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Application of the Adsorption Potential Theory to Hydrogen Adsorption on Zeolites above Critical Temperature
ACTA PHYSICO-CHIMICA SINICA Volume 23, Issue 6, June 2007 Online English edition of the Chinese language journal Cite this article as: Acta Phys. -Chim. Sin., 2007, 23(6): 813-819.
ARTICLE
Application of the Adsorption Potential Theory to Hydrogen Adsorption on Zeolites above Critical Temperature Xiaoming Du*,
Erdong Wu
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, P. R. China
Abstract:
The adsorption potential theory was applied to the study on the adsorption isotherms of hydrogen on four kinds of
zeolites above critical temperature and under a wide range of pressure. An approximate treatment was used to obtain the pseudo-saturated pressure of supercritical hydrogen and the affinity coefficients of adsorption systems under study. A formula for the generalized adsorption function to describe the supercritical adsorption of hydrogen on zeolites was derived by the analysis of the functional dependence of the adsorption amount on the adsorption potential and the affinity coefficients. The study showed that the affinity coefficients had a linear relation with the adsorption heat, which could be used as a parameter of the generalized adsorption function in characterization of an adsorption system. The fittings of the generalized adsorption function to experimental data exhibited that the hydrogen adsorption on zeolites above critical temperature could be satisfactorily described by the generalized adsorption function. Key Words:
Adsorption potential theory; Hydrogen; Zeolites; Generalized adsorption function; Affinity coefficients
The adsorption potential theory, composed of the DubininRadushkevich (DR) equation and the Dubinin-Astakhov (DA) equation, has been widely used to investigate the gas adsorption phenomena on microporous adsorbents, such as zeolites and activated carbons[1−3]. A prominent advantage of the adsorption potential theory is that, the relationship curve (characteristic curve) between the adsorbate volume and the adsorption potential can be established and the adsorption isotherms at different temperatures can be expressed uniquely by the characteristic curve by simplifying the interaction force between the gas molecules and the surface atoms of adsorbents in the temperature-independent dispersion force[4]. This assumption has been confirmed by a large number of experimental data in subcritical conditions. Recently, the adsorption potential theory was applied to describing the behavior of the supercritical gas adsorptions in nonpolar adsorption systems, such as hydrogen on activated carbons, methane or nitrogen on activated carbons, etc[5−7]. For the polar adsorption systems in supercritical conditions, however, the study on the adsorp-
tion potential theory is limited[8]. Rychlicki et al.[9] suggested that the limitation was due to the interaction force between the gas molecule and the surface atoms of the adsorbent, which was composed of not only dispersion force and repulse force, but also the temperature-dependent electrostatic field force, which would result in no overlap of the characteristic curves of the adsorption system. Actually, Ozawa and his coworkers tried to apply the adsorption potential theory to the polar adsorption systems (N2, CO2, CO, N2O, C2H6, C2H4, Ar, and CH4 on zeolites MS-5A and MS-13X)[8] and the nonpolar adsorption systems (Ar, CH4, N2, and CO2 on molecular sieving carbon, i.e., MSC-5A)[3] in the later 1970s, and provided a simple method to describe these adsorption systems, where the electrostatic field force was introduced as a correction in evaluation of the affinity coefficient of the nonpolar adsorption systems. It was shown that the supercritical adsorption of the gases in the above-mentioned polar adsorption systems could be satisfactorily described. Very few studies on the supercritical adsorption of hydro-
Received: December 1, 2006; Revised: January 22, 2007. * Corresponding author. Email: [email protected]; Tel: +8624-23971952. The project was supported by the fund of the Chinese Academy of Sciences. Copyright © 2007, Chinese Chemical Society and College of Chemistry and Molecular Engineering, Peking University. Published by Elsevier BV. All rights reserved. Chinese edition available online at www.whxb.pku.edu.cn
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
gen on zeolites have been conducted using the adsorption potential theory by far. In this article, therefore, the adsorption isotherms of hydrogen on zeolites in supercritical conditions were analyzed within the framework of the adsorption potential theory. The affinity coefficients of hydrogen-zeolite systems were obtained using nitrogen as a reference adsorbate, and then a formula for the generalized adsorption function to describe the supercritical adsorption of hydrogen on zeolites was derived; moreover, the applicability and influence factors of the function were also discussed. The adsorption isotherms of hydrogen on zeolites were predicted from the derived adsorption function at wider temperature regions.
1
Experimental
1.1
Materials
Four zeolites selected for the studies were commercial products, which are A-type (including NaA and CaA), X-type (NaX), and ZSM-5. Microporous structures of the zeolites have been characterized using small-angle X-ray scattering and nitrogen adsorption[10], and the characteristic parameters are listed in Table 1. Before the adsorption measurements, the zeolite samples were outgassed and dehydrated at 673 K and below 1 Pa for 4 h. The hydrogen gas used was of high-purity grade (99.999%). 1.2
Apparatus and procedures
appear at 77 K and in regions of pressures greater than 4 MPa. This phenomenon has been observed constantly in high-pressure adsorption of the gases. 2.2
Application of the adsorption potential theory
According to the adsorption potential theory, the volume of the adsorbed phase Wi,j for any adsorption system at a temperature and pressure is expressed by a single function f, of the adsorption potential εi,j and the affinity coefficient βi,j: ln(Wi,j/W0,i,j)=f(εi,j/βi,j) (1) where, W0,i,j, ε, β, i, and j denote the saturated adsorption volume of the adsorbent, the adsorption potential, the affinity coefficient, an adsorbate species, and an adsorbent species, respectively. As seen in Eq.(1), if the values of W0,i,j, εi,j, and βi,j are known, the volume of the adsorbed phase Wi,j can be expressed by a single curve representing the universal adsorption function f. Thus, the following task is to determine the values of W0,i,j, Wi,j, εi,j, and βi,j using an appropriate method. In previous studies[3,8], the saturated adsorption volume of the adsorbent W0,i,j can be approximated by the pore volume of the adsorbent. Table 1 lists the pore volumes of the adsorbents of the four zeolites. The volume of the adsorbed phase for hydrogen in zeolite pores is given by equation[8]: WH2,j=ΔNa,j/(ρa−ρg) (2)
High-pressure adsorption apparatus was used to volumetrically measure hydrogen adsorption isotherms at 77, 195, and 293 K under the pressure range of 0−7 MPa[11]. The principle and procedure of measurement were previously described[11]. The free volume of adsorption cell was corrected by zeolites helium density. The Benedict-Webb- Rubin (BWR) equation of state was used to calculate the compressibility factor of hydrogen[12].
2
Results and discussion
2.1
Adsorption isotherms
The measured isotherms for the adsorption of H2 on zeolites in the pressure range of 0−7 MPa at 77, 195, and 293 K are shown in Fig.1(a) (77 K isotherms) and Fig.1(b) (195 K and 293 K isotherms), respectively. The maximum deviations of the adsorption data were within 5%. The isotherms shown in Fig.1 have the features of Type-I[13]. However, the maximums Table 1 Microporous structure parameters of the zeolites Adsorbent NaX ZSM-5 CaA NaA
Specific surface area (m2·g−1) 565 445 428 −
Pore volume (cm3·g−1) 0.265 0.213 0.197 −
Effective pore diameter (nm) 0.9 0.5−0.6 0.5 0.4
Fig.1
Adsorption isotherms of hydrogen on various zeolites at (a) 77 K and (b) 195, 293 K
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
where, ΔNa,j is the amount of the excess adsorption of hydrogen on zeolite, which can be obtained experimentally, ρg is the bulk density of hydrogen, which can be obtained from the p-V-T relations reported in literature[14], and ρa is the density of the adsorbed hydrogen. Several methods[4,8] have been used to estimate ρa; the method recommended by Ozawa et al.[8] is, ρa=ρbexp[−0.0025(T−Tb)] (3) where, ρb is the liquid density, and Tb is the boiling temperature at ambient pressure for the adsorbate. According to the potential theory of Polanyi, the adsorption potential εi,j can be expressed as: εi,j=RTln(ps/p) (4) where, T and p are the equilibrium temperature and pressure, respectively, R is universal gas constant, and ps is the saturated vapor pressure under subcritical conditions. However, as the adsorption occurs at temperatures well above its critical temperature, where no liquid state exists, the saturated vapor pressure of gas becomes meaningless. Therefore, in supercritical adsorption, ps is generally regarded as the quasisaturated vapor pressure. Various workers[4,7,15,16] have used different empirical approaches to estimate ps above the critical temperature; among these, the Dubinin′s empirical equation[4] is most commonly used: ps=pc(T/Tc)2 (5) where, pc and Tc are the critical pressure and the critical temperature, respectively; pc=1.29 MPa, and Tc=33.2 K for hydrogen. It must be pointed out here that although βi,j=1 has been assumed in the following discussion of the characteristic curve, this will not affect the derived results. According to the adsorption potential theory, the relation between the amount of adsorption (or the volume of the adsorbed phase) at any temperature and pressure, and the adsorption potential can be expressed by a single characteristic curve, irrespective of the value of βi,j. The change in the value of βi,j will only induce a shift of the characteristic curve to the left side or the right side, whereas superposition or scatter of the curve will not occur. Fig.2(a) shows the characteristic curve of ln(W/W0)−ε for hydrogen adsorption on zeolite NaX, derived by Eq.(5) for the estimated ps above the critical temperature. It can be seen that the curves are not totally overlapped; certain degrees of scatter are obvious. Ozawa et al.[3] used Eq.(5) to estimate ps above the critical temperature for the adsorption of nitrogen on MSC-5A, but could not obtain a single characteristic curve either. He attributed the phenomenon to the insufficiency of the DA equation used to describe the characteristic curve. Amankwah et al.[7] also applied the Dubinin′s equation to the hydrogen-activated carbon system, and obtained the same results as Ozawa et al. and this study, that is, the characteristic curve of their system is not single. They attributed the problem to the fact that Dubinin′s equation (Eq.(5)) takes into account only the properties of the individual adsorbate above the
critical temperature, without considering the effect of the properties of the adsorption system on the adsorption process. Another common approach to evaluate ps above the critical temperature is the extrapolation of the ps evaluation approach at the subcritical region into the supercritical region. We have thus evaluated ps above the critical temperature for the adsorption of hydrogen on zeolites by equation[17]: T - Tc ΔH × ) (6) T RTc where, ΔH is the heat of vaporization, which is 904 J·mol−1 for hydrogen[18]. By substituting Eq.(6) into Eq.(4), and then making ln(W/W0)−ε plots, the characteristic curves of adsorption of hydrogen on zeolites can be obtained. Fig.2(b) shows the derived characteristic curve for hydrogen on zeolite NaX. Although the above method is still empirical, it can be seen in Fig.2(b) that the characteristic curve for the adsorption of hydrogen on zeolite NaX at 77, 195, and 293 K is nearly single. Similar results were also obtained for other zeolites, such as NaA, CaA, and ZSM-5. We now assume βi,j=1 for the adsorption systems in this study, and a reference adsorption system (N2-NaX) and the N2-CaA system in the literature[8]. The characteristic curves of these adsorption systems derived consequently are shown in Fig.3. A single characteristic curve can be obtained for the same adsorbate, such as hydrogen or nitrogen, but not for different adsorbates. This clearly indicates that the adsorption ps=pcexp (
Fig.2 Characteristic curves for the hydrogen-zeolite NaX system (a) ps values evaluated from Eq.(5); (b) ps values evaluated from Eq.(6)
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
force fields of the adsorbents are similar, and that the distinct difference of the characteristic curve for the adsorption of hydrogen and nitrogen on zeolites is because of the difference in the properties of the adsorbates. Furthermore, f(εi,j/βi,j) (where, βi,j=1) is not a universal adsorption function. To derive the generalized adsorption function f(εi,j/βi,j) for all adsorption systems, it is necessary that an appropriate value of the affinity coefficient βi,j is obtained. However, the theoretical methods used to evaluate βi,j in subcritical conditions cannot be extrapolated into the supercritical region[19], and new methods do not exist at the present stage[20]. Thus, an empirical method reported by Ding et al.[20] was adopted to obtain the βi,j value. The N2-NaX system has been defined as a reference system, i.e., βi,j=1 (i, N2; j, NaX). The values of βi,j for other systems were repeatedly assumed by trails so that the characteristic curves of these systems shifted to the reference system. The trails were continued until the deviation between the characteristic curves of other systems and that of the reference system became minimum. Finally, all characteristic curves were focused onto a single curve, as shown in Fig.4. The βi,j values thus obtained are listed in Table 2. As seen from Table 2 that the βi,j values are comparable within the hydrogen-zeolite systems or the nitrogen-zeolite systems. These results are consistent with those shown in Fig.3. In addition, we have also calculated the βi,j values of hydrogen-zeolite systems (NaX, NaA, and CaA, which are similar in framework structure) using the method proposed by Ozawa et al. for the polar systems[8]. The combination of polarizability (αp=7.9×10−25 cm3) and quadrupole moment (Q=0.66×10−26 esu·cm2) of hydrogen molecule[21] was used in the calculation, and the derived value is 0.42. It is in good agreement with the results obtained from the above empirical method (also see Table 2).
Fig.4
Generalized characteristic curves for the adsorption of H2 and N2 on several zeolites
2.3
Relation between βi,j and heat of adsorption
Since the adsorption systems in this study can be described by a single characteristic curve, the affinity coefficients βi,j of each system must be intimately related to a physical quantity characterizing the interaction between adsorbates and adsorbents. We inferred that the isosteric heats of adsorption will be the most pertinent quantity to be associated with the affinity coefficients βi,j. The isosteric heats of adsorption qi,j for hydrogen-zeolite systems under this experimental conditions and for nitrogen-zeolite systems at 298, 323, and 348 K were obtained by applying the Clausius-Clapeyron equation to the low-pressure regions (below 1 MPa) of the adsorption isotherms[8,11]. The qi,j values obtained are listed in Table 2. Fig.5 shows a plot of βi,j against qi,j. As seen from Fig.5, the affinity coefficients βi,j have a linear relation with the isosteric heats of adsorption qi,j for all systems. From the point of view of the adsorption potential theory, any adsorption system can be described by a single characteristic curve, whereas the differences between the adsorption systems depend on their affinity coefficients associated with the generalized adsorption function. On the other hand, from the point of view of the adsorption force field, the adsorption system is characterized uniquely and intrinsically by the heat of adsorption. Therefore, Table 2 Characteristic parameters for the adsorption system Adsorbate H2
Fig.3 The relation of ln(Wi,j/W0,i,j) and εi,j/βi,j βi,j was tentatively assumed to be unity;
N2 Ar
Adsorbent NaX CaA NaA ZSM-5 NaX* CaA NaX
βi,j 0.41 0.40 0.40 0.39 1.0 1.07 0.73
qi,j/(kJ·mol−1) 4.60 4.12 4.06 3.80 21.4 23.2 14.5
* reference system
Ref. this study this study this study this study [8] [8] [8]
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
Table 3 The fitting values of the coefficients kn in the generalized adsorption function n 1 2 3 4
Fig.5
Linear relationship between the affinity coefficient βi,j and the heat of adsorption qi,j
there must be a certain relationship between the affinity coefficient and the heat of adsorption, and by introducing the heat of adsorption as a parameter into the generalized adsorption function, the essential feature will be revealed from the adsorption experiment. 2.4
Determination of the generalized adsorption function
To obtain an expression for the generalized adsorption function f(εi,j/βi,j), an improvement of the DA equation reported by Ozawa et al.[3] was adopted to describe the adsorption data in this study: ¥ (7) ln(W/W0 ) = å k n (ε/β ) n n =1
where, kn is a constant assumed to be universal for any adsorbate, and n is an integer to be determined experimentally. The n-value was assumed to be 1, 2, 3, and 4, respectively, and then Eq.(7) was fitted to the experimental data of four hydrogen-zeolite systems in this study and nitrogen-zeolite systems in the literature[8]. The results are given in Fig.4, and the values of kn obtained from the fitting are listed in Table 3. As seen from Fig.4, all experimental data can be expressed satisfactorily by Eq.(7) with n=2. For the high order terms with n=3 and 4, however, the fitted lines nearly overlap, and deviate slightly from the experimental data at higher adsorption potential ε. This indicates that the higher n-value (or the higher order terms in Eq.(7)) does not improve the accuracy of Eq.(7) further. For n=1, Eq.(7) becomes a linear function, and there are considerable deviations from the experimental data. The values of kn in the generalized adsorption function mainly depend on the region of temperature and pressure of an adsorption system. The kn of the higher order terms will have significant contributions to the generalized adsorption function, only if the adsorption system has considerably high adsorption potential at low-pressure and high-temperature conditions. For high-pressure conditions, the adsorption is almost saturated, and the associated adsorption potential is very small; thus, the k1 term has predominant contribution to the generalized adsorption function. The adsorption potential in this study is mainly below 20 kJ·mol−1 (see Fig.4). As seen from Table 3,
103k1 −0.21 −0.17 −0.18 −0.17
108k2
1013k3
1017k4
−0.235 −0.123 −0.322
−0.314 0.904
−0.223
for the n-value mentioned above, the contributions from the k1 and k2 terms are considerably more significant than those from k3 and the followed terms. Furthermore, the accuracy of the experimental measurement also has an important influence on kn. The relatively low accuracy of the measurement, resulting from the limitation of the methods available at high-temperature and low-pressure conditions, will also affect the selection of the n-value to a certain extent. It is noticeable that if k2>> k1, k3···, the generalized adsorption function will be reduced to the DA equation, which is a special case of the generalized adsorption function. To illustrate the rationality of n=2, the DA equation was also applied to the experimental data: W/W0=exp[−(ε/E)n] (8) where, E is the characteristic energy of the adsorption system. Linearizing Eq.(8) gives: ln[ln(W0/W)]=n(lnε−lnE) (9) The results of applying Eq.(9) to the adsorption data of hydrogen on zeolite NaX are given in Fig.6. As seen in the figure, the curve representing experimental data has several linear sections with different slopes. Therefore, no constant n-value is obtainable from this curve, whereas the DA equation requires that the line must be linear and the slope of this straight line must have an integral value. This discrepancy indicates that the DA equation is invalid in this study. Applying Eq.(9) to the adsorption data of other systems provides the same result as above. Ozawa et al.[3] in his investigation of adsorption of gases on MSC-5A derived similar results, and provided a rational explanation. He considered that the differences in the n-value were attributed mainly to the differences in the experimental conditions under which the adsorption isotherms
Fig.6
Application of the DA equation to the hydrogen adsorption on NaX zeolite
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
Fig.7 Predicted adsorption isotherms of hydrogen on zeolites by the generalized adsorption function Symbols represent the experimental values, curves represent the values predicted from Eq.(7).
were taken. The data shown in Fig.6 strongly support this view. At 77 K, the n-values depended on the pressure regions. Similarly, the n-values were also associated with temperature. Based on the above discussion, we conclude that the adsorption isotherms in this study cannot be expressed by the DA equation with a constant n-value. In addition, the data in Fig.6 also show that the n-value increases from 1 to 2, and then reduces to 1 with an increase in the adsorption potential, which suggests that Eq.(7) with n=2 as the determined generalized adsorption function is rational. Fig.7 shows the adsorption isotherms of hydrogen on zeolites NaX and ZSM-5 with different framework structures, predicted from the generalized adsorption function (i.e., Eq.(7)) with n=2, at temperature regions of 77−350 K and pressure regions of 0−7 MPa. At the same time, the adsorption isotherms measured experimentally were compared with the predicted isotherms in Fig.7(a). As seen in Fig.7(a), the adsorption data predicted from Eq.(7) with n=2 agree with the experimental data satisfactorily at low-temperature (77 and 195 K) and high-pressure (4−5 MPa) conditions. The deviations between the predicted values and the experimental data are within 5%. However, in regions of low-pressure and high-temperature (293 K), larger deviations occur. The results obtained above are consistent with the properties of the generalized adsorption function in our study. To improve the prediction accuracy of Eq.(7) in wider regions of temperature and pressure (as shown in Fig.7(c, d)), large numbers of experi-
mental data have to be obtained in future.
3
Conclusions
The results obtained from the application of the adsorption potential theory to the supercritical adsorption of hydrogen on zeolites showed that the affinity coefficients βi,j, where nitrogen was defined as a reference adsorbate, of hydrogen-zeolite systems were 0.39−0.41. The expression of the generalized adsorption function was derived, i.e., Eq.(7), by analyzing the dependence of (εi,j/βi,j) on ln(Wi,j/W0,i,j). The fittings of Eq.(7) to the experimental data exhibited that the hydrogen adsorption on zeolites above the critical temperature could be satisfactorily described by the generalized adsorption function when the n-value in Eq.(7) was 2. Especially, the affinity coefficients have a linear relation with the heat of adsorption, which shows that the heat of adsorption can be used as a parameter of the generalized adsorption function in characterization of an adsorption system.
References 1 Dubinin, M. M.; Stoeckli, H. F. J. Colloid Interface Sci., 1980, 75: 34 2 Wood, G. O. Carbon, 2001, 39: 343 3 Ozawa, S.; Kusumi, S.; Ogino, Y. J. Colloid Interface Sci., 1976, 56: 83 4 Dubinin, M. M. Chem. Rev., 1960, 60: 235 5 Li, M.; Gu, A. Z. J. Colloid Interface Sci., 2004, 273: 356 6 Zhou, L.; Zhou, Y. P. Chem. Eng. Sci., 1998, 53: 2531
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7 Amankwah, K. A. G.; Schwarz, J. A. Carbon, 1995, 33: 1313 8 Wakasugi, Y.; Ozawa, S.; Ogino, Y. J. Colloid Interface Sci., 1981, 79: 399 9 Rychlicki, G.; Terzky, A. P. Adsorp. Sci. Technol., 1998, 16: 641 10 Du, X. M.; Wu, E. D. J. Phys. Chem. Solids, 2007, accepted 11 Du, X. M.; Wu, E. D. Chin. J. Chem. Phys., 2006, 19: 457 12 Benedict, M.; Webb, G. B.; Rubin, L. C. J. Chem. Phys., 1940, 8: 334 13 Gregg, S. J.; Sing, K. S. W. Adsorption, surface area and porosity. 2nd ed. New York: Academic Press, 1982: 118−120 14 Zhou, L.; Zhou, Y. P. Chinese J. Chem. Eng., 2001, 9: 110 15 Reich, R.; Ziegier, W. T.; Rogers, K. A. Ind. Eng. Chem. Process.
Des. Dev., 1980, 19: 336 16 Zhou, L.; Li, M.; Zhou, Y. P. Science in China B, 2000, 43(2): 143 17 Nakahara, N.; Hirata, M.; Ohmori, T. J. Chem. Eng. Data, 1975, 20: 195 18 Feng, G. X.; Huang, X. Y.; Shen, P. W.; Zhang, L. H.; Liu, Y. L.; Ren, D. H. Inorganical chemistry. Vol. 1. Rare gases, hydrogen, alkali metals. Beijing: Science Press, 1984: 178−179 19 Sircar, S.; Myers, A. L. AIChE J., 1986, 32: 650 20 Ding, T. F.; Ozawa, S.; Yamazaki, T.; Watanuki, I.; Ogino, Y. Langmuir, 1988, 4: 392 21 Golden, T. C.; Sircar, S. J. Colloid Interface Sci., 1994, 162: 182
ARTICLE
Application of the Adsorption Potential Theory to Hydrogen Adsorption on Zeolites above Critical Temperature Xiaoming Du*,
Erdong Wu
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, P. R. China
Abstract:
The adsorption potential theory was applied to the study on the adsorption isotherms of hydrogen on four kinds of
zeolites above critical temperature and under a wide range of pressure. An approximate treatment was used to obtain the pseudo-saturated pressure of supercritical hydrogen and the affinity coefficients of adsorption systems under study. A formula for the generalized adsorption function to describe the supercritical adsorption of hydrogen on zeolites was derived by the analysis of the functional dependence of the adsorption amount on the adsorption potential and the affinity coefficients. The study showed that the affinity coefficients had a linear relation with the adsorption heat, which could be used as a parameter of the generalized adsorption function in characterization of an adsorption system. The fittings of the generalized adsorption function to experimental data exhibited that the hydrogen adsorption on zeolites above critical temperature could be satisfactorily described by the generalized adsorption function. Key Words:
Adsorption potential theory; Hydrogen; Zeolites; Generalized adsorption function; Affinity coefficients
The adsorption potential theory, composed of the DubininRadushkevich (DR) equation and the Dubinin-Astakhov (DA) equation, has been widely used to investigate the gas adsorption phenomena on microporous adsorbents, such as zeolites and activated carbons[1−3]. A prominent advantage of the adsorption potential theory is that, the relationship curve (characteristic curve) between the adsorbate volume and the adsorption potential can be established and the adsorption isotherms at different temperatures can be expressed uniquely by the characteristic curve by simplifying the interaction force between the gas molecules and the surface atoms of adsorbents in the temperature-independent dispersion force[4]. This assumption has been confirmed by a large number of experimental data in subcritical conditions. Recently, the adsorption potential theory was applied to describing the behavior of the supercritical gas adsorptions in nonpolar adsorption systems, such as hydrogen on activated carbons, methane or nitrogen on activated carbons, etc[5−7]. For the polar adsorption systems in supercritical conditions, however, the study on the adsorp-
tion potential theory is limited[8]. Rychlicki et al.[9] suggested that the limitation was due to the interaction force between the gas molecule and the surface atoms of the adsorbent, which was composed of not only dispersion force and repulse force, but also the temperature-dependent electrostatic field force, which would result in no overlap of the characteristic curves of the adsorption system. Actually, Ozawa and his coworkers tried to apply the adsorption potential theory to the polar adsorption systems (N2, CO2, CO, N2O, C2H6, C2H4, Ar, and CH4 on zeolites MS-5A and MS-13X)[8] and the nonpolar adsorption systems (Ar, CH4, N2, and CO2 on molecular sieving carbon, i.e., MSC-5A)[3] in the later 1970s, and provided a simple method to describe these adsorption systems, where the electrostatic field force was introduced as a correction in evaluation of the affinity coefficient of the nonpolar adsorption systems. It was shown that the supercritical adsorption of the gases in the above-mentioned polar adsorption systems could be satisfactorily described. Very few studies on the supercritical adsorption of hydro-
Received: December 1, 2006; Revised: January 22, 2007. * Corresponding author. Email: [email protected]; Tel: +8624-23971952. The project was supported by the fund of the Chinese Academy of Sciences. Copyright © 2007, Chinese Chemical Society and College of Chemistry and Molecular Engineering, Peking University. Published by Elsevier BV. All rights reserved. Chinese edition available online at www.whxb.pku.edu.cn
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
gen on zeolites have been conducted using the adsorption potential theory by far. In this article, therefore, the adsorption isotherms of hydrogen on zeolites in supercritical conditions were analyzed within the framework of the adsorption potential theory. The affinity coefficients of hydrogen-zeolite systems were obtained using nitrogen as a reference adsorbate, and then a formula for the generalized adsorption function to describe the supercritical adsorption of hydrogen on zeolites was derived; moreover, the applicability and influence factors of the function were also discussed. The adsorption isotherms of hydrogen on zeolites were predicted from the derived adsorption function at wider temperature regions.
1
Experimental
1.1
Materials
Four zeolites selected for the studies were commercial products, which are A-type (including NaA and CaA), X-type (NaX), and ZSM-5. Microporous structures of the zeolites have been characterized using small-angle X-ray scattering and nitrogen adsorption[10], and the characteristic parameters are listed in Table 1. Before the adsorption measurements, the zeolite samples were outgassed and dehydrated at 673 K and below 1 Pa for 4 h. The hydrogen gas used was of high-purity grade (99.999%). 1.2
Apparatus and procedures
appear at 77 K and in regions of pressures greater than 4 MPa. This phenomenon has been observed constantly in high-pressure adsorption of the gases. 2.2
Application of the adsorption potential theory
According to the adsorption potential theory, the volume of the adsorbed phase Wi,j for any adsorption system at a temperature and pressure is expressed by a single function f, of the adsorption potential εi,j and the affinity coefficient βi,j: ln(Wi,j/W0,i,j)=f(εi,j/βi,j) (1) where, W0,i,j, ε, β, i, and j denote the saturated adsorption volume of the adsorbent, the adsorption potential, the affinity coefficient, an adsorbate species, and an adsorbent species, respectively. As seen in Eq.(1), if the values of W0,i,j, εi,j, and βi,j are known, the volume of the adsorbed phase Wi,j can be expressed by a single curve representing the universal adsorption function f. Thus, the following task is to determine the values of W0,i,j, Wi,j, εi,j, and βi,j using an appropriate method. In previous studies[3,8], the saturated adsorption volume of the adsorbent W0,i,j can be approximated by the pore volume of the adsorbent. Table 1 lists the pore volumes of the adsorbents of the four zeolites. The volume of the adsorbed phase for hydrogen in zeolite pores is given by equation[8]: WH2,j=ΔNa,j/(ρa−ρg) (2)
High-pressure adsorption apparatus was used to volumetrically measure hydrogen adsorption isotherms at 77, 195, and 293 K under the pressure range of 0−7 MPa[11]. The principle and procedure of measurement were previously described[11]. The free volume of adsorption cell was corrected by zeolites helium density. The Benedict-Webb- Rubin (BWR) equation of state was used to calculate the compressibility factor of hydrogen[12].
2
Results and discussion
2.1
Adsorption isotherms
The measured isotherms for the adsorption of H2 on zeolites in the pressure range of 0−7 MPa at 77, 195, and 293 K are shown in Fig.1(a) (77 K isotherms) and Fig.1(b) (195 K and 293 K isotherms), respectively. The maximum deviations of the adsorption data were within 5%. The isotherms shown in Fig.1 have the features of Type-I[13]. However, the maximums Table 1 Microporous structure parameters of the zeolites Adsorbent NaX ZSM-5 CaA NaA
Specific surface area (m2·g−1) 565 445 428 −
Pore volume (cm3·g−1) 0.265 0.213 0.197 −
Effective pore diameter (nm) 0.9 0.5−0.6 0.5 0.4
Fig.1
Adsorption isotherms of hydrogen on various zeolites at (a) 77 K and (b) 195, 293 K
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
where, ΔNa,j is the amount of the excess adsorption of hydrogen on zeolite, which can be obtained experimentally, ρg is the bulk density of hydrogen, which can be obtained from the p-V-T relations reported in literature[14], and ρa is the density of the adsorbed hydrogen. Several methods[4,8] have been used to estimate ρa; the method recommended by Ozawa et al.[8] is, ρa=ρbexp[−0.0025(T−Tb)] (3) where, ρb is the liquid density, and Tb is the boiling temperature at ambient pressure for the adsorbate. According to the potential theory of Polanyi, the adsorption potential εi,j can be expressed as: εi,j=RTln(ps/p) (4) where, T and p are the equilibrium temperature and pressure, respectively, R is universal gas constant, and ps is the saturated vapor pressure under subcritical conditions. However, as the adsorption occurs at temperatures well above its critical temperature, where no liquid state exists, the saturated vapor pressure of gas becomes meaningless. Therefore, in supercritical adsorption, ps is generally regarded as the quasisaturated vapor pressure. Various workers[4,7,15,16] have used different empirical approaches to estimate ps above the critical temperature; among these, the Dubinin′s empirical equation[4] is most commonly used: ps=pc(T/Tc)2 (5) where, pc and Tc are the critical pressure and the critical temperature, respectively; pc=1.29 MPa, and Tc=33.2 K for hydrogen. It must be pointed out here that although βi,j=1 has been assumed in the following discussion of the characteristic curve, this will not affect the derived results. According to the adsorption potential theory, the relation between the amount of adsorption (or the volume of the adsorbed phase) at any temperature and pressure, and the adsorption potential can be expressed by a single characteristic curve, irrespective of the value of βi,j. The change in the value of βi,j will only induce a shift of the characteristic curve to the left side or the right side, whereas superposition or scatter of the curve will not occur. Fig.2(a) shows the characteristic curve of ln(W/W0)−ε for hydrogen adsorption on zeolite NaX, derived by Eq.(5) for the estimated ps above the critical temperature. It can be seen that the curves are not totally overlapped; certain degrees of scatter are obvious. Ozawa et al.[3] used Eq.(5) to estimate ps above the critical temperature for the adsorption of nitrogen on MSC-5A, but could not obtain a single characteristic curve either. He attributed the phenomenon to the insufficiency of the DA equation used to describe the characteristic curve. Amankwah et al.[7] also applied the Dubinin′s equation to the hydrogen-activated carbon system, and obtained the same results as Ozawa et al. and this study, that is, the characteristic curve of their system is not single. They attributed the problem to the fact that Dubinin′s equation (Eq.(5)) takes into account only the properties of the individual adsorbate above the
critical temperature, without considering the effect of the properties of the adsorption system on the adsorption process. Another common approach to evaluate ps above the critical temperature is the extrapolation of the ps evaluation approach at the subcritical region into the supercritical region. We have thus evaluated ps above the critical temperature for the adsorption of hydrogen on zeolites by equation[17]: T - Tc ΔH × ) (6) T RTc where, ΔH is the heat of vaporization, which is 904 J·mol−1 for hydrogen[18]. By substituting Eq.(6) into Eq.(4), and then making ln(W/W0)−ε plots, the characteristic curves of adsorption of hydrogen on zeolites can be obtained. Fig.2(b) shows the derived characteristic curve for hydrogen on zeolite NaX. Although the above method is still empirical, it can be seen in Fig.2(b) that the characteristic curve for the adsorption of hydrogen on zeolite NaX at 77, 195, and 293 K is nearly single. Similar results were also obtained for other zeolites, such as NaA, CaA, and ZSM-5. We now assume βi,j=1 for the adsorption systems in this study, and a reference adsorption system (N2-NaX) and the N2-CaA system in the literature[8]. The characteristic curves of these adsorption systems derived consequently are shown in Fig.3. A single characteristic curve can be obtained for the same adsorbate, such as hydrogen or nitrogen, but not for different adsorbates. This clearly indicates that the adsorption ps=pcexp (
Fig.2 Characteristic curves for the hydrogen-zeolite NaX system (a) ps values evaluated from Eq.(5); (b) ps values evaluated from Eq.(6)
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
force fields of the adsorbents are similar, and that the distinct difference of the characteristic curve for the adsorption of hydrogen and nitrogen on zeolites is because of the difference in the properties of the adsorbates. Furthermore, f(εi,j/βi,j) (where, βi,j=1) is not a universal adsorption function. To derive the generalized adsorption function f(εi,j/βi,j) for all adsorption systems, it is necessary that an appropriate value of the affinity coefficient βi,j is obtained. However, the theoretical methods used to evaluate βi,j in subcritical conditions cannot be extrapolated into the supercritical region[19], and new methods do not exist at the present stage[20]. Thus, an empirical method reported by Ding et al.[20] was adopted to obtain the βi,j value. The N2-NaX system has been defined as a reference system, i.e., βi,j=1 (i, N2; j, NaX). The values of βi,j for other systems were repeatedly assumed by trails so that the characteristic curves of these systems shifted to the reference system. The trails were continued until the deviation between the characteristic curves of other systems and that of the reference system became minimum. Finally, all characteristic curves were focused onto a single curve, as shown in Fig.4. The βi,j values thus obtained are listed in Table 2. As seen from Table 2 that the βi,j values are comparable within the hydrogen-zeolite systems or the nitrogen-zeolite systems. These results are consistent with those shown in Fig.3. In addition, we have also calculated the βi,j values of hydrogen-zeolite systems (NaX, NaA, and CaA, which are similar in framework structure) using the method proposed by Ozawa et al. for the polar systems[8]. The combination of polarizability (αp=7.9×10−25 cm3) and quadrupole moment (Q=0.66×10−26 esu·cm2) of hydrogen molecule[21] was used in the calculation, and the derived value is 0.42. It is in good agreement with the results obtained from the above empirical method (also see Table 2).
Fig.4
Generalized characteristic curves for the adsorption of H2 and N2 on several zeolites
2.3
Relation between βi,j and heat of adsorption
Since the adsorption systems in this study can be described by a single characteristic curve, the affinity coefficients βi,j of each system must be intimately related to a physical quantity characterizing the interaction between adsorbates and adsorbents. We inferred that the isosteric heats of adsorption will be the most pertinent quantity to be associated with the affinity coefficients βi,j. The isosteric heats of adsorption qi,j for hydrogen-zeolite systems under this experimental conditions and for nitrogen-zeolite systems at 298, 323, and 348 K were obtained by applying the Clausius-Clapeyron equation to the low-pressure regions (below 1 MPa) of the adsorption isotherms[8,11]. The qi,j values obtained are listed in Table 2. Fig.5 shows a plot of βi,j against qi,j. As seen from Fig.5, the affinity coefficients βi,j have a linear relation with the isosteric heats of adsorption qi,j for all systems. From the point of view of the adsorption potential theory, any adsorption system can be described by a single characteristic curve, whereas the differences between the adsorption systems depend on their affinity coefficients associated with the generalized adsorption function. On the other hand, from the point of view of the adsorption force field, the adsorption system is characterized uniquely and intrinsically by the heat of adsorption. Therefore, Table 2 Characteristic parameters for the adsorption system Adsorbate H2
Fig.3 The relation of ln(Wi,j/W0,i,j) and εi,j/βi,j βi,j was tentatively assumed to be unity;
N2 Ar
Adsorbent NaX CaA NaA ZSM-5 NaX* CaA NaX
βi,j 0.41 0.40 0.40 0.39 1.0 1.07 0.73
qi,j/(kJ·mol−1) 4.60 4.12 4.06 3.80 21.4 23.2 14.5
* reference system
Ref. this study this study this study this study [8] [8] [8]
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
Table 3 The fitting values of the coefficients kn in the generalized adsorption function n 1 2 3 4
Fig.5
Linear relationship between the affinity coefficient βi,j and the heat of adsorption qi,j
there must be a certain relationship between the affinity coefficient and the heat of adsorption, and by introducing the heat of adsorption as a parameter into the generalized adsorption function, the essential feature will be revealed from the adsorption experiment. 2.4
Determination of the generalized adsorption function
To obtain an expression for the generalized adsorption function f(εi,j/βi,j), an improvement of the DA equation reported by Ozawa et al.[3] was adopted to describe the adsorption data in this study: ¥ (7) ln(W/W0 ) = å k n (ε/β ) n n =1
where, kn is a constant assumed to be universal for any adsorbate, and n is an integer to be determined experimentally. The n-value was assumed to be 1, 2, 3, and 4, respectively, and then Eq.(7) was fitted to the experimental data of four hydrogen-zeolite systems in this study and nitrogen-zeolite systems in the literature[8]. The results are given in Fig.4, and the values of kn obtained from the fitting are listed in Table 3. As seen from Fig.4, all experimental data can be expressed satisfactorily by Eq.(7) with n=2. For the high order terms with n=3 and 4, however, the fitted lines nearly overlap, and deviate slightly from the experimental data at higher adsorption potential ε. This indicates that the higher n-value (or the higher order terms in Eq.(7)) does not improve the accuracy of Eq.(7) further. For n=1, Eq.(7) becomes a linear function, and there are considerable deviations from the experimental data. The values of kn in the generalized adsorption function mainly depend on the region of temperature and pressure of an adsorption system. The kn of the higher order terms will have significant contributions to the generalized adsorption function, only if the adsorption system has considerably high adsorption potential at low-pressure and high-temperature conditions. For high-pressure conditions, the adsorption is almost saturated, and the associated adsorption potential is very small; thus, the k1 term has predominant contribution to the generalized adsorption function. The adsorption potential in this study is mainly below 20 kJ·mol−1 (see Fig.4). As seen from Table 3,
103k1 −0.21 −0.17 −0.18 −0.17
108k2
1013k3
1017k4
−0.235 −0.123 −0.322
−0.314 0.904
−0.223
for the n-value mentioned above, the contributions from the k1 and k2 terms are considerably more significant than those from k3 and the followed terms. Furthermore, the accuracy of the experimental measurement also has an important influence on kn. The relatively low accuracy of the measurement, resulting from the limitation of the methods available at high-temperature and low-pressure conditions, will also affect the selection of the n-value to a certain extent. It is noticeable that if k2>> k1, k3···, the generalized adsorption function will be reduced to the DA equation, which is a special case of the generalized adsorption function. To illustrate the rationality of n=2, the DA equation was also applied to the experimental data: W/W0=exp[−(ε/E)n] (8) where, E is the characteristic energy of the adsorption system. Linearizing Eq.(8) gives: ln[ln(W0/W)]=n(lnε−lnE) (9) The results of applying Eq.(9) to the adsorption data of hydrogen on zeolite NaX are given in Fig.6. As seen in the figure, the curve representing experimental data has several linear sections with different slopes. Therefore, no constant n-value is obtainable from this curve, whereas the DA equation requires that the line must be linear and the slope of this straight line must have an integral value. This discrepancy indicates that the DA equation is invalid in this study. Applying Eq.(9) to the adsorption data of other systems provides the same result as above. Ozawa et al.[3] in his investigation of adsorption of gases on MSC-5A derived similar results, and provided a rational explanation. He considered that the differences in the n-value were attributed mainly to the differences in the experimental conditions under which the adsorption isotherms
Fig.6
Application of the DA equation to the hydrogen adsorption on NaX zeolite
Xiaoming Du et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 813-819
Fig.7 Predicted adsorption isotherms of hydrogen on zeolites by the generalized adsorption function Symbols represent the experimental values, curves represent the values predicted from Eq.(7).
were taken. The data shown in Fig.6 strongly support this view. At 77 K, the n-values depended on the pressure regions. Similarly, the n-values were also associated with temperature. Based on the above discussion, we conclude that the adsorption isotherms in this study cannot be expressed by the DA equation with a constant n-value. In addition, the data in Fig.6 also show that the n-value increases from 1 to 2, and then reduces to 1 with an increase in the adsorption potential, which suggests that Eq.(7) with n=2 as the determined generalized adsorption function is rational. Fig.7 shows the adsorption isotherms of hydrogen on zeolites NaX and ZSM-5 with different framework structures, predicted from the generalized adsorption function (i.e., Eq.(7)) with n=2, at temperature regions of 77−350 K and pressure regions of 0−7 MPa. At the same time, the adsorption isotherms measured experimentally were compared with the predicted isotherms in Fig.7(a). As seen in Fig.7(a), the adsorption data predicted from Eq.(7) with n=2 agree with the experimental data satisfactorily at low-temperature (77 and 195 K) and high-pressure (4−5 MPa) conditions. The deviations between the predicted values and the experimental data are within 5%. However, in regions of low-pressure and high-temperature (293 K), larger deviations occur. The results obtained above are consistent with the properties of the generalized adsorption function in our study. To improve the prediction accuracy of Eq.(7) in wider regions of temperature and pressure (as shown in Fig.7(c, d)), large numbers of experi-
mental data have to be obtained in future.
3
Conclusions
The results obtained from the application of the adsorption potential theory to the supercritical adsorption of hydrogen on zeolites showed that the affinity coefficients βi,j, where nitrogen was defined as a reference adsorbate, of hydrogen-zeolite systems were 0.39−0.41. The expression of the generalized adsorption function was derived, i.e., Eq.(7), by analyzing the dependence of (εi,j/βi,j) on ln(Wi,j/W0,i,j). The fittings of Eq.(7) to the experimental data exhibited that the hydrogen adsorption on zeolites above the critical temperature could be satisfactorily described by the generalized adsorption function when the n-value in Eq.(7) was 2. Especially, the affinity coefficients have a linear relation with the heat of adsorption, which shows that the heat of adsorption can be used as a parameter of the generalized adsorption function in characterization of an adsorption system.
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