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Chem. Mater. 1990,2, 312-314
On the Templating of Curvature in Zeolites Zoltan Blumt and Stephen Hyde* Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Box 4, A.C.T. 2601, Australia Received December 7, 1989 The cage and tunnel descriptions of some zeolite crystal structures have previously been shown to be succinctly described as structural networks lying on periodic minimal surfaces, which are saddle-shaped surfaces whose average curvature vanishes everywhere on the surface. We establish here that the vanishing average curvature of these structures is due to the templating effect of typical cations (e.g., tetraalkylammonium ions) used to synthesize the zeolites. These cations form large hydrated spheres in solution. Given that these ions are locally ordered, the optimal locations for the silicon- and aluminum-containing solvated species are on surfaces of vanishing average curvature which lie between the hydrated cations. Upon crystallization, the average curvature of the aluminosilicate network is frozen in, forming periodic minimal surfaces. This model is applied to the synthesis of the zeolites sodalite, synthetic gismondine, and silicalite I.
Introduction The complex tunnel morphology of many zeolites has led to a plethora of differing structural descriptions. The large unit cells of these crystals result in complicated traditional crystallographic descriptions, involving many different polyhedra.' Over the past few years, it has been recognized that the framework structures of many zeolites lie on or close to periodic minimal surface^,^^^ and these surfaces offer an extremely useful description of crystal structure^.^ The intrinsic noneuclidean nature of these surfaces results in a radically different perspective of zeolite framework structures: the framework is viewed as a smoothly curved net lying on the surface, rather than an array of complex euclidean polyhedra. This description has been extended to many inorganic4s5 and organic structures6~'which are described as nets lying on minimal surfaces. The utility of periodic minimal surfaces as a language of crystal structure is clear, especially for complex structures containing many atoms per unit cell. We are now a t the stage where the language demands some justification. Calculations of equipotential surfaces for lattices made up of point charges4 as well as measurements of charge density distributions in real crystals5 lends support. In both cases, surfaces similar to periodic minimal surfaces appear. Furthermore, the trajectories of conducting ions in solid electrolytes lie on periodic minimal surfaces, and this has been interpreted as a natural consequence of minimal surface equipotential surface^.^?^ This observation is not surprising, given that periodic minimal surfaces arise naturally as spatial partitions of spheres forming crystallographic sphere packings.1° The partitioning effect is quantitatively expressed by the equipotential surfaces: these surfaces are valid for lattices of charged spheres as well as those made up of point charges. In essence, periodic minimal surfaces represent optimal steric and electrostatic loci for atoms forced to reside between lattices of charged spheres. Thus far, no explanation has been offered for the observation that the geometry of zeolite frameworks appears to be similar to periodic minimal surfaces. In this paper we suggest that aluminosilicate networks naturally form minimal surfaces under the templating effect of typical ions used during zeolite synthesis.
silica and alumina (or appropriate silicates and aluminates) in an alkaline solution, followed by crystallization of the zeolite within an aqueous aluminosilicate gel a t slightly elevated temperatures and pressures.' The composition of the initial mixture, as well as the temperature required for the synthesis, varies widely among zeolites.' In general, the complicated phase behavior in solution precludes any systematic prediction of the conditions required for zeolite synthesis. Most zeolites, such as Linde-A, sodalite, and faujasite can be synthesized by using sodium hydroxide as the alkali.' For some commercial applications, the silica to alumina ratio in the zeolitic framework must be maximized, in order to create a hydrophobic zeolite. In many cases, extremely high silicon contents can be achieved by using a wide variety of organic ions instead of sodium.'l The most common are the tetraalkylammonium ions (TAA) tetramethylammonium (TMA), tetraethylammonium (TEA), tetrapropylammonium (TPA), and tetrabutylammonium (TBA), although many other more or less exotic ions are also used. Other zeolites can only be synthesized by using TAA ions together with sodium ions or TAA with alcohols." It is widely acknowledged that the TAA ions act as "templating agents", although the specific nature of the templating action is unc1ear.l' Whether these ions act as straightforward "structure directors" for crystallizing aluminosilicate gels or whether they affect the gel chemistry is a matter of some debate in the literature. It is likely that the TAA ions do both. Force measurements of TAA ions deposited on mica indicate a strong affinity between TAA ions in solution and silicates,12suggesting that these ions affect the gel. However, even a cursory glance at the structures of TAA hydrate crystals, which form large
Results and Discussion Many zeolites can be routinely synthesized in the laboratory. In general, the synthesis involves dissolution of
(7) Blum, Z.; Lidin, S. Acta Chem. Scand. 1988, B42, 332. (8) Andersson, S.; Hyde, S. T.;Bovin, J.-0. Z. Kristallogr. 1985,173, 97. (9) Hyde, S.T.Philos. Mag. ( B ) 1988,B57,691. (10) Koch, E.;Fischer, W. 2.Kristallogr., in press. (11) Lok, B. M.; Cannan, T.R.; Messina, C. A. Zeolites 1983,3,282. (12) Claesson, P.; Horn, R. G.; Pashley, R. M. J. Colloid Interface Sci. 1984, 100,250.
On leave from the Department of Inorganic Chemistry 2, Lund University, Box 124, S-22100, Lund, Sweden.
(1) Breck, D.W. Zeolite Molecular Sieues; Wiley: New York, 1974. (2) Andersson, S. Angew. Chem., Znt. Ed. Engl. 1983, 22, 69. (3) Andersson, S.; Hyde, S. T.;von Schnering, H.-G. 2. Kristallog. 1984, 168, 1. (4) Nesper, R.;von Schnering, H.-G. Angew. Chem., Int. Ed. Engl. 1986,25, 110.
(5) Nesper, R.;von Schnering, H.-G. Angew. Chem., Znt. Ed. Engl. 1987,26, 1059.
(6) Andersson, S.; Hyde, S. T.;Lamson, K.; Lidin, S. Chem. Reu. 1988,
88, 221.
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Templating of Curvature in Zeolites
clathrate structures, lends convincing support to the templating concept.13-16 These clathrate structures are remarkably similar to the frameworks of zeolites. The clathrate hydrates occur up to very high water contents (40 water molecules per TAA ion 15). The water molecules crystallize around the TAA ions, forming a variety of hydrogen-bonded cages, including tetrakaidecahedra, pentakaidecahedra, and pentagonal dodecahedra.13-16 All of these polyhedra are similar to spheres. Thus, the clathrates can be pictured as a lattice of spherelike hydrated ions. There is evidence that the structure is retained, at least locally, upon dissolution. The heat of fusion of TBABr.30H20 is low,l7 indicating that all structure is not lost upon melting. Further, the partial molal volumes of TAABr salts in solution exhibit pronounced minima at certain water contents, suggesting the formation of clathrate-like structures. Given these facts, it is reasonable to suggest that the TAA ions form large, hydrated spheres in solution. While these spheres cannot exhibit long-range order, it is likely that some ordering occurs, at least locally. Accepting then that this is true, we find the formation of local body-centered cubic, body-centered tetragonal, or orthorhombic arrays are consistent with, and explain, the resulting geometries of the zeolites sodalite, gismondine, and ZSM 5 formed in this templating solution. The proposed geometry of the hydrated TAA ions leads naturally to the concept of minimal surfaces. This connection can be seen as follows. We shall establish that the mobile ions in fast ion conductors are confined to regions of space close to a periodic minimal surface under suitable conditions. Similar conditions are at work in the silicate mother liquor, so that the ensuing silicate crystal structure is also confined to periodic minimal surfaces. This argument is presented in detail below. It has been shown elsewhere that an equipotential surface for interpenetrating cationic and anionic sublattices is identical with a tangential field surface of the (geometrically) identical structure, where the ions in both sublattices carry the same charge, provided the equipotential surface is a minimal ~ u r f a c e . ~ J(The ~ tangential field surface is a surface that partitions the structure such that the electrostatic field at the surface is everywhere tangential to the surface, in contrast to an equipotential surface, for which the field is everywhere normal to the surface.) It is known that the zero20 equipotential surfaces for many interpenetrating lattices of oppositely charged spheres are close to periodic minimal surface^.^ For example, Schwarz' P-surface is very similar to the zero equipotential surface for the bcc CsCl structure, with the two interpenetrating cubic tunnel networks of the surface linking up the simple cubic cationic and anionic sublattices (Figure 1, top) all carrying the same charge. Mobile species, which interact with this bcc array (subjected to a repulsive interaction) must then be confined to regions (13)McMullan, R.;Jeffrey, G. A. J. Chem. Phys. 1959,31,1231. (14)Feil, D.;Jeffrey, G. A. J. Chem. Phys. 1961,35, 1863. (15)McMullan, R.;Bonamico, M.; Jeffrey, G. A. J. Chem. Phys. 1963, 39, 3295. (16)Beurskens, G.;Jeffrey, G. A.; McMullan, R. J . Chem. Phys. 1963, 39, 3311. (17)Frank, H.S. 2. Phys. Chem. (Leipzig) 1965,228,364. (18)Wen, W.-Y.; Saito, S. J . Phys. Chem. 1964,68,2639. (19)Hyde, S.T. Ph.D. Thesis, Monash University, 1986 and in ref 9. (20)The assignation of a zero of electrostatic potential is formally impossible for an (infinite) charged lattice. By analogy with a pair of oppositely charged ions, we define the zero of potential to be equal to the potential at a point midway between two neighboring oppositely charged ions.
Chem. Mater., Vol. 2, No. 3, 1990 313
Figure 1. Top: Schwarz P-surface,which forms a tangential field surface for the bcc array of iodine anions (large spheres) in the solid electrolyte a-AgI. Typical measured average silver ion positions are indicated by the smaller spheres on the surface. This tangential field surface also represents the locus of optimal positions for silica and alumina species in some zeolite precursor gels (e.g., sodalite), assuming that the templating ions (e.g., tetraalkylammonium) form a bcc array locally in solution. Subsequent crystallization of the zeolite from the gel thus results in a crystal network that tessellates the tangential field surface. It is significant that the average silver positions in a-AgI are the same as the silicon/aliminum positions in sodalite. Bottom: periodic minimal surface known as the D-surface, a second tangential field surface for a bcc array of cations or anions. The spheres on either side of the surface indicate sites of the bcc lattice.
of space on or close to this surface. Even in solution then, where for suitable concentrations the cations are expected to adopt a locally bcc geometry, solutes that interact with these cations will be confined to the neighborhood of this surface. This tangential field surface represents the collection of optimal paths through the lattice, equidistant everywhere from the charged lattice (since it is derived from the zero equipotential). Where more than one decomposition of a lattice into interpenetrating sublattices is possible, a number of TFS solutions exist. For example, a bcc lattice can be decomposed into two interpenetrating simple cubic sublattices or two interpenetrating diamond sublattices. Thus, for example, Ag' ions in the classical solid electrolyte a-AgI travel along the P-surface or the Schwarz D-surface,
314 Chem. Mater., Vol. 2, No. 3, 1990 which both pass between the bcc lattice of stationary Iionslg (Figure 1, bottom). Distinct tangential field surfaces pass between different pairs of ions, so the surface adopted by the solute depends upon the spacing between the ion pairs and the interactions betwen solute and ions. Since these and other as yet unknown tangential field surfaces are distinguishable by their dissection of the immobile ionic array, they will not be present simultaneously. Rather, they will be registered within a system as the extensive variables are altered. For the purposes of our analysis of the crystallization of zeolites, we shall ignore this multiplicity; we assume that under relevant crystallization conditions for a particular zeolite only a single tangential field surface is relevant. If these conditions are altered to yield a different tangential field surface, a new zeolite will result, which tessellates the new surface. We note also that this relation between tangential field and equipotential surfaces is valid not only for arrays of charged spheres. Any distortion of the charge distribution that does not change the point symmetry of the array leaves the tangential field and equipotential surfaces unchanged. For example, the zero equipotential surface for a bcc array of charged cubes is the same as that of a bcc array of spheres or point charges. This model of zeolite formation leads naturally to an explanation of the geometry of some zeolitic frameworks. We consider zeolites made with TAA ions alone, viz. sodalite, TMA-gismondine, silicalite I, and the isostructural synthetic zeolite ZSM-5. Sodalite has been synthesized by using TMA ions.21 The sodalite framework forms a tessellation of the Psurface, with four-rings around each neck of the surface (Figure 1,top). As we have seen, this surface is a tangential field surface for a bcc lattice of c h a r g e ~ . ~We J ~ propose that the TMA ions form a locally ordered bcc lattice in solution, with the P-surface as the resulting tangential field surface for this arrangement of TMA ions. Prior to and during crystallization then, we expect the aluminosilica species to lie on this surface. The subsequent crystal should thus tessellate the P-surface, with the TMA ions forming a bcc lattice, with two ions per (conventionalcubic) unit cell. This gives the TMA-sodalite structure, with a single TMA ion in each of the large cages of the P-surface, as measured.21 This local ordering in solution of the TMA ions can clearly be perturbed within the synthesis to give a locally body-centered tetragonal (bct) array of small tetragonal distortion, for which the tangential field surface is the T-surface.lg Such an arrangement provides the template for the TMA-gismondine structure, which has been synthesized under the same conditions as TMA-sodalite (below about 180 oC).22 This synthetic zeolite contains a single TMA ion for every cage of the structure, giving a bct array (slightly idealized). The idealized gismondine framework forms a tessellation of the Schwarz T-surface,6 with four-rings around each saddle. A more complicated local ordering of the templating TPA ions is expected in order to form silicalite I, or the ZSM-5 structure. This network is orthorhombic, and here too the largest cages of the structure contain a single templating TPA ion, giving a sphere packing of symmetry PnmaZ3 Sphere packings of this symmetry have been (21) Baerlocher, C.; Meier, W. M. Helu. Chim. Acta 1969, 52, 1853. (22) Baerlocher, C.; Meier, W. M. Helu. Chim. Acta 1970, 53, 1285.
Blum and Hyde proposed by Koch and F i s ~ h e r although ,~~ a periodic minimal surface partitioning the packing has yet to be derived. The topology per unit cell of this network can be shown from analysis of the atomic rings in the silicalite structure to be at least genus four per unit cell.25 This means that the tangential field surface must have this topology and symmetry Pnma. A surface fulfilling these requirements may be an orthorhombic distortion of the D-surface, although this is still uncertain. Nevertheless, it is clear from molecular models that the framework in silicalite I and ZSM-5 lie on a periodic minimal surface. Again, we expect this surface to be a tangential field surface for the orthorhombic sphere packing.
Conclusion We have chosen three simple examples to demonstrate the link between the tangential field surface of the templating array and the resulting geometry of the zeolite. Given the small number of tangential field surfaces known to date, we cannot broaden the discussion a t this stage. This must await the generation of new equipotential and tangential field surfaces, which is underway. Nevertheless, it is clear that many zeolites can be simply described as aluminosilicate nets that tessellate minimal surfaces, rather then connected cages. This paper has attempted to explain that description. The conventional description in terms of connected cages-each cage formed about a templating ion-is insufficient to explain the overall topology of the zeolite framework, since the tunnels that connect cages are no more than passive links. It is difficult to rationalize their presence, let alone why they link the cages they do. In our model, the tunnels are an integral part of the structure, and the network topology is set by the topology of the tangential field surface. At first glance, the proposed constraints on the solution geometry of the cations seem unreasonable. However, there is ample evidence that the TAA ions are locally ordered in solution, as discussed in the previous section of this paper. We emphasize that long-range ordering is not required for this mechanism of zeolite crystallization. Initial crystallization of a “seed” zeolite about a locally ordered region is sufficient to form a larger crystal. The crystallization front can order the cation distribution as it passes through the gel. This model of zeolite formation provides many clues to future directions in zeolite synthesis. Given that many of these structures lie on periodic minimal surfaces, efficient templates should form regions that correspond to periodic minimal surfaces. For many technical applications of zeolites, the porosity should be as high as possible. In the context of our analysis, this implies that the minimal surface topology should be as high as possible. Work is underway in our laboratories to investigate these possibilities. Acknowledgment. We are grateful to Barry Ninham and Sten Anderson for many useful discussions on this topic. Z.B. thanks the Department of Applied Mathematics, A.N.U, for hospitality and the Swedish Board of Technical Development for financial support. (23) Chao, K.-J.; Lin, J.-C.; Wang; Y.; Lee, G. H. Zeolites 1986, 6, 35-38. (24) Koch, E.; Fischer, W. 2. Kristallogr. 1978, 148, 107. (25) For an outline of the calculation technique, see: Hyde, S. T. 2 . Krzstallogr. 1987, 179, 53.
