 1.902 0.592 22.7905 16.8620 9.4836 7.7210 22.7357 5.0000

0.483 4.730 0.844 1.9604 2.7645 4.4086 5.3593 1.9100 1.4930

0.649 4.014 0.694 9.1627 6.2108 4.8773 4.3394 7.3677 5.0000

0.397 5.407 0.775 1.0851 1.4942 1.9678 2.5546 1.2990 1.5275

0.923 4.124 0.652 6.3007 5.6788 3.1817 2.7377 7.4707 4.8609

0.495 5.858 0.748 1.4922 1.5844 2.7752 3.1799 1.2376 2.5537

WG12

a


UmFS aFS nFS SSE HYBRID ARE MPSD SAE SNE

0.487 4.689 0.840 0.2298 0.4981 1.8917 2.6364 0.2350 0.5909


0.328 6.145 0.808 0.0725 0.1435 0.4113 0.5954 0.1454 0.2723


0.549 5.519 0.732 0.1557 0.1632 0.9691 0.9458 0.1171 0.6711

0.986 2.764 3.281 2.132 0.745 0.626 1.3303 10.7744 0.8724 8.3738 1.7082 5.7710 2.3301 6.1912 1.3283 10.7234 0.6504 2.8514 WG12_ZnCl2 0.430 0.546 5.210 4.448 0.765 0.725 0.3215 4.6667 0.2198 3.4389 0.3381 2.8933 0.4174 3.0295 0.2589 3.8168 0.2711 2.8724 WG12_KOH 0.571 0.876 5.433 4.199 0.727 0.662 0.2098 3.3440 0.1977 3.1636 0.5851 2.1499 0.5163 2.2364 0.2456 3.7440 0.4473 2.9680

a


that the SNE values are considerably high and for each activated carbon are pairwise similar. The best overall fit is obtained by SSE for WG12 and by HYBRID for modified WG12 using both Fritz−Schlunder and Radke−Prausnitz equations. Neither Fritz−Schlunder nor Radke−Prausnitz plots fit the experimental data (Figures S5 and S6) although some of the data at lower pressure were within reasonable accord with both models. The SSE error measure produced the parameter set providing the lowest sum of normalized errors in 12 out of 21 systems for all the isotherms examined. The HYBRID error measure was the second best for nine systems.

The equilibrium adsorption of carbon dioxide on pristine activated carbon WG12 and on modified WG12 was examined. The equilibrium results were modeled and evaluated by means of seven different isotherms and five different optimization and error functions. On the basis of the sum of normalized errors the comparison of error function was made, and the best isotherm equations were found. The order of goodness for all tested models for the description of adsorption equilibrium isotherms CO2 on WG12 is Sips > Unilan > Langmuir > Toth > Fritz−Schlunder > Radke−Prausnitz > Freundlich and on both WG12_ZnCl2 andWG12_KOH is Sipis > Toth > Unilan > Fritz−Schlunder > Radke−Prausnitz > Langmuir > Freundlich. The error function analysis found that sum of the squares of the errors and hybrid fractional error function provided the best overall results. The Sips isotherm gives the best prediction as it is the best fit model with the experimental data. On the basis of UmS maximum adsorption capacity values were found: 10.305, 15.745, 15.74 mmol/g for WG12, WG12_ZnCl 2, and WG12_KOH respectively. Taking into account the values of nS it is evident that KOH treatment does not change heterogeneity of the surface, but the ZnCl2 treatment makes the surface slightly more homogeneous.

5. CONCLUSIONS On the basis of EDXRF investigations it was found that WG12 contained Al, Ca, Cl, Cu, Fe, K, Mg, Na, P, S, Si that blocked pores and made specific surface area low. Treating WG12 by ZnCl2 eliminated some amount of elements but also resulted in reaction between them. The Znl‑xFexAl2O4 spinels were able to be produced. This caused an increase of specific surface area and pore volume. KOH activation eliminated a significant amount of elements. The specific surface area and pore volume, especially micropore volume were considerably higher. The increase specific surface area and pore volume increased CO2 adsorption. The physical adsorption would be assumed as dominating the adsorption process. 3156



Article

(3) Yu, K. M. K.; Curcic, I.; Gabriel, J.; Tsang, S. Ch. E. Recent Advances in CO2 capture and utilization. ChemSusChem 2008, 1, 893− 899. (4) Michalkiewicz, B.; Majewska, J.; Kądziołka, G.; Bubacz, K.; Mozia, S.; Morawski, A. W. Reduction of CO2 by adsorption and reaction on surface of TiO2-nitrogen modified photocatalyst. J. CO2 Utilization 2014, 5, 47−52. (5) Yu, Ch. H.; Huang, Ch. H.; Tan, Ch. S. A review of CO2 capture by absorption and adsorption. Aerosol Air Qual. Res. 2012, 12, 745− 769. (6) Wang, Q.; Luo, J.; Zhong, Z.; Borgn, A. CO2 capture by solid adsorbents and their applications: current status and new trends. Energy Environ. Sci. 2011, 4, 42−55. (7) Xiao, P.; Zhang, J.; Webley, P.; Li, G.; Singh, R.; Todd, R. Capture of CO2 from flue gas streams with zeolite 13X by vacuumpressure swing adsorption. Adsorption 2008, 14, 575−582. (8) Nandi, M.; Okada, K.; Dutta, A.; Bhaumik, A.; Maruyama, J.; Derks, D.; Uyam, H. Unprecedented CO2 uptake over highly porous N-doped activated carbon monoliths prepared by physical activation. Chem. Commun. 2012, 48, 10283−10285. (9) Britt, D.; Furukawa, H.; Wang, B.; Glover, T. G.; Yaghi, O. M. Highly efficient separation of carbon dioxide by a metal-organic framework replete with open metal sites. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 20637−20640. (10) Schell, J.; Casas, N.; Pini, R.; Mazzotti, M. Pure and binary adsorption of CO2, H2, and N2 on activated carbon. Adsorption 2012, 18, 49−65. (11) Schell, J.; Casas, N.; Blom, R.; Spjelkavik, A. I.; Andersen, A.; Hafizovic Cavka, J.; Mazzotti, M. MCM-41, MOF and UiO-67/MCM41 adsorbents for pre-combustion CO2 capture by PSA: adsorption equilibria. Adsorption 2012, 18, 213−227. (12) Shao, W.; Zhang, L.; Li, L.; Lee, R. L. Adsorption of CO2 and N2 on synthesized NaY zeolite at high temperatures. Adsorption 2009, 15, 497−505. (13) Hamdaoui, Q.; Naffrechoux, E. Modeling of adsorption isotherms of phenol and chlorophenols onto granular activated carbon Part II. Models with more than two parameters. J. Hazard. Mater. 2007, 147, 401−411. (14) Ho, Y. S. Isotherms for the sorption of lead onto peat: comparison of linear and non-linear methods. Polym. J. Environ. Stud. 2006, 15 (1), 81−86. (15) Shahmohammadi-Kalalagh, Sh.; Babazadeh, H. Isotherms for the sorption of zinc and copper onto kaolinite: comparison of various error functions. Int. J. Environ. Sci. Technol. 2014, 11, 111−118. (16) Ho, Y. S.; Chiu, W. T.; Wang, Ch. Ch. Regression analysis for the sorption isotherms of basic dyes on sugarcane dust. Bioresour. Technol. 2005, 96, 1285−1291. (17) Kumar, K. V.; Sivanesan, S. Comparison of linear and non-linear method in estimating the sorption isotherm parameters for safranin onto activated carbon. J. Hazard. Mater. 2005, 123, 288−292. (18) Myers, R. H. Classical and Modern Regression with Applications; PWS-KENT; 1990. (19) Ho, Y. S.; Porter, J. F.; Mckay, G. Equilibrium isotherm studies for the sorption of divalent metal ions onto peat: copper, nickel and lead single component systems. Water, Air, Soil Pollut. 2002, 141, 1− 33. (20) Kumar, K. V.; Sivanesan, S. Sorption isotherm for safranin onto rice husk: comparison of linear and non-linear methods. Dyes Pigm. 2007, 72, 130−133. (21) Armagan, B.; Toprak, F. Optimum isotherm parameters for reactive azo dye onto pistachio nut shells: comparison of linear and non-linear methods. Polym. J. Environ. Stud. 2013, 22, 1007−1011. (22) Malek, A.; Farooq, S. Comparison of isotherm models for hydrocarbon adsorption on activated carbon. AIChE J. 1996, 42, 3191−3201. (23) Ho, Y. S. Selection of optimum isotherm. Carbon 2004, 10, 2115−2116.

Table 10. Radke−Prausnitz Isotherm Constants with Error Analysisa SSE

HYBRID

ARE

MPSD

SAE

1.902 4.403 0.592 22.8347 16.8620 8.9554 7.7210 20.5382 5.0000

3.958 0.655 0.797 1.9570 2.7645 4.5289 5.3593 2.1362 1.5535

4.014 0.649 0.694 9.5750 6.2108 4.9102 4.3394 5.2612 5.0000

4.782 0.492 0.745 1.0861 1.4942 1.9429 2.5546 1.6967 1.6609

4.124 0.923 0.652 8.9087 5.6788 2.8786 2.7377 9.2693 4.7244

6.461 0.420 0.772 1.1114 1.5844 3.3336 3.1799 1.0588 2.5180

WG12 UmRP aRP nRP SSE HYBRID ARE MPSD SAE SNE

4.702 0.484 0.841 0.2297 0.4981 1.9755 2.6364 0.3188 0.6172

UmRP aRP nRP SSE HYBRID ARE MPSD SAE SNE

6.316 0.314 0.814 0.0704 0.1435 0.3779 0.5954 0.2657 0.2951

UmRP aRP nRP SSE HYBRID ARE MPSD SAE SNE

6.358 0.432 0.768 0.0727 0.1632 1.1364 0.9458 0.0746 0.6833

3.281 2.089 0.986 2.993 0.745 0.620 1.3377 10.7978 0.8724 8.3738 1.7834 5.7864 2.3301 6.1912 1.0629 9.6061 0.6630 2.8852 WG12_ZnCl2 5.210 4.490 0.430 0.538 0.765 0.728 0.3500 4.8933 0.2198 3.4389 0.3183 2.9024 0.4174 3.0295 0.2661 2.9822 0.2835 2.9208 WG12_KOH 5.433 3.937 0.571 0.993 0.727 0.641 0.3182 4.3879 0.1977 3.1636 0.6478 2.0505 0.5163 2.2364 0.3471 4.5421 0.4647 2.8580

a


■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00294. Experimental data in graphs and tables (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The research leading to these results has received funding from the Polish-Norwegian Research Programme operated by the National Centre for Research and Development under the Norwegian Financial Mechanism 2009−2014 in the frame of Project Contract No. Pol-Nor/237761/98. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Pham, T. D.; Xiong, R.; Sandler, S. I.; Lobo, R. F. Experimental and computational studies on the adsorption of CO2 and N2 on pure silica zeolites. Microporous Mesoporous Mater. 2014, 185, 157−166. (2) Chen, Ch.; Ahn, W. S. CO2 adsorption on LTA zeolites: effect of mesoporosity. Appl. Surf. Sci. 2014, 311, 107−109. 3157



Article

(24) Kumar, K. V. Optimum sorption isotherm by linear and nonlinear methods for malachite green onto lemon peel. Dyes Pigm. 2007, 74, 595−597. (25) Kumar, K. V. Comparative analysis of linear and non-linear method of estimating the sorption isotherm parameters for malachite green onto activated carbon. J. Hazard. Mater. 2006, 136 (21), 197− 202. (26) Sreńscek-Nazzal, J.; Kamińska, W.; Michalkiewicz, B.; Koren, Z. C. Production, characterization and methane storage potential of KOH-activated carbon from sugarcane molasses. Ind. Crops Prod. 2013, 47, 153−159. (27) Wong, Y. C.; Szeto, Y. S.; Cheung, W. H.; McKay, G. Adsorption of acid dyes on chitosan−equilibrium isotherm analyses. Process Biochem. 2004, 39, 695−704. (28) Allen, S. J.; Gan, Q.; Matthews, R.; Johnson, P. A. Comparison of optimized isotherm models for basic dye adsorption by kudzu. Bioresour. Technol. 2003, 88, 143−152. (29) Ho, Y. S.; Porter, J. F.; McKay, G. Equilibrium isotherm studies for the sorption of divalent metal ions onto peat: copper, nickel and lead single component systems. Water, Air, Soil Pollut. 2002, 141, 1− 31. (30) Kumar, K. V.; Porkodi, K. Mass transfer, kinetics and equilibrium studies for the biosorption of methylene blue using paspalumnotatum. J. Hazard. Mater. 2007, 146, 214−226. (31) Biniak, S.; Szymanski, G.; Siedlewski, J.; Swiatkowski, A. The characterization of activated carbons with oxygen and nitrogen surface groups. Carbon 1997, 35, 1799−1810. (32) Vinke, P.; van der Eijk, M.; Verbree, M.; Voskamp, A. F.; van Bekkum, H. Modification of the surfaces of a gas activated carbon and a chemically activated carbon with nitric acid, hypochlorite, and ammonia. Carbon 1994, 32, 675−686. (33) Keramati, M.; Ghoreyshi, A. A. Improving CO2 adsorption onto activated carbon through functionalization by chitosan and triethylenetetramine. Phys. E 2014, 57, 161−168. (34) Houshmand, A.; MohdAshri, W.; Daud, W.; Shafeeyan, M. S. Exploring potential methods for anchoring amine groups on the surface of activated carbon for CO2 adsorption. Sep. Sci. Technol. 2011, 46, 1098−1112. (35) Guo, B.; Chang, L.; Xie, K. Adsorption of carbon dioxide on activated carbon. J. Nat. Gas Chem. 2006, 15, 223−229. (36) Soave, G. Equilibrium constants from a modified Redkh-Kwong equation of state. Chem. Eng. Sci. 1972, 27, 1197−1203. (37) IMI Systems User Manual; Hiden Isochema Ltd.: England, 2011. (38) Rexer, T. F. T.; Benham, M. J.; Aplin, A. C.; Thomas, K. M. Methane adsorption on shale under simulated geological temperature and pressure conditions. Energy Fuels 2013, 27, 3099−3109. (39) Hasell, T.; Armstrong, J. A.; Jelfs, K. E.; Tay, F. H.; Thomas, K. M.; Kazarian, S. G.; Cooper, A. I. High-pressure carbon dioxide uptake for porous organic cages: comparison of spectroscopic and manometric measurement techniques. Chem. Commun. 2013, 49, 9410−9412. (40) Langmuir, I. The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc. 1918, 40, 1361−1403. (41) Langmuir, I. The constitution and fundamental properties of solids and liquids. J. Am. Chem. Soc. 1916, 38, 2221−2295. (42) Freundlich, H. M. F. Uber die adsorption in losungen. Z. Phys. Chem. 1906, 57, 385−470. (43) Sips, R. On the structure of a catalyst surface. J. Chem. Phys. 1948, 16, 490−495. (44) T́ oth, J. Calculation of the BET-compatible surface area from any type I isotherms measured above the critical temperature. J. Colloid Interface Sci. 2000, 225, 378−383. (45) Wang, Y.; Ercan, C.; Khawajah, A.; Othman, R. Experimental and theoretical study of methane adsorption on granular activated carbons. AIChE J. 2012, 58, 782−788. (46) Radke, C. J.; Prausnitz, J. M. Adsorption of organic solutions from dilute aqueous solution on activated carbon. Ind. Eng. Chem. Fundam. 1972, 11, 445−451.

(47) Fritz, W.; Schlunder, E. U. Simultaneous adsorption equilibria of organic solutes in dilute aqueous solution on activated carbon. Chem. Eng. Sci. 1974, 29, 1279−1282. (48) Porter, F.; McKay, G.; Choy, K. H. The prediction of sorption from a binary mixture of acidic dyes using single- and mixed isotherm variants of the ideal adsorbed solute theory. Chem. Eng. Sci. 1999, 54, 5863−5885. (49) Khan, A. R.; Al-Bahri, T. A.; Al-Haddad, A. Adsorption of phenol based organic pollutants on activated carbon from multicomponent dilute aqueous solutions. Water Res. 1997, 31 (8), 2101− 2112. (50) Marquardt, D. W. An algorithm for least squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math. 1963, 11, 431−441. (51) Foo, K. Y.; Hameed, B. H. Insights into the modeling of adsorption isotherm systems. Chem. Eng. J. 2010, 156, 2−10. (52) Ng, J. C. Y.; Cheung, W. H.; McKay, G. Equilibrium studies for the sorption of lead from effluents using chitosan. Chemosphere 2003, 52, 1021−1030. (53) Chan, L. S.; Cheung, W. H.; Allen, S. J.; McKay, G. Error analysis of adsorption isotherm models for acid dyes onto bamboo derived activated carbon. Chin. J. Chem. Eng. 2012, 20 (3), 535−542. (54) Porter, J. F.; McKay, G.; Choy, K. H. The prediction of sorption from a binary mixture of acidic dyes using single- and mixed-isotherm variants of the ideal adsorber solute theory. Chem. Eng. Sci. 1999, 54, 5863−5885. (55) Qi, X.; Blizanac, B.; DuPasquier, A.; Meister, P.; Placke, T.; Oljaca, M.; Li, J.; Winte, M. Investigation of PF6- and TFSI- anion intercalation into graphitized carbon blacks and its influence on high voltage lithium ion batteries. Phys. Chem. Chem. Phys. 2014, 16, 25306−25313. (56) Zhao, J.; Yang, L.; Li, F.; Yu, R.; Jin, C. Structural evolution in the graphitization process of activated carbon by high-pressure sintering. Carbon 2009, 47, 744−751. (57) Waerenborgh, J. E.; Figueiredo, M. O.; Cabral, I. M. P.; Pereira, L. C. J. Powder XRD structure refinements and 57 Fe Mossbauer effect study of synthetic Znl_xFexAl2O4 (0 < x ≤ 1) spinels annealed at different temperatures. Phys. Chem. Miner. 1994, 21, 460−8. (58) Larsson, L.; O’Neill, H. S. C.; Annertsen, H. Crystal chemistry of synthetic hercynite (FeAl2O4) from XRD structural refinements and Mössbauer spectroscopy. Eur. J. Mineral. 1994, 6, 39−51. (59) Gaarenstroom, S. W.; Winograd, N. Initial and final state effects in the ESCA spectra of cadmium and silver oxides. J. Chem. Phys. 1977, 67, 3500−3506. (60) Seals, R. D.; Alexander, R.; Taylor, L. T.; Dillard, J. G. Core electron binding energy study of group IIb-VIIa compounds. Inorg. Chem. 1973, 12, 2485−2487. (61) Wagner, C. D.; Passoja, D. E.; Hillery, H. F.; Kinsky, T. G.; Six, H. A.; Jansen, W. T.; Taylor, J. A. Auger and photoelectron line energy relationships in aluminum−oxygen and silicon−oxygen compounds. J. Vac. Sci. Technol. 1982, 21, 933−944. (62) Nefedov, V. I.; Gati, D.; Dzhurinskii, B. F.; Sergushin, N. P.; Salyn, Y. X-Ray Electron Study of Oxides of Elements. Zh. Neorg. Khim. 1975, 20, 2307−2314. (63) Zhdan, P. A.; Shepelin, A. P.; Osipova, Z. G.; Sokolovskii, V. D. The extent of charge localization on oxygen ions and catalytic activity on solid state oxides in allylic oxidation of propylene. J. Catal. 1979, 58, 8−14.

3158


Comparison of Optimized Isotherm Models and Error Functions for

Recommend Documents