1641
ADSORPTION N I MORDENSTE
Adsorption in Mordenite. I. Calculation of Adsorption Potentials of Nonpolar Molecules1 by Guillermo D. Mayorga and Donald L. Peterson" Calijornia State College, Hayward, Hayward, California 9.4642
(Received October 16, 1971)
Publication costs assisted by California State College, Hayward
Adsorption potential contour maps are presented for a series of six nonpolar molecules of varying siee within the H-mordenite lattice. The interactions were found with the aid of inverse 6-8-10-12 summations within a sufficient volume to assure convergence. The adsorption volume in mordenite consists of parallel channels lined with small side pockets. The potential maps show that double occupancy of the side pockets may occur with atoms as large as argon, that propane is the largest molecule which the side pocket can accommodate, that greater than one-dimensional diffusion may occur with molecules as small as hydrogen, helium, and neon, and that minima along the channels occur outside the side-pocket entrances. It is found that essential features of the maps are produced by Lennard-Jones sums extending only moderately beyond nearest neighbors.
Studies of adsorption in zeolites are timely for a t least three major reasons. First, the wide variety of stereospecific environments of known geometry presented by the various zeolites offers a spectrum of cases against which predictions of postulated models may be tested. Second, a knowledge of the specific interactions existing in zeolites may be of practical value, both in surface chemistry research and in commercial applications. Third, the vast deposits of natural zeolites represent an as yet untapped natural resource of appreciable dimensions. While great strides have been made in recent years, it is still not possible to predict with any reasonable certainty, on the basis of atomic and molecular properties and a known crystal structure, adsorption properties of a pure compoumd,'let alone of mixtures. At the base of such predictions is a description of the adsorption potential between an adsorbed molecule and the crystal lattice. Even with a precise description the expectations of a given model are usually subject to uncertainties due to numerous remaining approximations. Of practicable procedures for evaluating adsorption potentials, the most reliable is that utilizing a summation of interactions between an adsorbed molecule and all the atoms of the host adsorbent. Summations evaluated by computer over enough of the lattice to assure convergence have been reported in few instances. An example is that of COzadsorbed in zeolite A2 wherein the summation for each position of the adsorbed molecule was found to require of the order of lo4 terms. There are more examples of hand computations in which only nearby atoms are considered3-6 or in which all but nearest atoms are treated as distributed cont i n u o u ~ l y . ~This ~ ~ approach may be likened to the more familiar example of adsorption on graphite. I n this case it has been shown* that the results of sum-
mations are very closely approximated by treating the carbon atoms as distributed continuously in infinite planar sheets. I n zeolites A and X, the distribution of oxygen atoms lining the large cavities approximates a spherical one, providing convenient lower limits for the analytical integration over the presumed continuously distributed matter beyond.6 Comparisons with results of summations like that available for graphite would still be needed to justify this significant simplification. I n the case of all other zeolites, however, the replacing of summations by integrations is exacerbated by the lower crystal symmetry. The intracrystalline channel network in mordenite, for example, consistsa of parallel right elliptical cylinders girthed by rings of 12 oxygen atoms. These are lined with subsidiary cavities entered through eight-membered rings. A view parallel to one of the main channels is shown in Figure 1. Some earlier calculations6 of adsorption potentials in mordenite were confined to molecules sufficiently small as to enter these side pockets and in(1)Adapted from a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Chemistry by G. D. Mayorga, California State College, Hayward, Aug 1971,and presented in part at the 7th Western Regional Meeting of the American Chemical Society, Oct 18-20, 1071,Anaheim, Calif. (2) R. W. H. Sargent and C. J. Whitford, Advan. Chem. Ser., No. 102, 144 (1971). (3) R. M. Barrer and G. C. Bratt, J . Phys. Chem. Solids, 12, 154 (1959). (4) R. M. Barrer and R. M. Gibbons, Trans. Faraday Soe., 59, 2569 (1963). (5) R. M. Barrer and D. L. Peterson, Proc. Roy. SOC.,Ser. A , 280, 466 (1964). (6) R. M. Barrer and W. I. Stuart, ibid., 249, 464 (1959). (7) R. M.Barrer and P. J. Reucroft, ibid., 258, 449 (1960). (8) A. D.Crowell, J . Chem. Phys., 22, 1397 (1954). (9)W.M. Meier, 2.Kristallogr., 115, 439 (1961). The Journal ojPhy8ical Chemistry, Vol. 76, No. 11, 197.9
1642
G . D. MAYORGA AND D. L. PETERSON
I n
n l
always to be advisable. Inclusion of these terms requires only moderate additional computer time. The potential energy gained by molecules i and j on being brought from infinity to internuclear separation sij is written thus as p . . = -A..s..-6 - Bijsij-8- Cijsij-10 RijSij-" (1) 11 11
+
The total interaction of a guest molecule i with the crystal lattice is then ,pi =
cpij= -EAijsij-6 j
j
CBjjsij-8
- CCjjsij-"
j
j
+ CRijsij-" j
(2)
The summations include the 96 oxygen, 40 silicon, and 8 aluminum atoms in each of the unit cells covered. The Kirkwo~d-Miiller~~ formula was used for A i j Aij
Figure 1. View parallel to the e axis of the oxygen atom network in mordenite.
cluded interactions only with the 37 oxygen atoms forming the wall of the pocket. As the starting point of a general program aimed at providing accurate adsorption potential surfaces in a variety of zeolites, lattice summations were undertaken for nonpolar molecules in H-mordenite. The objects of the general program are (1) to provide a body of information with the aid of which reliable predictions of models of adsorption may be made, ( 2 ) to provide a sound basis for approximate potential calculations by integration or other simplified methods, and (3) to help decide the most appropriate values for the interaction parameters. The use of mordenite permits a comparison with earlier measurements and calculations, provides an example for parallel-channel networks, and allows the neglect of interactions with counterions.
Adsorption Potential Calculation A highly siliceous zeolite, mordenite enjoys a high acid stabilitylO and capability of essentially complete counterion exchange with hydronium ion. The dehydrated form contains too little water to account for all the cation positions6 and therefore must contain the protons in intimate association with the anionic oxygen network. This makes the close approach of a guest molecule to a cation site unlikely, so that lattice monopole-guest molecule interactions, and particularly the induction terms, will tend to cancel." The interaction, at least for the nonpolar molecules considered here, is therefore adequately described by dispersion and repulsion terms, Whereas it is usual to ignore the inverse eighth and tenth terms in the (attractive) dispersion potential, Kiselev and coworkers12find this not The Journal
of
Physical Chemistry, Vol. 76, No. 11, 1078
and related ones12for Bij
=
1
= 6~~~~aiaj-
-+-
Bij
45h2aiaj
and
ai
aj
Xi
Xi
Cij
+
1
1
+
Cij =
3
arilai
1
Where ri and rj are the van der Waals radii of the guest molecule and of a lattice atom, respectively, the repulsion constant was evaluated by Rij
=
Aij(ri
+
2
Values of ri, ai, and xi used in the calculations are given in Table I.14-17 The value of a for oxygen is (IO) L. B. Sand in "Molecular Sieves," Society of Chemical Industry, London, 1968, p 71. (11) Even when the more numerous cations of type A zeolite are included in calculations of COZ interactions, the monopole-induced dipole contribution is observedl in general to be small. The monopole-quadrupole term, however, dominates in regions of potential minima near cations. (12) N. N. Avgul, A. A. Isirikyan, A. V. Kigelev, I. A. Lygina, and D. P.Poshkus, Bull. Acad. Sci. USSR, Div. Chem. Sci. (Eng. Transl.), 11, 1334 (1957).
(13) J. G. Kirkwood, Phys. Z., 33, 57 (1932), and H. R. Moller, Proc. Roy. SOC.,Ser. A , 154, 624 (1936). (14) R. M . Barrer and D. J. Ruzicka, Trans. Faraday Soc., 58, 2253 (1962). (15) H. H. Landolt-Bornstein, "Zahlenwerte und Functionen," Springer-Verlag, Berlin, 1961. (16) C. K. Hersch, "Molecular Sieves," Reinhold, New York, N. Y., 1961, p 33.
1643
ADSORPTION I:N MORDENITE based on the refractivity of the representative aluminosilicate mineral, K-feldspar.6 Values of all three parameters for silicon are for the quadruply charged ion. The same values are used for aluminum, whose positions in the structure have not been definitely identified anyway. I n any event the effect of this substitution and of the use of parameters for bare Si4+ ions is unlikely to lead to significant errors, not only because of the preponderance of oxygen atoms in closer proximity with the channel volume, but also because even in chemical combination with oxygen, the polarizability and magnetic susceptibility of Si4+ are necessarily much smaller than those of bound oxygen. Several nonpolar guest molecules were employed mainly to bring out clearly the effect of molecular size. Thus, light paraffins are used as a convenient homologous series, but all members are necessarily treated as spherical. ~~
Table I : Values of Atomic and Molecular Parameters
Radius Ti,
Molecule(i)
Argon Krypton Methane Ethane Propane n-Butane Oxygen (zeolitic) Silicon
b
Polarisability ai,
cm3/mol
Magnetic sueoeptibility -xi, cm3/mol x 108
Ionization potential si,
eV
1.91" 2.01" 2.lgb 2.50b 3.26d 3.89d 1.408
0. 981a
1,493" 1.565b 2.992b 3.788C 4,890" 0.994"
19.39" 28.ooa 12.2b 27.3b 40.5c 57.40 12.58"
15.7@ 14.OOb 14.40b 12.80" 11.21c 10.80" 13.55"
0.42"
0.01204c
1.oof
166.73c
(Si4+) 0
16.
Reference 5. b Reference 14. c Reference 15. Reference 4. Reference 17.
Figure 2. View along the c axis of the oxygen network in the vicinity of z = 0. Numbers in parentheses are z coordinates of 0 atoms.
Reference
Values of the parameters in eq 2 are contained in Table 11. I n a few instances calculations were made using the Lennard-Jones potential ( A and R terms only), and in others, the London formula18 (3) The ionization potentials used are in Table:. The potential was evaluated a t 0.4 A increments in a grid whose plane is normal to the main channels (parallel to the c direction), and at a sufficient number of points (up to 200) to span regions of attractive potential within the main channel and the side pocket. Because of the cylindrical shape of the channels, maps were constzucted only at two elevations, x = 0 and x = c/4 (1.88 A). The (001) planes, as well as the (002), bisect the openings to the side pockets, and therefore contain the adsorption potentials within the pocket, at
least in a plane normal to e. The oxygen atoms nearest to these planes are shown in Figure 2 along with their x coordinates; the plane of the paper, x = 0, is a reflection plane. Most of the important features within the pocket are shown by maps in these planes, from which a plane bisecting the pocket entrance and at right angles (normal to a) differs only in minor details. So far as adsorption in the main channels is concerned, the picture is expected to vary fairly regularly in the c direction, reaching a modest extremum halfway between opposed eight-membered rings, vix., at the equivalent elevations, x = c/4 and x = 3c/4. The sums were evaluated within a rectangular parallelopiped of dimensions 3a (51.39 A), 3b (61.47 A), and 9c (67.68 8). The center of this roughly cubic volume lies simultaneously also on the axes of a main channel and of a side pocket, and is the origin in Figure 2. As an expedient, sums were formed by varying the position of the guest molecule within this volume and including interactions with all lattice atoms within it. The effect of this simplification on results was checked in the instance of methane at the origin by summing within spheres of increasing size. These values are compared with that for the entire 81 cells in Table 111. It appears that the major contribution is made by atoms within the nearest 10 A, although accumulation of 99% of an extrapDolated limit necessitates summing within nearly 20 A. Since the mini(17) J. 0. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," Wiley, New York, N. Y.,1954, p 193. (18) F. London, 2. Phys. C'hem. (Leipzig), B11, 222 (1930). The Journal of Physical Chemistry, Vol. 76,N o . 11, 197B
G.D. MAYORGA AND D. L. PETERSON
1644 Table I1 : Values of Pairwise Interaction Parameters Equilibrium separation,
Guest molecule
Ti
(9
+
4
x
Cij,
Bij,
Aij,
,ke-kcal/mol
~ j ,
H@-kcal/mol
x
108
Argon Krypton Methane Ethane Propane n-But ane
3.31 3.41 3.59 3.90 4.66 5.29
1.467 2.186 1.462 2.936 4.253 5.769
Argon Krypton Methane Ethane Propane n-Butane
2.33 2.43 2.61 2.92 3.68 4.31
0.037 0.054 0,026 0.057 0.084 0.118
101
Oxygen (j 1 1.328 2.021 2.119 3.643 5.126 6.618 Silicon (j) 0.016 0.025 0.026 0.044 0.062 0.080
AlO-kcal/mol
x
108
2.728 4.201 7.018 9.949 13.54 16.55 0.021 0.034 0,097 0.124 0.184 0.191
Rij,
ALij,
Al2-kcal/mol x IO'
Hbkcal/mol
0.964 1.718 1.565 5.165 21.77 63.22
0.681 0.974 1.028 1.716 2.265 2.809
0.0029 0.0055 0.0041 0.0177 0.1045 0.3783
x
108
0.016 0.022 0.024 0.037 0.047 0.057
Table I11 : Convergence of Summations Evaluated at the Origin for Methane
-P, Volume summed
Sphere of Sphere of Sphere of Sphere of Sphere of 81 cells
radius 5 1 radius 10 A radius 15 1 radius 20 A radius 25 A
Fraction
kcal/mol
of summation over 81 cella
1.699 2.926 3.033 3.063 3.074 3.078
0.553 0.951 0.985 0.995 0.9985 1.0000
mum distance to the bounsaries of the 81 cells encountered was slightly over 20 A, the effect of this simplification is considered negligible.
Results and Discussion Contour maps of eq 2 are shown for four of the molecules studied in Figures 3 through 6 at the more informative elevation, x = 0. The outermost contour of cp = 0 encloses in each case the region of net attractive potential in which contours are drawn at 2 kcal/ mol increments. The van der Waals molecular diameter is shown near the top of each figure. From the map for argon, it may be noted that a molecule of this size enjoys considerable translational freedom within the zeolite. There appears to be sufficient space, for example, for two argon atoms to pass each other with ease in the main channel, and perhaps even within the side pocket. The closer quarters of the latter produces a minimum potential of 9.1 kcal/ mol, about 25% lower than the minimum near the wall of the main channel. The contour map for kryptonlo is similar to that for argon except that the relative depth in the pocket is now 30% lower than near the channel wall. The regions of slowly varying potential within the steep rises near the oxygen atoms The Journal of Physical Chemistry, Vol. 76, No. 11, 1978
Figure 3. Potential energy contour map for argon at z = 0. Contours are drawn at 2 kcal/mol increments starting at (p = 0; numerical values of contours are shown in possibly ambiguous cases. The scale at the top shows the van der Waals radius in angstroms of an argon atom (3.84 A).
of the channel walls are much smaller in size, and although free passage of atoms still is possible in the main channel, it does not now appear likely within the pocket. (19) Contour maps for the other two molecules, krypton and nbutane, at z = 0, and for a representative molecule, ethane, at z = 4 4 , together with a view of the oxygen network along the c axis at z = c/4, will appear immediately following this article in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 1155 Sixteenth Street, N.W., Washington, D . C. 20036 by referring to code number JPC-72-1641. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche.
ADSORPTIONIN MORDENITE
Figure 4. Potential energy contour map of methane a t z = 0. See caption of Figure 3 for conventions.
-7
ETHANE
Figure 5. Potential energy contour map of ethane at z = 0. See caption of Figure 3 for conventions.
The maps for methane and ethane (Figures 4 and 5) also predict single occupancy of side pockets with increasing relative stabilities in this location. A small activation energy accompanies passage of an ethane molecule through the eight-membered ring. Further, ethane molecules can pass one another in the main channel without experiencing an appreciable repulsion only by making use of entrances to side pockets. To account for self-diffusion of propane (Figure 6) and butanelg in IK-mordenite, relaxation of the spherical
1645
Figure 6. Potential energy contour map of propane at z = 0. See caption of Figure 3 for conventions.
molecule assumption appears necessary. The fact that the saturation capacity of H-mordenite for n-butane is very close to the “geometrical” free volume of the main channels6 suggests that n-butane molecules must at least partially occupy the side pockets or their entrances. From the contours in Figure 6 it may be concluded that the propane molecule closely measures the adsorption capacity of the side pocket. An idea of the variation of the potential surface in the c direction was gained from a comparison of the maps constructed at z = 0 and x = c/4. In the instance of ethane, the region of appreciable aitractive potential shrinks from a breadth of 4 to 4.5 A to one of only 3 to 3.5 A, while the minimum rises by 15%. It is believed that these (xy) minima at x = c/4 are maxima with variation in x (saddle points in cp(x,z)) and thus that all locations of potential minima lie on (002) planes. Values at the minima are contained in Table IV. Those for argon and methane lie below the lower boundaries of Figures 3 and 4. It is well known that an adsorbed molecule can approach a lattice atom more closely than it can the same atom outside the influence of the other lattice atoms. Thus one has long accepted the rapid adsorption of normal paraffins (diayeter EZ 5.0 8) by zeolites 5A (critical diameter g 4.2 A). The present calculations afford some interesting comparisons along these lines. Table IV contains internuclear separations for isolated guest molecule-oxygen atom pairs at the equilibrium position, re, for which qmin is given, and at the position corresponding to cp = 0, r o (according to eq 1). These data are to be compared with the same quantities from the potential contour maps. Guest The Journal of Physical Chemistry, Vol. 76, No. 11 1979
G. D. MAYORGA AND D. L. PETERSON
1646 Table IV:
Comparison of Isolated Pair Interactions t o Those Occuring within the Zeolite -Guest re,
H
Argon Krypton Methane Ethane Propane n-Butane a
3.4 3.55 3.45 3.9 4.4 5.3
-
moleoule-0 atom interaction(omin, rQ, A kcal/mol
-
2.75 2.95 3.05 3.35 4.1 4.7
POPa
3.1 3.4 3.5 4.1 4.7 4.9
2.6 2.7 2.75 3.0 3.4 4.0
A
0.58 0.78 0.45 0.47 0.24 0.14
Measured from lattice oxygen atom nearest the location of
Guest molecule-lattice interaction-(omin, Location of A kcal/mol minimum
reva
pmin. a
molecule-lattice internuclear separations are measured from the oxygen atom nearest the position of cpmin. Because of the gradual variation in cp on the inside of the minimum, comparisons based on re values can be misleading. According to the ro values, an argon atom, for example, cap approach an oxygen atom in Hmordenite 0.15 A more closely than it can an isolated atom without experiencing a net repulsion. The lattice structure of Na-mordenite is such that halfway between adjoining channels in the b direction there are two sodium ions, each in the center of a distorted eight-membered ring. These rings are roughly normal to the c axis, face into pockets on neighboring channels, and have a free diameter of only 2.8 A. If the hydrogen ions replacing the sodium ions are indeed buried in the oxygen framework as suggested earlier, these apertures may be open to the possible passage of sufficiently small molecules between pockets. Calculations carried out with guest molecules at the position of a vacant sodium atom (Table V) show that
9.8 13.4 7.9 13.0 7.4 7.3
Pocket Pocket Pocket Pocket Channel Channel
Overlap,b
A
0.15 0.25 0.3 0.35 0.7 0.7
Differences of columns 3 and 6.
sumptions. Comparisons are made only for positions along the axis of the side pocket. Three cases are included : (1) Kirkwood-Muller formula, 6-12 potential, 81-cell summation; (2) London formula (eq 3), 6-12 potential, 81-cell summation; and (3) London formula, 6-12 potential, 37 nearest 0-atom summations (Ar and Kr only). Compared to (1) above, the 6-810-12 potential surface is qualitatively similar, but displaced by amounts leading in extreme cases to as much as 0.5 A in positions of minima. Values at the minima are compared in Table VI for the four procedures. Differences are representative in the range of coordinates covered. Inclusion of the inverse eighth and tenth terms has the effect of increasing the magnitude of the potential by about 10% on the average. As is usually the case, use of the London formula leads to about one-half the interaction potenbial. The summation over nearest lattice oxygen atoms includes about 80% of the total interaction.
Table VI : Comparison of Adsorption Potential Minima Table V : Potential Energy of Molecules Located a t the Sodium Ion Lattice Position
Molecule
Potential at the sodium ion position, kcal/mol
Argon Krypton Methane Ethane
-3.71 $0.29 $7.1 $58.5
argon may be the only molecule of those considered here which could literallr squeeze through the window (the “overlap” is 0.55 A). However, even this atom encounters an activation energy of about 6 kcal/mol, which is almost as large as (the negative of) its calculated heat of adsorption. Thus, two-dimensional diffusion, if it occurs in H-mordenite, would be expected to take place freely only with molecules of smaller He, orNe. diameter than that of argon, ie., with Hz, Finally, the results of the potential calculations may be compared with those making use of alternate asThe Journal of Physical Chemistry, Val. 76,No. 11, 1072
on 21 Axis Computed by Alternate Procedures
5
Molecule
KirkwoodMuller 6-8- 10- 12 81 cells
Argon Krypton Methane Ethane Propane %-Butane
9.8 13.4 7.9 13.0 7.4 7.3
KirkwoodMUer e-12 81 cells
8.8 12.2 6.8 11.8
7.0 6.8
London 6-12 81 cells
4.1 5.3 4.8 6.9 3.7 3.3
London 6-12
37 0 atomsa
3.3 4.5
Reference 5 .
Conclusion The reported calculations of adsorption potentials of nonpolar molecules in H-mordenite appear to limit the size of molecules capable of rapid two-dimensional diffusion to that of neon, of multiple occupancy of side pockets to that of argon, and of single occupancy of side pockets to that of propane. It is inferred that these conclusions, as well as other semiquantitative
ADSORPTION IN MORDENITE features of the adsorption potential surfaces within Hmordenite, would be as accurately predicted by use of the simple Lennard-Jones potential, by summations including lattice atoms up t o about only 10 distance from the adsorbed molecule, and that inclusion of only nearest neighbors in summations may for many purposes be adequate. Although these approaches differ vastly in complexity and required computer time, their predictions are far more coincident, at least in
1647 the present instances, than those of procedures using the alternate formulas for interaction parameters. It is concluded that the use of the 6-12 potential in summations extending only moderately beyond nearest lattice atom neighbors, with scaling between Kirkwood-Muller and London parameters, and perhaps beyond, left as an empirical degree of frcedom, offers the most expedient means of seeking generalities characteristic of adsorption in zeolites.
Adsorption in Mordenite. 11. Gas Chromatographic Measurement of Limiting Heats of Adsorption of Nonpolar Molecules by Guillermo D. Mayorga and Donald L. Peterson" California State College, Hayward, Hayuard, California 94648 (Received October 18, 1971) Publication costs assisted by California State College, Hayward
A comparison between heats of adsorption derived from chromatographic retention-volume measurements and values predicted on the basis of adsorption potential calculations shows the latter to be quite successful in the case of atomic adsorbates when the interaction parameters are evaluated by the London formula. The poor agreement in the case of nonpolar molecular adsorbates reflects an inadequacy of treating the molecules as spherical, possibly even in the case of methane.
The availability of contour maps of adsorption potentials of a series of nonpolar molecules in H-mordenitel makes possible the prediction of their heats, free energies, and entropies of adsorption. For comparisons of the predicted heats, available experimental data2 were augmented by a series of chromatographic measurements of adsorbabilities of these compounds at several temperatures, from which heats of adsorption at vanishing coverage were estimated. A further purpose of the reported measurements is to augment a prior demonstration* of the utility of mordenite as a gas chromatographic packing material. The unidimensionality of mordenite's pore structure raises some doubts about whether equilibrium will be reached, and the operating assumption of chromatography realized, on the time scale of practicable chromatographic measurements.
Experimental Section A Varian Aerograph Model 90-P3 chromatograph, which comes equipped with a flow control system that operates under 65 psi pressure of carrier gas, was modified with the aid of a Moore Flow Control and a precision Whitey needle valve t o allow use of a lower
pressure (10 psi or less), and precise control of the flow rate. A modified 0.25411. Swagelock tee was attached to the injection port with one of the free sides of the tee serving as the new injection port. The free side of the tee was connected through a valve to a mercury manometer. The inlet pressure was read to within 0.005 cm with the aid of a cathetometer. The carrier gas was helium; this and the argon, methane, ethane, propane, and n-butane used in the experiments mere instrument grade gases from Matheson Co. The neon and krypton were high-purity grade gases from the General Electric and Air Reduction Go., respectively. The H-mordenite was produced by exchanging Na-mordenite (Zeolon Lot HB-gE, Code SR4710) thrice with 1 M "*NO3 over a period of 3 days. Between exchanges the sample was washed with deionized water. After the final exchange the (1) G . D. Mayorga and D. L. Peterson, J . Phys. Chem., 76, 1641 (1972). (2) R. M.Barrer and D. L. Peterson, Proc. Roy. Soc., Ser. A , 280, 466 (1964). (3) K. Torii, M. Asaka, and H. Yamazaki, Kogyo Kagaku Zasshi, 72, 661,664 (1969).
The Journal of Physical Chemistry, Vol. 76, No. 11, 1078
