J. Phys. Chem. 1989,93, 923-926
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Influence of Swelling on Reaction Efflciency in Intercalated Clay Minerals. 2. Pillared Clays Philip A. Politowicz, Linda Bik San hung, Research School of Chemistry, Australian National University, Canberra, Australia ACT 2601
and John J. Kozak* Department of Chemistry and Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 (Received: May 6, 1988; In Final Form: June 21, 1988)
Methods for intercalating thermally stable, polynuclear hydroxy metal cations and/or metal cluster cations in smectite clays have been developed in recent years as a means of keeping separate the silicate layers in the absence of a swelling solvent. Since the pillaring cations are space filling, the interlamellar reaction space will be broken up into an interconnected set of channels through which a diffusing species can migrate. In this paper, a lattice model is designed to determine how different spatial distributions of pillaring agents and different interlamellar spacings can influence the efficiency of reaction between a fixed target molecule and a diffusing coreactant. We study two regular distributions of pillaring cations and calculate the mean reaction time (as calibrated by the mean walklength ( n ) ) of the diffusing coreactant as a function of the separation between silicate layers. All other factors being held constant, we find a significant increase in the reaction efficiency with increase in the number of channels available to the coreactant. We also find that for each distribution there is a decrease in reaction efficiency as one increases the interlayer spacing, with the surprising result that for large arrays the addition of one or two layers above the basal plane (where the target molecule is anchored at the centrosymmetricsite) leads to essentially the same relative changes in the reaction efficiency regardless of the spatial distribution considered.
I. Introduction Recent discussions of intercalated clay catalysts’+ have stressed the relative advantages of these materials over other inclusion catalysts. As noted by Pinnavaia,’ two principal advantages are realized when one considers the intercalation of polynuclear metal cations or metal ion clusters in smectites (“pillared clays”). First, in ordinary metal-ion-exchange forms of smectite clays, there occurs dehydration at high temperatures (>200 “C);the subsequent collapse of the interlayer region thereby precludes the study of a great variety of possible reactions. The introduction of pillaring cations, however, keeps the silicate layers separated in the absence of a swelling solvent and affords the study of reactions in the high-temperature regime. Second, the use of different pillaring cations allows the design of new catalytic materials with pore sizes that can be made much larger than those of available zeolite catalysts. We wish to explore the consequences of assuming different distributions of pillaring cations and different interlamellar spacings on the efficiency of reaction between a diffusing coreactant and a stationary target molecule. Since the pillaring cations are space filling, the interlamellar reaction space will be bifurcated into an interconnected set of lateral and vertical channels through which the diffusing coreactant can migrate. Following the approach taken in our previous communication,s we construct a partially ordered, layer lattice model to describe this situation and calculate the mean walklength ( n ) of the diffusing coreactant (a measure of the mean reaction time), using the theory of finite Markov processes. In ref 5 , the target molecule was placed at the centrosymmetric site of a two-dimensional lattice of coordination number (connectivity or valency) v = 3 . The consequent (hexagonal) lattice was assumed to be of finite extent containing, overall, N total sites (one reaction center and N - 1 satellite sites). A partially ordered layer lattice was then constructed by ”stacking” first one and then two hexagonal layers above the basal plane. Thus,in the two-layer lattice the number of satellite sites is 2N - 1 and in the three-layer lattice it is 3N - 1 . (1) Pinnavaia, T. J. Science 1983, 220, 365. (2) Laszlo, P. Science 1987, 235, 1473. (3) Thomas, J. K. The Chemistry of Excitation at Interfaces; ACS Monograph 181; American Chemical Society: Washington, DC, 1984. (4) Kalyanasundaram, K. Photochemistry in Microheterogeneous Systems; Academic: New York, 1987. (5) Politowicz, P. A.; Kozak, J. J. J . Phys. Chem. 1988, 92, 6078.
The above description provides the starting point for the approach taken in this paper. Instead of regarding the “holes” in the stacked hexagonal assembly to be “empty space”, we regard these volumes to be regions of reaction space excluded to the diffusing coreactant owing to the presence of the space-filling, pillaring cations. The links (or bonds) of the lattice then represent channels through this array that are accessible to a migrating species in its random motion through the partially ordered lattice. Assuming a hexagonal structure for the underlying lattice defines one possible distribution of pillaring cations. What is of interest here is to consider how different distributions of pillaring cations influence the reaction efficiency. In this paper we shall consider a second regular distribution of cations, that which induces in a (planar) lattice a local coordination or valency v = 6;this choice of coordination allows the construction of a partially ordered layer lattice built up of triangular lattice arrays. In future work we plan to consider the case of random distributions of pillaring cations, considering first the lattice called the Sierpinski gasket,6 a lattice of fractal dimension d = In 3/ln 2 = 1.585. Before taking up this more intricate problem, however, it is essential to establish first for integer dimension lattices what the upper and lower bounds on the reaction efficiency are, and these can be established by considering the v = 6 triangular and the v = 3 hexagonal lattice arrays described above. Since the theoretical approach taken here has been developed and discussed extensively in the literature7” with many applications to reaction-diffusion processes in structured media: we move directly in the following section to a comparison of the results obtained for the mean walklength ( n ) for the two cation distributions noted above. A summary of our conclusions is presented in the concluding section. (6) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: San Francisco, 1983. (7) Montroll, E. W.; Shuler, K. E. Ado. Chem. Phys. 1958, 1, 361. (8) (a) Walsh, C. A,; Kozak, J. J. Phys. Reu. Lett. 1981, 47, 1500. (b) Walsh, C. A.; Kozak, J. J. Phys. Rev. B: Condens. Matter 1982, 26, 4166. (c) Politowicz, P. A.; Kozak, J. J. Phys. Rev. B: Condens. Matter 1983, 28, 5549. (d) Musho, M. K.; Kozak, J. J. J. Chem. Phys. 1984,81, 3229. ( e ) Politowicz, P. A.; Weiss, G. H.; Kozak, J. J. Chem. Phys. Lett. 1985, 120, 388. (f) Politowicz, P. A.; Kozak, J. J. Chem. Phys. Lett. 1986, 27, 257. (9) For recent applications of our approach to monolayer assemblies and to zeolites, see (a) and (b) and (c,d), respectively. (a) Politowicz, P. A.; Kozak, J. J. Longmuir 1988, 4, 305. (b) Mandeville, J. B.;Golub, J.; Kozak, J. J. Chem. Phys. Lert. 1988, 143, 117. (c) Politowicz, P. A.; Kozak, J. J. Mol. Phys. 1987, 62, 939. (d) Mandeville, J. B.; Golub, J.; Kozak, J. J. J . Phys. Chem. 1988, 92, 1575.
0022-3654/89/2093-0923$01.50/0 0 1989 American Chemical Society
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The Journal of Physical Chemistry, Vol. 93, No. 2, 1989
Politowicz et al.
TABLE I: Data for the Average Walkleneth as a Function of System Geometry for Y = 6 two lattice layers
N (layer) 7 19 37 61 91 127 169 217 27 1
one lattice layer N entire total CT lattice 7 0.14286 6.000 19 0.052 63 20.750 37 0.027 03 46.562 61 0.016 39 84.635 91 0.01099 135.83 127 0.007 87 200.82 169 0.005 92 280.17 217 0.004 61 374.37 27 1 0.003 69 483.82
N total 14 38 74 122 182 254 338 434 542
CT 0.071 43 0.026 32 0.01351 0.008 20 0.005 49 0.003 94 0.002 96 0.002 30 0.001 85
entire lattice 15.256 43.877 92.145 161.07 251.51 364.23 499.87 658.99 842.07
11. Formulation and Results The efficiency of diffusion-controlled reactive processes in one-, two-, and three-layer lattices is studied by calculating the mean walklength (n),of a coreactant diffusing from a given site i in the interlamellar reaction space to a reaction center anchored at the centrosymmetric site of the basal plane. The assembly is subject to nontransmitting (confining) boundary conditions such that if the diffusing particle attempts to exit the system from a boundary site, it is reset at that site (from whence it may return eventually to the interior of the assembly). For arrays of hexagonal symmetry, the common valency v of all sites of the onelayer lattice is v = 3; for the two-layer assembly, all sites are of valency v = 4;and, for the three-layer assembly, the lattice sites in the upper and lower layers are of valency v = 4, while the lattice sites in the middle layer are of valency v = 5. The new results presented in this paper were calculated assuming the same class of boundary conditions but for arrays having an underlying triangular symmetry. Here, the common valency v of all sites of the one-layer lattice is v = 6 ; for the two-layer assembly, all sites are of valency v = 7; and, for the three-layer assembly, lattice sites in the upper and lower layers are of valency v = 7, while sites in the middle layer are of valency v = 8. To place both studies on a common footing, we assume the characteristic length (or metric) I of each lattice to be the same. And, as in our previous study: we calibrate the interlayer spacing in units of 1. Thus, both the “in-plane” and ”out-of-plane” displacements of the diffusing coreactant are scaled by the length 1. Since what is of interest here is the overall, mean walklength ( n )(constructed from the individual ( n)i), we present in Table I the results for (n)as a function of N , the total number of lattice sites defining the assembly. To explore the conseqences of different choices of initial conditions, we have carried out calculations in which walks were initialized from sites on the uppermost layer only, the lowest layer only, or all possible sites comprising the assembly; the results obtained in these three cases are listed in Table I under the headings “upper lattice layer”, “lower lattice layer”, and “entire lattice”, respectively. In all calculations, the position of the stationary target molecule is assigned to be the centrosymmetric site in the basal plane of the array with its concentration CT(= 1/ N ) bracketed between the values of 0.143 B CTB 0.001 23 for the lattices studied here. These concentration bounds are to be compared with the ones characterizing our previous study5 on partially ordered arrays of hexagonal symmetry, viz., 0.25 B CT 3 0.001 15. Focusing on the class of initial conditions wherein reactant trajectories are initiated from all possible nontrapping sites of the system (the “entire lattice” results), we present in Figures 1-3 results calculated for (n)versus N for one-, two-, and three-layer lattices, respectively. In each figure, two profiles are displayed; the uppermost one corresponds to results calculated for an ensemble based on dimension d = 2 planar lattices of hexagonal symmetry (v = 3) while the lower curve is based on d = 2 planar lattices of triangular symmetry (v = 6 ) . The spatial extent of the arrays considered is such that a wide range of concentrations C, can be studied. Using the notation (n)*,(n)II,and (n)IIIto denote the average walklength calculated for one-, two-, and three-layer
three lattice layers
W
(n) lower lattice layer 12.444 41.401 89.827 158.85 249.37 362.15 497.84 657.00 840.12
upper lattice layer 17.667 46.222 94.399 163.25 253.63 366.30 501.89 660.97 844.02
N total 21 57 111 183 273 38 1 507 65 1 813
CT 0.047 62 0.01754 0.009 01 0.005 46 0.003 66 0.002 62 0.001 97 0.001 54 0.001 23
entire lattice 30.522 75.006 149.67 255.1 1 391.90 560.61 761.85 996.14 1264.0
lower lattice layer 19.525 64.765 139.76 245.41 382.33 551.15 752.46 986.83 1254.7
upper lattice layer 38.736 83.356 157.98 263.39 400.13 568.81 770.01 1004.3 1272.1
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Figure 2. A plot of the average walklength (n)ll versus total number of lattice sites for a two-layer, partially ordered lattice subject to confining boundary conditions with a reaction center placed at the centrosymmetric site of the lower layer. Displayed here are the results for lattices of coordination Y = 3 (0)and Y = 6 (A).
lattices, respectively, one can also compare the reaction efficiency ratio ( n ) I l / ( n ) , versus N (Figure 4) and (n)III/(n)Iversus N
Influence of Swelling on Pillared Clays
The Journal of Physical Chemistry, Vol. 93, No. 2, 1989 925
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Figure 3. A plot of the average walklength (n),]]versus total number of lattice sites for a three-layer, partially ordered lattice subject to confining boundary conditions with a reaction center placed at the centrosymmetric site of the basal plane. Displayed here are the results for lattices of coordination v = 3 (0)and v = 6 (A).
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Figure 4. A plot of (n)II/(n)lversus the total number of lattice sites for lattices of coordination v = 3 (0)and v = 6 (A). (Figure 5) for the two lattice architectures studied in this paper. In the following section we shall analyze the above results and discuss their implications. 111. Discussion
The interlamellar pore structure induced by space-filling pillaring cations necessarily compromises somewhat the efficiency of reaction between a freely diffusing coreactant and (here) an immobilized target molecule. The principal objective of this study was to determine how the reaction efficiency changes when two different regular distributions of pillaring cations (and attendant interlamellar channel patterns) are considered. The first generalization that emerges from our study is evident from an examination of the results displayed in Figures 1-3. There it is seen for one-, two-, and three-layer systems that values of the mean walklength ( n ) calculated for lattices built up from planar layers of triangular symmetry (v = 6) are systematically lower than those calculated for layers of hexagonal symmetry (v = 3). As noted previously in our study of monolayer^,*^.^^ this behavior can be understood by recognizing that for a given choice of N, and for a common choice I of lattice spacing, increasing the
coordination number of the lattice allows one to cluster more satellite sites closer to the central target molecule at each interparticle separation (thereby enhancing the probability that the diffusing species encounters the target molecule in a given number of random displacements). Since the mean walklength (n) of the Markovian problem is simply related to the zero-mode relaxation time of the associated stochastic master equation for the same problem,1° our overall conclusion is that for fixed ( N , I ) the characteristic reaction time 7 decreases with increasing coordination number v (Le., with increase in the number of channels available to the diffusing coreactant). It is also significant that this conclusion seems not to depend on the choice of initial conditions for the lattice architectures considered. Assuming that the trajectories of the diffusing coreactant are initialized from the upper, lower, or all nontrapping sites of the array leads to only small differences in the values calculated for (n) (especially for larger lattices). A second, rather striking result follows from Figures 4 and 5, where the reaction efficiency ratios (n)II/ (n)I and ( n)III/(n)]are plotted versus N for the two distributions. Although the results for small systems are quite different (say, N < 60 for two-layer lattices and N < 90 for three-layer lattices), the results obtained in the limit of N large ( N 600 for two-layer lattices and N 900 for three-layer ones) tend to coalesce. In particular, for two-layer systems, (n)II/(n)I 1.7 and for three-layer systems ( n)III/ ( n)I 2.5, for both distributions. In expanding the interlamellar reaction space accessible to the diffusing coreactant, the mean walklength (and hence the mean reaction time) should increase (and the reaction efficiency should decrease). What the above results demonstrate, however, is that, for large arrays, increasing the number of satellite sites from N - 1 (one layer) to 2 N - 1 (two layers) to 3 N - 1 (three layers) does not compromise the reaction efficiency by simple factors of 2 for two-layer systems or 3 for three-layer systems but by somewhat smaller factors (of 1.7 and -2.5, respectively) which seem not to depend on the particular distribution of pillaring cations. In fact, from the structural similarity of the profiles displayed in Figures 1-3, it would appear that there is a kind of "superposition principle" at play here, one in which stochastic events in higher than two-dimensional spaces are representable in terms of spaces of dimension d = 2. A third conclusion follows directly from the remarks of the previous paragraph. Clearly, if one wants to design intercalated systems for which different distributions of pillaring cations do influence in a significant way the overall reaction efficiency, the
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J. Phys. Chem. 1989, 93, 926-931
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way to achieve this is to utilize small “crystallites” of smectite clays rather than extended, ordered arrays. Decreasing the size of the crystallite will also influence the relative efficiency of twoversus three-dimensional (stochastic) flows of the diffusing coreactant to the target molecule. This effect, first formalized by Adam and Delbriick” and referred to as “reduction of dimensionality”, has been documented for reaction-diffusion process taking place within symmetrical and asymmetrical lattice geometries in previous work (see especially Fig. 7 in ref 12). While the insights drawn from Figures 1-5 are of interest, it is clear that a number of further factors need to be taken into account before contact can be made with, for example, the experimental studies of photochemical water cleavage in clays.13-15 (1 1) Adam, G.; Delbriick, M. I n Structural Chemistry and Molecular Biology; Rich, A., Davidson, N., Eds.;Freeman: San Francisco, 1968; p 198. (12) Lee, P. H.; Kozak, J. J. J. Chem. Phys. 1984,80, 705. (13) (a) Ghosh, P. K.; Bard, A. J. J. Phys. Chem. 1984, 88, 5519. (b) Ghosh, P. K.; Bard, A. J. J. Am. Chem. Soc. 1983, 105, 5691. (c) Ghosh, Bard, A. J. J. Electroanal. Chem. 1984, 169, 315. P. K.; Mau, A. W.-H.; (14) (a) Schoonheydt, R. A.; De Pauw, P.; Vlien, D.; DeSchrijver, R. C. J. Phys. Chem. 1984,88, 5113. (b) Schoonheydt, R. A.; Cenens, J.; DeSchrijver, F. C. J. Chem. Soc., Faraday Trans. 1 1986, 82, 281. (c) Viane, K.; Caigui, J.; Schoonheydt, R. A.; DeSchrijver, F. C. Lmgmuir 1987, 3, 107.
Nonrandom distributions of cations (see section I), the clustering of target molecules in the interlayer aqueous environment, multipolar correlations between reactants, and, perhaps most importantly, the influence of layer charge (electrostatic charge density on the clay surface) are factors whose influence has yet to be assessed theoretically. These matters are presently under investigation, and the results will be reported in the near future.
Acknowledgment. This paper is based in part on work done at the Physical Chemistry Laboratory of the University of Oxford, Oxford, United Kingdom, supported by the North Atlantic Treaty Organization under a grant awarded in 1984 to P.A.P.; the kind hospitality of Professor J. S. Rowlinson is gratefully acknowledged. The research described herein was also supported in part by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-3097 from the Notre Dame Radiation Laboratory. The authors are grateful to Roberto A. Garza-LBpez for preparing the figures presented in this paper. (IS) (a) Frenski, D.; Abdo, S.; Van Damme, H.; Cruz, M.; Fripat, J. J. J. Phys. Chem. 1980,84,2447-2457. (b) Habti, A.; Keravis, D.; Levitz, P.; Van Damme, H. J. Chem. Soc.,Faraday Trans. 2 1984,80,67. (c) Nijs, H.; Fripat, J. J.; Van Damme, H.J. Phys. Chem. 1983, 87, 1279.
Fourier Transform Infrared Spectroscopic Studies of Microstructures Formed from 1,2-Bls( 10,l2-tricosadlynoyt)-sn -giycero-3-phosphochollne K. A. Bunding Lee* Bio/Molecular Engineering Branch, Naval Research Laboratory, Washington, D.C. 20375-5000 (Received: May 1I , 1988; In Final Form: July 6. 1988)
The interaction of ethanol and methanol with 1,2-bis(lO,12-tricosadiynoyl)-sn-glycero-3-phosphocholineas studied with Fourier transform infrared spectroscopy is reported. This phospholipid forms hollow tubules and long, open helical structures approximately 0.3-1 .O-pm diameter by tens of micrometers length. These tubules and helical structures formed from ethanol-water solvent mixtures are compared spectroscopically to tubules formed by thermal cycling aqueous suspensions. These two microstructures have similar IR signatures; they are both highly ordered microstructures with rigid acyl chain packing and dehydrated interfacial regions. The effect of ethanol on the hydrocarbon vibrations of the lipid microstructures is very slight.
Introduction It has been shown that 1,2-bis( 10,12-tricosadiynoyl)-snglycero-3-phosphocholine(DC8,9PC)forms hollow tubules having dimensions of approximately 0.3-1 .O-pm diameter by tens of micrometers length.’ There are two procedures by which tubules can be formed, namely, precipitation from mixed solvents and thermal cycling of aqueous suspensions of this lipide2 The resulting morphology of the structures produced by precipitation and thermal cycling varies. As seen by electron microscopy, structures made from mixed solvent precipitation can include tubules with 1-3 bilayers and about 2%open helices, whereas thermally grown microstructures have up to 10 bilayers and are rarely open helices though they can have subtle regular spiral patterns. (See Figure 1.) The mixed-solvent procedure can be more readily adapted to large-scale production of tubules of specific lengths, so it is important to identify any alterations in structural properties of tubules grown by this procedure. We have undertaken an infrared spectroscopic study of the vibrational modes of the structures grown by these two methods in an effort to assess the effect of solvent on the molecular order of these microstructures. Although nonaqueous solvent tends to disorder saturated lipids, the microstructures formed from DC&C *Present address: S. C. Johnson & Son, 1525 Howe St., M.S.056, Racine, WI 53403.
in solvent-water mixtures appear to be highly ordered. Lipid structure, including headgroup charge and composition and diacetylenic constraints on chain packing, plays an important role in tubule microstructure f ~ r m a t i o n . In ~ water, only tubules are formed, but in nonaqueous-water solvent mixtures, a small proportion of helices are formed, suggesting that the nonaqueous solvent causes minor perturbation during microstructure formation. Previous studies of the effect of ethanol on lipids are primarily studies of effect on T,. To our knowledge, infrared studies have not been conducted on lipids in ethanol-water, particularly on tubule-forming lipids. Experimental Section The 1,2-bis(10,12-tricosadiynoyl)-sn-glycero-3-phosphocholine (DC8,gPC) was made by Singh and Herendeen according to their published procedure4 and produced a single spot when analyzed by thin-layer chromatography on silica gel plates developed with 65:25:4 ch1oroform:methanol:water. The method for making (1) Yager, P.; Schoen, P. E.; Davies, C. A.; Price, R.; Singh, A. Biophys. J. 1985, 43, 899. (2) Georger, J. H.; Singh, A.; Price, R. R.; Schnur, J. M.; Yager, P.; Schoen. P. E. J. Am. Chem. Soc. 1987, 109. 616945175. (3) Singh, A., private communication. (4) Schnur, J. M.; Price, R. R.; Schoen, P. E.;Yager, P.; Calvert, J.; Georger, J. H.; Singh, A. Thin Solid Films 1987, 152, 181-206.
This article not subject to U S . Copyright. Published 1989 by the American Chemical Society
