Langmuir 1993,9, 2661-2664
2661
Energy Distribution Function Associated with Dubinin's Description of Water Adsorption on Zeolite Y+ M. Rozwadowski,' J. Wloch, K. Erdmann,and J. Kornatowski Institute of Chemistry, Nicholas Copernicus University, Gagarina 7, 87-100 Toruh, Poland Received August 10, 1992. In Final Form: January 11,199P Different equations based on the Polanyi-Dubinin potential theory and applicable to the description of adsorptionisothermson zeolites are presented. Specifically,these equationsare suitable for characterizing the adsorption potential distributions, the parameters of which are related to the energetic and structural heterogeneities of zeolites. The results presented show that the equation which takes into account both the surface and structural heterogeneities as well as the distribution of sizes of micropores participating in the process of adsorption is especially interesting. This equation represents the experimental adsorption data better than the other equations considered. Different heterogeneities of the samples of zeolite Y used in this study were achieved by modification by ion exchange.
Introduction The total heterogeneity of adsorbent, which is the sum of the structural and surface heterogeneities, is usually characterized by the distribution functions of either the adsorption energy1 or the adsorption potential.lP2 These distribution functions may be evaluated from the total adsorption isotherm. A simple and effective way for evaluating the energy distribution function from the total adsorption isotherm is offered by the condensation approximation method.2ts This method offers a satisfactory accuracy especially a t low temperature, as the accuracy increases with a decrease of the adsorption temperature.2 According to this method, the adsorption potential distribution, X ( A ) ,is defined by the relationship7p8 X(A) = -dO,(A)/dA
(1)
where A is the adsorption potential equal to RT ln@$p) (according to the Polanyi-Dubinin potential theory2) and 0, is the total adsorption capacity. The fundamental integral equation for the total adsorption isotherm may be written as follows4-6 0, = J!&@,Q)
f(Q) dQ
(2)
where Ol@,Q) is the isotherm equation describing the local adsorption, f(Q) is the differential distribution of adsorption energy, and Q is the range of variance of energy Q. In this paper we study a series of zeolite Y samples with different concentrations of acidic sites formed as the result of exchangeof hydrogen for sodium. Such sites are a source of energetic heterogeneity of z e o l i t e ~ . ~We J ~ present a comparative study of the applicability of equations based + Presented at the International Symposium Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, Kazimierz Dolny, Poland, July 12-19,1992. 0 Abstract published in Advance ACS Abstracts, August 16,1993. (1)Jaroniec, M.;Maday, R. Physical Adsorption on Heterogeneoh Solids; Elsevier: Amsterdam, 1988; p 320. (2) Jaroniec, M.; Choma, J. In Chemietry and Physics of Carbon; Thrower, P. A., Ed.; Marcel Dekker: New York, 1989; Vol. 22, p 209.
(3) Cerofolini, G. F. Thin Solid Films 1974,23, 129. (4) Ross, 5.;Olivier, J. P. On Physical Adsorption;Wiley Interscience: New York, 1964. (5) Jaroniec, M.; BrHuer, P. Surf. Sci. Rep. 1986,6, 66. (6) Jaroniec, M. Adu. Colloid Interface Sci. 1983, 18, 149. (7) Jaroniec, M. Longmuir 1987, 3, 795. (8) Rozwadowski, M.; Wojsz, R.; Wihiewski, K. E.; Kornatowski, J. Zeohtes 1989, 9, 503. (9) Rozwadowski, M.; Wloch, J.; Erdmann, K.; Komatowski, J. Bull. Soc. Chim. Belg. 1992,101, 463.
7
ion exchange
? ! 0 0001
i
' i ' i ' ' ' idol
t
;.';I P/R
' A ' 4 " ' '0.1
j
'
A'"?
Figure 1. Isotherms of water-vapor adsorption at 298.2 K on parent and hydrogen-exchanged zeolite Y. on the Polanyi-Dubinin potential theory to the description of isotherms of adsorption on zeolitesll with the aim to indicate which of those equations can be recommended as most suitable for characterizing the distribution of the adsorption potential and thus of the adsorption energy of such solids. Experimental Section The parent NaY zeolite was obtained according to the procedure given elsewhere.12 The zeolite samples of various sodium-to-hydrogen ratios were prepared by ion exchange of ammoniumfor sodium and subsequent calcinationof the material. The calcination was carried out in a stream of dry air initially at 653 K for 3 h and then at 723 K for 2 h. The levels of ion exchange were 10, 30, 50, 70, and 95 mol %. Isotherms of adsorption of water vapor were determined at 298.2K in avacuum system equipped with a McBain balance. The pressure of water vapor was measured with a "Baratron",resistance,and differential vacuummeters, dependingon the pressure range. The details of the whole procedure were given previ~usly.~J* The results of adsorption of water vapor on the samples under study are shown in Figure 1. Results and Discussion Based on eq 2, the general adsorption isotherm for a microporpous solid may be represented by the following (10)Barrer, R. M. Zeolites and Ckay Minerals 08 Sorbents and Molecular Sieves; Academic Press: London, New York, San Francisco, 1987; pp 92,171,342. (ll)Rozwadowski, M.; Wloch, J.; Erdmann, K.; Kornabwski, J. Submitted for publication in J. Chem. SOC., Faraday Trona 1. (12) Komatowski, J.; Rozwadowski, M.; Woezek, B. Pol. Pat. Appl. P 278720. (13) Rozwadowski,M.;Wloch,J.;Erdmann,K.;Komatow&i, J. Collect. Czech. Chem. Commun. 1992,57,959.
0743-746319312409-2661$04.QQ10 0 1993 American Chemical Society
Rozwadowski et al.
2662 Langmuir, Vol. 9, No. 10, 1993 integral equation:1"6 (3)
The first factor in the integral may be defined as
O@B)= exp(-By)
(4)
with (5)
whereB is the structural parameter,f(B) is the distribution function of this parameter, characterizing heterogeneity of a microporous solid, R is the universal gas constant, T and p are the temperature and equilibrium pressure of adsorption,respectively,p, denotes the saturation pressure of adsorbate vapor, and B is the affinity coefficient depending only on the nature of the adsorbate. Equation 4 denotes the Dubinin-Radushkevich (DR) isotherm which has been postulated to describe the local adsorption on homogeneous microporous solids.1617 Instead of it, a more general Dubinin-Astakhov (DA) equation18Jgis often used to describe the local adsorption on homogeneous microporous solids:
Table I. Parameters of Equation 4 and Equations 6-8 with n = 3, the Determination Coefficient (DC) and Sorption Capacities at 79% Relative Humidity on Parent and Hydrogen-Exchanged SamDles of Zeolite Y sorption ion exchange, eq capacity, wo, mol % no. dmalmol dmslmol DC 0.9479 0 4 0.323 0.3813 0.9824 6 0.2919 7 0.9812 0.2919 0.9824 8 0.2919 10 4 0.9574 0.309 0.3900 6 0.2990 0.9845 7 0.2990 0.9845 8 0.2990 0.9845 30 4 0.321 0.3958 0.9928 0.2980 6 0.9968 7 0.3142 0.9995 8 0.3135 0.9995 50 4 0.334 0.4031 0.9927 6 0.3116 0.9960 7 0.3285 0.9993 8 0.3271 0.9994 70 4 0.339 0.4042 0.9845 0.3092 6 0.9984 7 0.3116 0.9985 8 0.3117 0.9985 95 4 0.315 0.3195 0.9968 6 0.9713 0.2466 7 0.3001 0.9992 8 0.2707 0.9940
Here, W is the volume of the liquid adsorbate filling the micropores under pressure p and at temperature T , W Ois Equation 7 provides information on heterogeneity of the total volume of the micropores, EOis the characteristic microporous solids but it does not account for the energy of adsorption, k is the structural parameter distribution of sizes of micropores participating in the correlated with micropore dimensions, and n is the process of adsorption. It may be assumed that the parameter characterizing the shape of the distribution of parameter k in eq 7, associated with the range of micropore the adsorption potential in microporous adsorbents. sizes, satisfies the condition: 0 Ik Ikmm. Using that When the distribution functionf(B)is equal to the Dirac condition, one obtains from eq 78J1 function, eq 3 has the form of eq 4 or eq 6. Stoeckli20 solved eq 3 while assuming the Gaussian W o e x pA(2TPdistribution for f ( B )and obtained an isotherm equation (DRS)" which was discussed also by other a ~ t h o r s . l ~ ~ ~ ~ - ~ ~ A limitation of the DRS equation is that it can only be used with the parameter n I2. In order to obtain a more general form of the DRS equation, we introducedlg the DA isotherm (eq 6) instead of the DR isotherm (eq 4) into eq 3. As a result, the following expression was obtained8JlJ7 where Y = (A/B)n,k , is the parameter correspondingto the maximum dimension of the micropores, and erf is the error function. As shown previously,ll eq 8 with n = 3 provides the best description of adsorption of water vapor on zeolite Y.This is concluded from the values of the determination coefficient (DC)13of the best fit to the experimental data as well as from the comparison between the parameters WO obtained from equations used and the sorption capacity where ko represents k at the maximum of the distribution of the samplesdetermined13from separate measurements. function f ( k ) ,A is the half-width of the distribution, and All these data for eqs 4 and 6-8 with n = 3 are listed in erfc is the error function complement. Table I. Jaroniec and Piotrowskals as well as Jaroniec and (14) Stoeckli, H. F. J. Colloid Interface Sci. 1977,59, 184. Choma16126*26 proposed an alternative solution of eq 3 (the (16)Jaroniec, M.;Piotrowska, J. M o m k h . Chem. 1986, 117, 7. JC equation) using the gamma-type distribution for f ( B ) . (16) Jaroniec, M.; Choma, J. Mater. Chem. Phys. 1986, 15, 521. (17) Dubinii, M. M.; Stoeckli, H. F. J. Colloid Interface Sci. 1980,75, In this case, the function f ( B ) has the form
w=
34.
(18)Dubinin, M. M.; Aetakhov,V. A.Izu. ANSSSR, Ser. Khim. 1971,
5.
(19) Rozwadowski, M.; Wojsz, R. Carbon 1984,22, 363. (20) Stoeckli, H. F. J. Colloid Interface Sci. 1977,59, 184. (21) Dubinin, M. M. In Characterization of Porous Solids; Gregg, S . J., Sing, K. 5.W., Stoeckli, H. F., as. The ; Societyof ChemicalIndustry: London, 1979; p 1. (22) Janow, A.; Stoeckli, H. F. Carbon 1979,17,466. (23) Stoeckli, H. F.; Perret, A.; Mena, P. Carbon 1980,18,443. (24) Huber, U.; Stoeckli, H. F.; Hounet, J. P. J. Colloid Interface Sci. 1978, 67, 195.
where n > -1 and q > 0 are the parameters of the r distribution. Assuming Q = (0, -1, the solution of eq 3 is very simple (25) Jaroniec, M.; Choma, J. Colloids Surf. 1989, 37, 183. (26) Choma, J.; Jaroniec, M. Momtsh. Chem. 1988,119,646.
Langmuir, Vol. 9, No. 10, 1993 2663
Energy Distribution Function
jY !.,, 0 '
5
- I
0
0
2b
10
l i A , kJ/mol
is
Here, 6 = a/ao, where a is the amount of adsorbate in the micropores under the equilibrium pressure p and at temperature Tand a0 is the maximum amount of adsorbate in the micropores, and A and /3 denote the same as above. Equation 10 is a good representation of vapor-adsorption data for microporous solids, especially for active carbons,16,25,27 As mentioned above, the energetic heterogeneity of microporous solids is characterized by the distribution of the adsorption potential, X(A) (see eq 1). Introducing successively eqs 4,6-8, and 10 into eq 1,one obtains the following relations, respectively X(A) = (2W,,kA/d2)e~p[-k(A/P)~l
(11)
X(A) = (nW,,kAn-lIB)exp[-k(A/b)"I
6
06
( k , - kd2 2A2 ex,(
where
u =erf(A) A2lI2
X(A) = 2(n
(12)
- A2A")/j32"+
(d2)112nW0AAn-1~xp[ --k-A"
1-
",)
- 2A2
(14)
+ erf(k- A2lI2 - ko)
+ l)q"+1(A/@2)[q+ (A/,3)21-'"+2'
(15)
The above functions (eqs 11-15) are plotted in Figures 2-5 for the samples under study. (27) Jaroniec, M.;Madey, R.;Lu,X.Longmuir 1988,4,911.
I
I
5
10
15
--...---.._____ I
20
25
A , kJ/mol
Figure 2. Functions of the distribution of adsorption potential, calculated from different equations for the parent zeolite Y 1, eq 11;2-5, eqs 12-15 with n = 3, respectively.
X(A) = n W,,A"-'(k&"
I
Figure 3. Functions of the distribution of adsorption potential, calculated from different equations for the 30% hydrogenexchanged zeolite Y: 1, eq 11; 2-5, eqs 12-15 with n = 3,
respectively.
w
-I
oi-J
,
0
5
I
10
I
15
I
20
.--_._ I 25
A , kJ/mol
Figure 4. Functions of the distribution of adsorption potential, calculated from different equations for the 70% hydrogenexchanged zeolite Y: 1, eq 11; 2-5, eqs 12-15 with n = 3, respectively.
The parameters characterizing the distribution functions X-, A(X-), and the half-width of the distribution, 6, are listed in Table 11. The shape of the curves (Figures 2-5) characterizing the heterogeneity of microporous solids and the distribution parameters listed in Table I1 depend generally on the isotherm equation used although application of the Jaroniec-Choma (JC)equation gives the same results as the DR isotherm (except for the 95 % -exchanged sample). the JC equation provides According to the a good representation of the experimental adsorption data for solids with different structural heterogeneities. On the other hand, the DR equation represents satisfactorily the results of adsorption on uniform and weakly heterogeneous microporous solids.21u The complexity of the crystallographicand geometrical structure of zeolites and their chemical composition are the main sources of surface heterogeneity. On the other hand, the process of adsorption of water vapor on zeolites is also very complex. As the shape of water-vapor adsorption isotherms depends generally on the number of hydrophilic centers of the s o l i d s , ~it ~is~clear that the
Rozwadowski et al.
2664 Langmuir, Val. 9, No. 10,1993
Table 11. Characteristics of the Functions of the Distribution of Adsorption Potential, Obtained from Equation 11 and Equations 12-16 with n = 3, for Water-VaporAdsorption at 298.2 K on Parent and Hydrogen-Exchanged Samules of Zeolite Y
;'; I: I'
W
' I
W W
0
10
30
50 N-
j
\\
,'.,*e'
(.-'
I
, I
I
I
1
70
95
differences in the shape of the isotherms observed in Figure 1 result from the variation of exchange of hydrogen for sodium. It is to be noted that water molecules are very mobile at or near room temperaturelo so that the positions occupied are average over time. These molecules are frequently in association with cations as indicated by the visible electronic absorption spectra.'O They can also form hydrogen bonds with the anionic framework atoms and bridges between pairs of cations or between cations and other water molecules or frameworkoxygens. In addition, two types of cavities accessible to water molecules are present in zeolite Y: supercages and &cages which determine the structural heterogeneity of the zeolite, too. As seen from Figure 2 and Table 11, the distribution functions for the parent and 10%-exchanged samples are the same for eqs 6-8. In contrast, noticeable differences are present for the samples with the 30% and higher exchange (see Figures 3-5, Table 11). Presumably, these differences result from decationization leading to formation of strong centers of Bronsted acidity1O which play an important role in the process of adsorption. ~
(28) Stoeckli,H. F.; Kraehenbuehl, F.; Morel, D. Carbon 1983,21,589. (29) Kraehenbuehl, F.; Quellet, C.; Schmitter, B.; Stoeckli, H. F. J. Chem. SOC.,Faraday Trans. 1 1986,82,3439. (30) Rozwadowski, M.;Wloch, J.; Erdmann, K.; Kornatowski, J. Proceedings of the Polish-German Zeolite Colloquium; Wydawnictwa U M K Torufi, Poland, 1992.
11 12 13 14 15 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15
2.503 2.268 2.268 2.268 2.504 2.540 2.308 2.308 2.308 2.540 2.566 2.263 3.402 2.372 2.566 2.489 2.290 3.898 2.383 2.488 2.566 2.319 3.060 2.330 2.566 1.925 1.773 7.046 2.179 2.221
9.238 13.216 13.208 13.208 9.240 9.312 13.306 13.296 13.296 9.312 9.357 13.520 8.952 12.472 9.352 9.824 13.971 8.184 12.752 9.824 9.555 13.690 10.256 13.504 9.552 10.067 14.282 3.848 10.304 8.408
14.813 12.438 12.500 12.500 14.813 14.875 12.500 12.500 12.500 14.875 14.938 12.750 8.688 12.438 14.938 15.750 13.188 8.OOo 12.813 15.750 15.313 12.875 9.813 12.875 15,313 16.188 13.438 3.688 11.750 14.625
Conclusions The total heterogeneity of zeolite which is the s u m of the structural and surface heterogeneities, can be characterized according to the literature by the adsorption-potential distribution function. This function can be evaluated from the isotherm equations based on the , Polanyi-Dubinin potential theory. Ita parameters, X A(X,,), and the half-width of the distribution, 6, are recommended as characteristic of the energetic and structural heterogeneities of zeolites. The above considerations show that, from all equations presented resulting from the Polyani-Dubinin potential theory, eq 8seems to be the most useful for the description of the curves of the adsorption potential distribution. This equation has three parameters (ko,Wo,and A) similarly to the DRS equation and, in many cases, it fits the experimental adsorption isoterms better." It is due to the fact that eq 8 includes not only the structural heterogeneity of solid but also the distribution of sizes of micropores participating in the process of adsorption. Acknowledgment. This work was supported by the Polish Committee for Scientific Research (KBN) within the Project No. PB 47812191.
