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Toward a Silicate-Based Molecular Nanotechnology
II. Modeling, Synthesis Review, and Assembly Approaches

by
Stephen L. Gillett

Dept. of Geological Sciences
Mackay School of Mines, University of Nevada
Reno, Nevada 89557 USA
e-mail: [email protected]
Based in part on a presentation given at the
Fifth Foresight Conference on Molecular Nanotechnology. Palo Alto, California, 8 Nov 1997.
This version was submitted 1 Dec 1998.

Abstract

Three-dimensional (3D) frameworks linked by T-O-T bonds, where T is an atom in tetrahedral coordination (Si, Al, B, Ga, P, etc.) form a promising alternative to the "diamondoid" (sp³ C) structures generally proposed in theoretical studies of molecular nanotechnology (MNT). Silicate and substituted silicate frameworks ("tectosilicates"), the most abundant compounds on the Earth, are the prototypical examples of such structures.

In the last few years the molecular modeling of silicates and related materials has become amply adequate to examine possible structures of potential interest. Both fundamentally ionic and force-field approaches yield reasonable results, but high-precision results require including the directionality of the Si-O bond. In addition, explicit ionic forces must be included for charged frameworks. There is also a large literature on the topology of possible 4-connected framework structures, of which only a fraction have been realized as actual crystal structures with present-day synthesis techniques.

Present synthesis techniques for tectosilicates and related compounds do not yield molecular control except in the haphazard sense of crystallization of particular species through empirical "recipes." Zeolite and other molecular sieve syntheses represent empirical self-assembly approaches in which "templating" agents, generally cationic organic molecules, favor the nucleation and crystallization of particular structures. Although both experimental and theoretical progress is being made on understanding the molecular basis of such self-assembly, the fundamental mechanisms remain controversial. Moreover, molecular control does not extend beyond the individual crystallites. Sol-gel techniques based on alkoxide hydrolysis are potentially attractive due to their low temperatures and potential for greater molecular control of the silicate species, but still yield glasses with no long-range molecular ordering.

A mechanosynthetic molecular assembler, as for extraction of silicate species from aqueous solution, may be based on complementary fits to particular desired oligomeric building blocks, but must be robust enough to withstand the molecular jostling in aqueous solution. Appropriation of the biological mechanisms for handling silica may be one approach to making a molecular machine.

Silicate nanotechnological assembly seems to especially lend itself to a "building block" approach as (1) it is relatively easy to form disiloxy bonds by condensation of silanol (SiOH) or silanol+SiOR groups; and (2) void-bearing structures are a desired synthetic goal. Small, "stackable" cyclic and polyhedral silicate oligomers seem obvious building blocks. Many exist as independent entities already, as anions in aqueous solution or crystalline silicates, or as the silicate cores of silsesquioxanes. Either mechanosynthetic or self-assembly approaches seem reasonable, although the latter seems nearer term as it might represent a fairly straightforward extension of current templating syntheses.

Although blocks up to the single six-ring and single 8-ring are known as independent entities, at least formally, synthesis of larger building blocks is a serious issue, especially since they would be much more convenient for building structures. Large building blocks in particular are currently unknown as independent entities, but may be possibly be made with a molecular templating approach.

1. Introduction.

The previous paper outlines in detail the motivations for considering three-dimensional (3D) silicate frameworks ("tectosilicates") as a basis for molecular nanotechnology (MNT), in particular their advantages as an alternative to the "diamondoid" (sp³ carbon) frameworks that have dominated theoretical discussions of MNT structures. That paper gives an overview of silicate chemistry, especially as contrasted to C. Tectosilicates are based on SiO₄ tetrahedra linked by disiloxy (Si-O-Si) bonds; substitution of another atom (e.g., Al, Ge, B, etc.) into the tetrahedrally coordinated site (a "T-atom") yields an even more diverse set of possible structures, in part by imposing a net charge to the framework that must be compensated by included ions.

This follow-up paper will treat possible approaches to a silicate MNT. It includes a review of molecular modeling and topological description of silicate frameworks and an overview of conventional synthesis approaches. This is followed by some suggestions for molecular assembly of silicates, including consideration of the molecular machinery in organisms that precipitate silica, possible silicate building blocks, and the simplest structures that could be built with them.

2. Molecular Modeling of Silicates.

As emphasized by Drexler (1992), reasonably detailed modeling of sophisticated molecular structures is necessary, if only to winnow the vast number of possibilities down to a subset of promising designs for further investigation. Thus, another attractive aspect of carbon-based structures has been the variety of computing tools (such as the MM2 package used in Drexler, 1992) available for investigating them theoretically. Silicate modeling has traditionally not been nearly so well developed, but in the last few years there has been a surge of efforts using both empirical and ab initio approaches, such that there is now something of an embarras du choix. Indeed, the different groups that have developed silicate models, out of organic and siloxane chemistry, mineral physics, materials science, and industrial zeolite chemistry, underscore the interdisciplinary position (or limbo?) wherein silicate chemistry resides. Hence, although to the author's knowledge there is no dedicated silicate modeling package analogous to MM2 for organics, there are now a number of different parameter sets that can be (and have been) incorporated into commercial molecular dynamics packages (e.g., Cerius² from Molecular Simulations).

Because of their potential importance to nanotechnological endeavors these modeling efforts will be reviewed in some detail. Although references cannot be comprehensive due to space limitations, those given will lead the reader into the literature; in addition, Erikson & Hostetler (1987), Sauer (1989) and Tossell & Vaughn (1992) survey much earlier work, while Vashishta et al. (1990), Boisen & Gibbs (1993), and Hill & Sauer (1994) include useful reviews. Moreover, not all modeling approaches are equally useful for nanotechnological applications, and the differences will be noted.

2.1 Atomistic modeling.

The giant-molecule nature of silicate structures of potential nanotechnological interest seems at first sight a formidable barrier to realistic modeling, because the computational costs of representing a reasonable fraction of such a crystal would seem prohibitive. Of course, the translational symmetry of a crystalline structure can be exploited, and this is routinely done even in molecular mechanics approaches to modeling crystal structure, as also in simulated annealing techniques (e.g., Deem & Newsam, 1989, 1992). Sophisticated quantum-mechanical approaches, such as periodic pseudopotential models (e.g., Nada et al., 1990; Allan & Teter, 1987; Chelikowsky et al., 1991; Cohen, 1994; Silvi et al., 1990, 1992) also directly exploit the translational symmetry, though the large unit cells and low symmetries of most zeolites make modeling difficult, especially since many features of interest, such as catalytic sites, are less constrained by symmetry.

In any case, however, many nanotechnological constructs are not periodic, so such modeling methods are of limited use; models with specific atom-atom interactions are required instead. As even in giant-molecule structures most forces are short-range, such modeling proves more practical than might have been expected.

2.1.1 Pairwise models.

Two distinct approaches to such atomistic modeling exist. One approach treats all atoms fundamentally pairwise, with an electrostatic interaction term modified by some sort of short-range repulsion term. The inclusion of electrostatic terms means that such models explicitly contain long-range forces, and so such models must sum these forces over all pairs of atoms, not just nearest neighbors. Hence, they require an evaluation of the Madelung energy, which to speed convergence is generally done with the Ewald summation technique (e.g., Kieffer & Angell, 1989); nonetheless, because of this long-range nature the computational cost is considerably greater than might be expected from the relatively simple functional forms. Furthermore, the Ewald summation only works with a periodic array of charges, such as in crystals.

This type of model is, unsurprisingly, appropriate for ionic solids. A great deal of variation in functional form is possible; typically the short range repulsion term is an exponential "Born-Mayer" type, commonly with additional terms, as in the Born-Mayer-Huggins (Garofalini, 1982; Feuston & Garofalini, 1988; Delaye et al., 1997), or Buckingham (e.g., Sanders et al., 1984; Tsuneyuki et al., 1988; van Beest et al., 1990; Purton et al., 1993; de Boer et al., 1994) potentials. The Coulomb energy term is also commonly expressed in terms of "effective" charges, rather than the full formal ionic charges, and these then become additional parameters that also must be fitted (e.g., Erikson & Hostetler, 1987; Tsuneyuki et al., 1988; van Beest et al., 1990). To speed evaluation of the Ewald summation, some sort of "cutoff", beyond which the Coulomb interactions are ignored, is commonly employed (e.g., Garofalini, 1982; Feuston & Garofalini, 1988). Another variation is "shell" models, in which large ions (generally anions) are treated as consisting of a charged but massless "shell" harmonically coupled to a separately charged core (e.g., Sanders et al., 1984; de Man et al., 1990; de Boer et al., 1995; Schröder & Sauer, 1996); these also yield better dielectric properties and elastic constants (e.g., Collins & Catlow, 1992) because polarizability is explicitly included.

2.1.2 Valence force field models.

Alternatively, valence force-field models, which are appropriate for covalent molecules, can be devised. In such models, typified by MM2 and MM3, atoms are assumed to interact with their nearest neighbors only by some sort of force field. Next nearest-neighbors must also be treated, commonly by 3-body bond angle bending terms (Sanders et al., 1984; Lasaga & Gibbs, 1987; Hill & Sauer, 1994), or by "next-nearest neighbor" potentials, such as the 1-3 "Urey-Bradley" potential. These implicitly assume an atom between the nominally interacting atom-pair and so might be called "implied" 3-body interactions (Lasaga & Gibbs, 1988; de vos Burchart et al., 1992ab). Such 3-body terms implicitly recognize the directionality of covalent bonds. A simpler but much less general approach is to impose unit-cell and crystallographic symmetry constraints from a known structure on a two-body model (e.g., Demontis et al., 1991), though results from this approach are disputed (Smirnov & Bougeard, 1995).

2.1.3 Model fitting.

Irrespective of the model chosen, its parameters can be found by fitting with empirical data, using observed crystal structures to determine equilibrium atomic distances, and spectroscopy and/or elastic constants to determine the atomic force-field constants (e.g., Stixrude & Bukowinski, 1988; Smirnov & Bougeard, 1993ab). Spectroscopic observations on siloxanes (e.g., Bärtsch et al., 1994), which are more readily interpreted than those of tectosilicates such as zeolites (No et al., 1986), have also been used. These models in turn have been used to model the vibrational frequencies of silicate and siloxane structures, both for interpreting spectroscopic data (Bärtsch et al., 1991; Calzaferri et al., 1994), and to model shape changes during zeolite vibrations (Bornhauser & Calzaferri, 1996). The constants have also been inferred from molecular geometries of siloxanes, particularly for models that are direct extensions of MM2 (Timofeeva et al., 1984; Abraham & Grant, 1988).

Alternatively, the parameters can be determined by ab initio quantum-mechanical calculations, ideally using no empirical data other than fundamental constants (e.g., O'Keeffe & McMillan, 1986; McMillan & Hess, 1990; Hill & Sauer, 1994, 1995; Gonze et al., 1994; Rustad & Hay, 1995 & refs. therein). Despite their computational intensity, such approaches are becoming more common as computer power has continued to plummet in cost, as they avoid biasing the results by the idiosyncrasies of specific compounds. Nonetheless, it is often found that such models must be "tweaked" with macroscopic empirical data (e.g., van Beest et al., 1990; Boisen & Gibbs, 1993; de Boer et al., 1995), or else experimental results, such as the Si-O bond length, are implicitly incorporated (e.g., Tsuneyuki et al., 1988). Presumably, though, such "semiempirical" models are still less biased by the idiosyncrasies of particular structures.

For pair and 3-body potentials, small molecules have proven to be good models of the Si-O interactions in silicates, presumably because, after all, short-range forces dominate the bonding (Gibbs, 1982; Gibbs & Boisen, 1986; Lasaga & Gibbs, 1987; Sauer, 1989; Boisen & Gibbs, 1993). Hence detailed modeling of the forces in such molecules provides a widely explored pathway to larger structures, especially in the ab initio studies (e.g., Lasaga & Gibbs, 1987, 1991; van Beest et al., 1990; Kramer et al., 1991; Hill & Sauer, 1994; Ermoshin et al., 1996ab). H₄SiO₄ and H₆Si₂O₇ (the smallest molecule with an Si-O-Si linkage) have been studied in particular, but as computer power has become cheaper, bigger units have been treated (Grigoras & Lane, 1988; Nicholas et al., 1992; Purton et al., 1993; Hill & Sauer, 1994, 1995). (Quite a number of additional ab initio studies on small silicates and siloxanes have also been carried out, but without the additional parametrization needed to generalize to molecular modeling.)

2.1.4 Results of different modeling approaches.

As the Si-O bond has about 50% covalent character (e.g., Liebau, 1985, p. 46-48), it might be expected that both ionic and covalent models would work reasonably well, and this is true as a first cut. Simple pairwise models give good results on vitreous silica or melts (e.g., Garofalini, 1982; Kieffer & Angell, 1989; Scamehorn & Angell, 1991; Della Valle & Andersen, 1992; Poe et al., 1992), and yield passable results on silica (Della Valle & Andersen, 1991) and even zeolites, if unit-cell and symmetry constraints are also imposed (Demontis et al., 1991). Modeling crystal structures and elastic constants, however, requires more sophistication, and modeling vibrational modes, not just their frequencies but their relative intensities, is much more demanding yet. Further stringent tests lie in modeling changes in structure as functions of temperature and pressure, the latter especially of interest in geophysics where modeling is used to glean insight into experimentally inaccessible regions. Indeed, even silica glass is significantly better modeled if 3-body interactions are included (Feuston & Garofalini, 1988; Vashishta et al., 1990; Vessal et al., 1993).

One result is that as the models become more detailed they acquire a "hybrid" status. For example, it is widely acknowledged that in detailed models it is critical to include three-body bond-bending terms or other next-nearest-neighbor interactions, because the Si-O bond is after all not purely ionic (e.g., Sanders et al., 1984; Nicholas et al., 1991; Smirnov & Bougeard, 1993b; de Boer et al., 1994). Hence bending or other three-body terms are widely incorporated into basically ionic models (Sanders et al., 1984; Feuston & Garofalini, 1988). Ionic shell models, in which the oxygens are treated as shells but the Si atoms are rigid, yield a considerable improvement over simple rigid-ion models as well (Jackson & Catlow, 1988; de Man et al., 1990; de Boer et al., 1995; Schröder & Sauer, 1996), probably because the "shells" model the electrostatic screening due to polarization (de Man et al., 1990). In general, including polarization in ionic models improves them (Wilson et al., 1996).

Conversely, long-range forces are commonly added to basically covalent models (e.g., No et al., 1987, 1989; de vos Buchart, 1992ab; Demontis et al., 1995). Though perhaps not needed for neutral structures (Stixrude & Bukowinski, 1988; Nicholas et al., 1991; Hill & Sauer, 1994), they must be included in structures containing ionic species, such as in substituted frameworks in which the frame is a giant anion whose charge is compensated by included cations (e.g., Smirnov et al., 1994). The modeling of silicate minerals (e.g., micas, Collins & Catlow, 1992; feldspars, Purton & Catlow, 1990), which contain metal ions (Na⁺, K⁺, Mg⁺⁺, Fe⁺⁺, and so on) with polymeric aluminosilicate anions, indicates how such ionic solids can be treated.

As described earlier, substitution of Si by other T-atoms is one cause of the enormous variety of silicate and related compounds. Aluminum, the abundant substituent in natural systems, and phosphorus have been modeled (van Beest et al., 1990; Kramer et al., 1991; de vos Burchart, 1992b). Indeed, because of the statistical distribution of Al vs. Si in many aluminosilicates, modeling an "average" Al-Si atom is sometimes convenient (No et al., 1987; Ooms et al., 1988; Collins & Catlow, 1992). Other recently modeled T-atoms include Ge (George et al., 1993) and Ti (de Man & Sauer, 1996).

For nanotechnological applications, force-field models are probably most convenient, as they more directly dovetail into MM2 and similar packages already used for C compounds. They also seem more intuitive in terms of "building things by sticking atoms together." The models of Hill and Sauer (1994, 1995), based on ab initio methods, are probably the most sophisticated at the present time, but work seems to be continuing by other groups. (Indeed, in a subsequent paper, Schröder & Sauer (1996) find that an ionic shell model based on the same ab initio calculations yields as good if not better results as the valence force field.) However, as emphasized above, long-range electrostatic forces cannot be ignored if ions are present; as ion-bearing structures include some likely to be goals of near-term nanotechnology, such as ion-exchangers, catalysts, and solid electrolytes, this unfortunately adds a serious additional complication to nanotechnological modeling. Furthermore, because the Ewald summation technique can only be applied to a periodic array of charges, the modeling of aperiodic ion-bearing nanotechnological structures is likely to be even more computationally intensive.

2.2 Crystal structure prediction and MNT.

From the above, it is obvious that a great deal of modeling has been directed toward predicting and simulating crystal structures ab initio. Although this is an interesting and valid scientific problem, it is of limited relevance to designing MNT structures. Locating the thermodynamically stable macrostructure involves finding a global energy minimum that may depend heavily on second and third order effects that have been approximated out (Price et al., 1992). This is not directly relevant for MNT modeling, as useful structures are highly likely to be metastable thermodynamically anyway, as indeed are nearly all zeolites. Of much more interest is whether (1) a proposed structure represents a local energy minimum, and (2) the activation energy necessary for this structure to change into another. In other words, how high is the lowest "saddle" or "col" on the potential energy surface above the local minimum occupied by the structure? For useful structures, this activation energy must be sufficiently high that thermal perturbations are extremely unlikely to allow its spontaneous rearrangement. To put it another way, it is not important that the structure be at a global minimum; what is important is that the barriers between local minima be high enough that the structure does not change easily. Note also that these considerations do not depend on the absolute strength of the chemical bonds involved. A simple illustration is the well-known explosiveness of NCl₃. Although the N-Cl bond is relatively strong (~199 kJ/mol), the N₂ bond is even stronger, and the activation barriers to rearrangement of NCl₃ to N₂ and Cl₂ are low.

Such considerations of the local stability of a structure, as opposed to the irrelevance of a global analysis, are a general feature of MNT endeavors. Predicting the thermodynamically stable arrangement for an arbitrary collection of atoms, for example, is similar to the notorious "protein-folding" problem (cf. Berendsen, 1998). For nanotechnological purposes, we need not solve the general problem but instead can choose a well-behaved subset of structures whose configuration and properties do not depend strongly on small energy differences (Drexler, 1992).

3. Topological Modeling of Silicates.

There is a large literature on classifications of possible T-frameworks; Smith (1988) gives a thorough introduction, including a subset of stereopairs of zeolite structures from Meier & Olson (1987). Extensive catalogs of the structures and compositions of known molecular sieves have also been compiled (Meier & Olson, 1987; Szostak, 1992).

The T-frameworks can be visualized as a 3-dimensional (3D) "4-connected" network (4-net), in which the fully-polymerized tetrahedra are represented as the nodes of four connecting line segments. Many authors (e.g., Wells, 1977; Akporiaye, 1989; Akporiaye & Price, 1989; Brunner, 1990, 1993ab; O'Keeffe & Brese, 1992; O'Keeffe, 1991, 1992, 1995) have studied such 4-nets. J.V. Smith and co-workers, in particular, have conducted a systematic study and enumeration of such networks for many years (early references in Smith, 1988; also Andries & Smith, 1994; Han & Smith, 1994). One motivation for such study is to determine what geometric constraints may exist on the size and shape of any included voids, and of any channels connecting the voids. These are critical parameters in steric selectivity for catalysis, a major motivation for the synthesis of new zeolite structures. Such networks have proven useful both in determining the structures of zeolites, and in suggesting potential structures as targets for synthesis.

Obviously, 4-nets can be generated by assembling polyhedra in various ways (Moore & Smith, 1964, 1967; Hawthorne & Smith, 1986). Indeed, zeolites themselves can be thought of as being built up of smaller polyhedral units, as described in detail by (e.g.) Price et al. (1992) and van Koningsveld (1991). However, the requirement that only four lines can meet at a node, due to the tetrahedral coordination of Si or other T-atom, proves to be stringent constraint, as many polyhedral stacking schemes (e.g., of regular prisms) yield nodes with coordination >4.

Many 4-nets can also be found by extending a 2D 3-connected net (3-net) with an additional linkage up or down from each 3-node (e.g., Smith, 1977, 1978, 1979). The originating 2D 3-nets are conveniently described by their Schäfli symbol (e.g., Smith, 1977). This is based on the number of circuits around a node of the net and the number of points in those circuits. For example, the Schäfli symbol of the simple hexagonal net (the hexagonal tiling of the plane) in Figure 3d is 6³: there are three circuits around any node, and all circuits contain 6 points. The square-octagonal net in Figure 3e is 4·8²; any node lies both in a single circuit of four points and two containing eight. All nets considered here are of sufficiently high symmetry as to have only one type of node.

Only a handful of the vast number of topologically conceivable nets are actually realized by known tectosilicates (e.g., Dent Glasser, 1979; O'Keeffe, 1995). As the flexibility of the Si-O-Si bond has been emphasized, this restriction seems puzzling, and it may result from more than simple kinetic barriers to nucleation of certain structures. As described below, present zeolite syntheses are based on crystallizing of silicate gels with large organic "templating" ions, and the packing of such ions with the intervening silicate structure may strongly limit the resulting geometries by imposing symmetry constraints (Brunner, 1990). Here, then, may be another strong limitation on fabrication due to current "shake and bake" techniques. Presumably molecular assemblers could assemble most if not all of the topologically permitted arrays.

4. Tectosilicate and Related Syntheses: State of the Art

Though modeling is necessary, synthesizing (or attempting to synthesize) what has been modeled obviously remains the ultimate goal. Here silicate structures probably have an advantage for near-term development. Assembling tetrahedral carbon ("diamondoid") frameworks, which has been the usual focus of theoretical studies of MNT, is especially difficult. The sp³ carbon-carbon link is not thermodynamically stable at STP, so that extreme conditions are required; either diamond crystallization must be favored kinetically, as in CVD processes, or high pressure must be used to enter the diamond thermodynamic stability field. MNT studies have suggested assembly of carbon atoms in vacuum by molecular-scale assemblers, but this hardly makes the engineering easier or nearer-term!

In stark contrast, 3D polymerization of silicates can take place over conditions ranges from aqueous solution at STP to melts at hundreds of degrees C. Hence, possibly the most attractive aspect of silicate-based MNT is its potential ease of assembly. Indeed, one has the opposite problem from C-based structures: not of imposing a disfavored tetrahedral coordination to build 3D polymeric structures but of guiding spontaneous 3D polymerization to form molecularly ordered structures. As mentioned in the previous paper, the usual results of spontaneous polymerization of silicates at STP are molecularly disordered structures such as gels or glasses, due to the haphazard manner in which the disiloxy links are generated.

Controlling this polymerization at the molecular level is thus the main issue, and possible approaches will be discussed in section 5. All will focus on polymerization at STP, as this seems by far the most convenient.

4.1 High-temperature synthesis.

Many simple silicates can be synthesized directly by melting stoichiometric combinations of oxides together, generally in the presence of fluxing agents such as H₂O vapor or fluoride, and generally with fO₂ buffered. This "brute force" approach dominates experimental petrology, in which the thermodynamic stability ranges of particular silicate phases are generally of most interest. Traditional ceramics are synthesized in a similar manner, with the additional twist that most are glassy rather than crystalline.

Obviously, atomistic control in such circumstances is likely to be problematic.

4.2 Hydrothermal synthesis.

Although carried out at much lower temperatures, the present synthesis of zeolites and molecular sieves also leaves much to be desired in terms of molecular-level control. Typically alkaline aluminosilicate gels are "cooked", usually at temperatures <200° C and sometimes much less (e.g., in a boiling water bath; Milton, 1989), under specified conditions for times ranging up to several days (e.g., Barrer, 1989; Jansen, 1991). Such low temperatures favor the formation of the desired open structures, and the results also strongly depend on the thermal history. Different alkaline cations (Na, Ca, etc.) favor different structures; in part, this seems to result from ion-pairing effects, with larger cations favoring larger silicate oligomers by preferential association with them (McCormick et al., 1989). Alkali cations must also influence both nucleation and growth of silicate polymers, as they have a large effect on the crystallization kinetics of even pure-silica structures (Goepper et al., 1992). The crystallized products also strongly depend on Al/Si ratio (Szostak, 1989, Ch. 2; Jansen, 1991) and pH, as well as the presence of additional anions, especially fluoride (F^-). pH would be expected to have a profound influence owing to the ability of OH^- to cleave Si-O bonds, and F^- would also be expected to interrupt disiloxy bonds; indeed, Guth et al. (1989) found that fluoride-bearing gels could be stabilized at significantly lower pH, which facilitated substitution of other T-atoms. Not all effects are straightforward, however: F^- also catalyzes silica polymerization in small quantities, evidently by electrostatic neutralization between adjacent oligomers (Rabinovich & Wood, 1986). Dutta et al. (1989) found that alcohols in the gel have a profound kinetic effect in accelerating crystallization, probably through imposing a molecular-level organization of H₂O molecules and cations. Occelli & Robson (1989), Feijen et al. (1994), and Helmkamp & Davis (1995) give recent reviews on hydrothermal synthesis.

A synthesis breakthrough was the discovery that different organic molecules mixed into the gel (commonly large substituted-ammonium cations such as tetraalkylammonium and 1-adamantammonium) could lead to crystallization of a wide variety of new zeolite structures, including ones with much larger internal voids (Barrer, 1982, p. 162-166; Milton, 1989). Generally the organic ions are interpreted to direct crystallization by acting as "templates", by favoring certain configurations of small Si polymers and their self-assembly in certain ways. (It was once thought that subunits in various zeolite types (e.g., rings, cubes) reflected oligomers in the original gel (e.g., Szostak, 1989, Ch. 3), but this is now widely discounted (Keijsper & Post, 1989; Knight, 1990; Kinrade et al., 1998b).) The templating molecules become incorporated into the large voids in the growing crystal, and the incorporation of such large molecules favors void-bearing structures by lending a degree of thermodynamic stabilization (Liebau, 1985, p. 241). "Templating effects" are, of course, widely observed phenomena in chemical syntheses (e.g., Anderson et al., 1993, & refs therein).

"Templating" alone seems to be an oversimplification (Szostak, 1989, p. 92-95), however, as there is no one-to-one correspondence between the included templating species and the structure obtained. For this reason the term "structure-directing agent" is commonly preferred (Davis, 1996). Structure-directing effects must exist; for example, different organic molecules yield different silica clathrasils, and the size and shape of the open cage in the particular structure crystallized correlates well with the included molecule (Liebau, 1985, pp. 240-244). Burkett & Davis (1994) presented ²⁹Si NMR evidence that TPA directs the synthesis of pure-silica ZSM-5 by preorganizing silicate oligomers out of the gel. Kinrade et al. (1998a), however, suggest instead that the alkylammonium cations shield small cage-like silica oligomers (the D3Ra and D4Ra anions discussed below) from hydrolysis of the Si-O bond.

Of course, to judge by the profound effects of the history of gel on its crystallization, a great deal of the "favoritism" must also involve kinetic factors, presumably by enhancing certain reaction pathways at the expense of others. Indeed, entire books (e.g., Jacobs & Martens, 1987) exist of ad hoc recipes specifying the composition and pH of the gel, the heating time, the proportion of included organic template, and so on.

4.2.1 Post-synthesis modification.

This can also be carried out and indeed is generally necessary (Szostak, 1991). The templating molecules usually must be burned out to leave the voids behind, and this can also alter the chemistry of the included cations in useful ways; e.g., the thermal dissociation of included NH₄⁺ to NH₃ and H⁺. The NH₃ is driven off, leaving the H⁺ to yield a fixed acid (e.g., Thomas, 1992).

Other common modifications include ion exchange of the original cations, as with the replacement of Na⁺ and Ca⁺⁺ with H⁺ cations to make catalysts. In addition, structural Al can be replaced with Si by (e.g.) SiCl₄ treatment, or with other T-atoms using other reagents, or even by H⁺ to leave a T-site surrounded by hydroxyl groups (e.g., Szostak, 1991).

The emplacement of guest molecules or clusters, too, happens "after the fact". Although a great deal is possible (see the references above), again it is on an ad hoc basis with no atomistic control. Finally, the zeolite crystals from such synthesis techniques are typically very small (~1 µm), and this limits their potential utility greatly as noted above.

4.3 Sol-gel synthesis.

Sol-gel processes are now the focus of a great deal of research as alternative pathways to the fabrication of silicate (and other) ceramics (e.g., Klein, 1985; Hench & West, 1990; Brinker & Scherer, 1985, 1990; Brinker, 1994; Coltrain & Kelts, 1994). As reviewed in the previous paper, a silica "sol" is a colloidal dispersion of silica polymers ranging in size from a few repeat units to macromolecules consisting of many thousands; as polymerization continues, the sol sets, or "gels", to form what is essentially a hydrated glass. This glass can then be densified and dehydrated by relatively modest heating (i.e., below the melting point).

As the results are nearly always glassy rather than crystalline, sol-gel derived ceramics hardly exemplify atomistic control. Nonetheless, by providing an alternative to glass fabrication by brute-force melting, they allow much greater control over the composition and structure of the final product, and indeed this motivates the great interest in them. Sol-gel processing is an example of the so-called current "chimie douce" ("soft chemistry") approach to chemical synthesis, which attempts to eschew brute force approaches (e.g., high temperature, powerful reagents) in favor of low temperatures and more direct synthetic control (e.g., Delmas & Borthomieu, 1993). Such a philosophical approach should dovetail nicely with many nanotechnological approaches.

As described previously, aqueous silica polymerizes spontaneously unless very dilute. Therefore, a silica sol does not consist of a single dissolved species, but a wide variety of oligomers, polymers, and colloidal particles. Although different mixtures can be rendered metastable by variations of preparation, pH, and so on, such a sol is hardly a well-defined chemical entity, and this reduces the level of molecular control.

4.3.1 Alkoxide hydrolysis.

An approach toward better molecular control of polymerization that has received an enormous amount of attention in recent years is based on the hydrolysis of silicon alkoxides ("organic silicates"). Indeed, sol-gel synthesis is now usually construed to involve alkoxide hydrolysis (e.g., Brinker & Scherer, 1990; Coltrain & Kelts, 1994). The alkoxides are usually tetramethoxysilane (tetramethyl orthosilicate, TMOS), Si(OMe)₄, or tetraethoxysilane (tetraethyl orthosilicate, TEOS), Si(OEt)₄. As noted in the previous paper, both compounds can be considered esters of orthosilicic acid.

The Si-O-R link is readily hydrolyzed to yield silanol groups and the corresponding alcohol:

Si-O-R + H₂O ==> Si-O-H + ROH;

the silanol groups can then condense and polymerize as before. In addition, silanol groups, once formed, can condense with an alkoxide:

Si-O-H + ROSi ==> Si-O-Si + ROH.

Note that the process can be self-sustaining once begun, because the H₂O molecules formed by silanol condensation can trigger further alkoxy hydrolysis and generate more silanol groups. The process is catalyzed by either acid or base, but with differences in the resulting gels: acid catalysis generates linear polymers which are "spinnable" (i.e., capable of being drawn into a fiber), whereas basic catalysis yields colloidal particles somewhat as aqueous solutions do (e.g., Brinker & Scherer, 1990, p. 109 ff.). Because the alkoxysilanes are immiscible with H₂O, a co-solvent such as CH₃OH is generally used.

Note that the R group acts like a protective group in organic synthesis, because it blocks spontaneous silicate polymerization in the absence of H₂O. This is extremely attractive, as it provides a way to overcome some of the disadvantages of precipitating silicates from aqueous solution. A high concentration of a particular silicate species can be obtained, rather than a thermodynamic or kinetic mishmash of oligomers.

An approach toward even greater molecular control is to use oligomeric alkoxysiloxanes as the precursors. Day et al. (1985) found that octamethoxyoctasilsequioxane (D4R(OCH₃)₈) yields a gel in which the D4R units are preserved, although the gel is disordered. Similarly, Klemperer et al. (1986), in a study on the hydrolysis of several small methoxy oligomers (hexamethoxydisiloxane, octamethoxytrisiloxane and D4R(OCH₃)₈) found that the oligomeric structures were retained during hydrolysis. Cagle et al. (1990) found that a gel based on D4R(OCH₃)₈ yielded a microporous glass when baked out at 110°C. Although the ordering seemed better and the D4R units seemed to be preserved, the material was not crystalline. Hence, such "building blocks" have so far been disappointing in terms of imposing long-range molecular order.

In a different approach, Lee et al. (1994) used hydridospherosiloxanes to construct well-ordered SiO₂ layers on Si surfaces.

4.3.2 Alkoxide-based synthesis of silicates.

Silicon alkoxides have also been used to prepare gels as precursors for crystalline silicates. A major motivation is that alkoxides give a much more uniform, molecularly mixed gel, which favors nucleation and growth of uniform crystals (e.g., Pouxviel et al., 1986), often at lower temperatures than conventional methods (Treadwell et al., 1996). In particular, colloidal precipitates formed by hydrolysis can have much lower sintering temperatures (Duldulao & Burlitch, 1991; Chen et al., 1992).

4.4 Hybrid Organic-Siloxane Polymerizations.

Some groups have used organic-functionalized silica oligomers as building blocks, which are then linked by organic or siloxane bridges to form 3D polymeric structures. Herren et al. (1991) demonstrated a synthetic pathway to substituted cubosiloxanes D4R(R₆R'R"), where R' and R" were complementary organic units capable of forming a covalent bond, whereas R was inert. Haddad et al. (1996) and Lichtenhan et al. (1996) presented a somewhat different synthetic approach to polymers also based on D4R units linked by organic moieties. Hoebbel et al. (1989, 1990) functionalized D4Ra units with vinyl-substituted dimethylsilyl groups (Si(CH₃)₂CHCH₂), using a version of the trimethylsilylation technique (Lentz, 1964) discussed previously. These units can then polymerize via the vinyl units. Similarly, Agaskar (1989, 1992b) carried out low-temperature polymerization of vinyl-functionalized polyhedral silicate oligomers, including D3Ra and D5Ra as well as D4Ra.

Hasegawa and coworkers (Hasegawa et al., 1994; Hasegawa & Nakane, 1996) polymerized D4Ra in CH₃OH-TMA by the addition of dichlorodimethylsilane (SiCl₂(CH₃)₂), which established a dimethylsiloxy link between the D4R units. Harrison & Kannengiesser (1996) polymerized both D3R and D4R units with methylene crosslinks. Finally, a number of groups (e.g., Loy et al., 1996; McClain et al., 1996; Wolter et al., 1996) have demonstrated polymers based on "hybrid" monomers that contain both siloxane and purely organic linkages.

In all these cases, retention of the oligomeric building units in the resulting polymer imposes a higher degree of ordering at the nanometer scale, but no additional large-scale ordering occurs. The products remain glassy, like conventional polymers.

In many cases these organic-siloxane polymers are used as "ceramic precursors," being subsequently fired to yield a silicate-organic composite ceramic. Obviously this disrupts at least some of the atomistic ordering. Hasegawa and coworkers (Hasegawa et al., 1994; Hasegawa & Nakane, 1996) found that although D4R units were preserved after treatment at 350°C no long-range ordering was present. Similarly, Hoebbel et al. (1991, 1994) found that although the D4R unit was preserved, heat treatment >250°C eventually yielded a crosslinked silicate glass as all organic links were burned out. Finally, Agaskar (1992a) discovered that on pyrolysis at 800°C the D4R building unit was largely destroyed.

4.5 Biological systems.

Although silicates have no vast sets of intricate biochemical mechanisms for their assembly, as exists for the stepwise assembly of complex organic biomolecules, silicon is known to be involved in cellular development and metabolism (Hildebrand et al., 1997).

4.5.1 Biomineralization.

In particular, a number of single-celled organisms (radiolarians, diatoms) make hydrous glass tests (shells) of "opaline" silica. Such a precipitate has no crystalline order and contains an "interrupted" T-framework in which many vertices are terminated with OH groups; the mineral opal is a silica glass containing such an OH-interrupted framework. Among higher organisms, sponges and certain plants also lay down silica structures, called "spicules" and "phytoliths", respectively. These organisms evidently have molecular mechanisms for binding highly selectively with Si(OH)₄ and transporting it, presumably as some sort of complex (Hildebrand et al., 1997). The extraction system--or systems--are particularly remarkable given the low concentration of aqueous Si(OH)₄.

Diatoms are the best studied silica-precipitating organisms, but even so, critical details of their biomineralization processes remain unknown (Sullivan, 1986; Lowenstam & Weiner, 1989, pp. 58-60 & references therein). A silicate-transporting molecule--"silicophore"--has been isolated from diatoms, but evidently not characterized chemically (Bhattacharyya & Volcani, 1983). As reviewed in the previous paper, Si(OH)₄ forms a strong complexes with a few agents having "hard" bidendate oxy ligands. These include catechol (ortho-dihydroxybenzene) and the tropolone anion, and both are possibly involved in biological handling of Si (Iler, 1977; Sjöberg et al., 1985a; Evans et al., 1990, 1992). Catechol in particular has high affinity for small, "hard" cations (e.g., Fe³⁺, V⁵⁺, as well as Si⁴⁺) (Evers et al., 1989), and some "siderophore" proteins for transporting ferric iron include catechol moieties (Raymond & Smith, 1988; Raymond, 1990). It is tempting to speculate that the "silicophore" also employs catechol, and may even be related evolutionarily to siderophores.

It also seem probable that organic templates direct some of the actual silica precipitation (Sullivan, 1986; Mann & Perry, 1986). Biogenic silica bodies in higher plants ("phytoliths"), for example, contain protein residues interpreted have a role in controlling the silica precipitation (Harrison, 1996). Much biomineralization uses ionic compounds such as phosphates (apatite) and carbonates (calcite, aragonite) (Lowenstam & Weiner, 1989), and in many cases these biominerals are not only crystalline but the crystals are also highly ordered with respect to one another. The detailed cellular mechanisms by which this is accomplished remain largely obscure, although (for example) there is evidence that acid-rich b-protein sheets may orient layers of Ca ions (Lowenstam & Weiner, 1989, p. 23).

In the case of silica, however, since the product is a glass the templating does not dictate a crystalline structure. Indeed, forming a covalent T-framework crystal seems extremely difficult for biosystems, in contrast to templating ionic crystals (Williams, 1986). Nonetheless, biological sheets containing H-bonding moieties may structure silica precipitation even though they do not impose crystalline ordering. The reason is that, although Si(OH)₄ and small silicate oligomers do not form hydrogen bonds with their silanol groups, larger polymeric species (with >~40 Si atoms) and colloidal silica surfaces form strong hydrogen bonds, if the pH is ~7 (Iler, 1977) . As described in the previous paper, silanol H-atoms become more acidic with increasing polymerization of the silicate structure, and this favors hydrogen bonding. Such silicate polymers can form multiple H-bonds to organic polymers having H-bonding moieties such as polymeric ethers and polysaccharides. Indeed, this evidently accounts for some of the toxic effects of small silica species, because such bonding can denature proteins; colloidal silica causes albumin precipitation, for example (Iler, 1977).

4.5.2 Phosphate and phosphorylation.

Biological systems also have a fundamental enzyme system for linking phosphate (PO₄) tetrahedra: phosphorylation, which is used to store energy by making ATP from ADP (e.g., Lehninger et al., 1993). This could perhaps be adapted to linking arbitrary TO₄ tetrahedra with a bridging oxygen. Although the exact, atomistic mechanisms of this enzyme system still have not been completely worked out (Cox et al., 1992; Cross, 1992), the mechanism seems to involve binding of the entire polyphosphate oxyanion and its organic ligand to the enzyme, and perhaps involves rotation of a large enzyme subunit. Such a mechanism may be difficult to adapt to attaching tetrahedra to 3D T-frameworks.

Perhaps more encouraging is adaptation of inorganic pyrophosphatase, an enzyme that can link (or cleave) isolated phosphate groups (Baltsheffsky & Baltsheffsky, 1992). This system may be to some degree relict from an early bioenergetic pathway; it is simpler and seems to have been worked out in greater detail, although questions also remain as to its exact mechanism.

Other phosphorylation mechanisms attach PO₄ groups to other molecules, e.g. lipids to make phospholipids, and certain bacteria have been reported to incorporate SiO₄ groups to make "silicolipids" instead (Heinen, 1967ab). Biological formation of such organosilicon compounds remains controversial, however (Williams, 1986). In any event, as such mechanisms involve attaching a TO₄ group to an organic molecule, they may not be useful for attaching TO₄ groups to each other.

5. Nanotechnological Assembly of Silicates: Some Considerations.

Obviously an atomistic synthesis of tectosilicate structures, perhaps by some sort of molecular assembler, is necessary to fully realize the MNT prospects of these compounds. At the least, arbitrary structures could be fabricated of macroscopic size. The inclusions, or "guests", could also be built in directly as the structure is assembled. Ozin et al. (1989) noted that the 3D nature of devices using zeolitic substrates vastly increases the problems with assembly techniques such as are used for current microchips, because such intrinsically two-D processes as chemical vapor deposition (CVD) cannot be employed without major modification.

A host of further variations, which would probably be impossible to carry out with current techniques, would also become possible with atomistic assembly. Instead of the current statistical (i.e., thermodynamic) ordering of T-atoms (e.g., Al vs. Si), desired T atoms could be inserted into the framework at specific places, and indeed the overall framework composition could be varied systematically from place to place. The framework structure could even be varied as a function of location; e.g., large channels for nanowires could be built in at selected points. Finally, not only could the "guests" be included during assembly, their nature, distribution, and composition could be varied systematically as well. This could lead (say) to novel semiconductor or nonlinear optical devices, in which electronic properties could be varied in a controlled way as a function of position.

5.1 Assemblers.

Only speculations about silicate assemblers can be made at this point to motivate further research and modeling. Several broad approaches (which are not mutually exclusive) are outlined below.

SiO₄ tetrahedra, or more likely small oligomeric sub-units such as exist in concentrated silicate solutions ("T-fragments"), might be handled by a sterically fitting organic ligand. Such a ligand could be attached to a movable "molecular arm" as described in previous proposals for assemblers (e.g., Merkle, 1995). This seems attractive because the bonds between the fitting ligand and the T-fragment could be weak (hydrogen bonds and van der Waals forces); the "lock and key" conformation of the ligand versus the T-fragment both would provide enough strength to bind the fragment and move it. It could also select only appropriate fragments out of a feedstock solution.

Furthermore, once the T-fragment was attached to the growing T-framework via strong bridging oxygen bonds, it would be easy for the fitting ligand to "let go". This contrasts with the conceptual difficulties in (say) designing assemblers to attach atoms to a diamondoid framework, in which a molecular extractor must bind strongly enough to remove individual atoms for assembly, and yet be able to let the atoms go again once they are positioned properly (e.g., Merkle, 1995).

As discussed above, although orthosilicic acid and small silicate oligomers form weak hydrogen bonds, larger oligomers and polymers, having at least 40-50 Si atoms, form strong hydrogen bonds (Iler, 1977). Hence an organic polymer with multiple hydrogen-bonding sites, such as a polyether, polysaccharide, or polypeptide, might furnish an obvious handle for such larger units. Indeed, it seems conceptually straightforward to design the organic molecule to have a shape that will strongly select for only particular polymeric silicate units. However, such units, with dozens of Si atoms, may be too big for most molecular assembly applications.

The formation of such hydrogen bonds, however, may be particularly useful in acting as a template for crystallization of silicate structures. As described above, hydrogen bonds to organic macromolecules may have a role in precipitating biogenic silica, although they do not impose crystallographic ordering. Presumably there is scope for molecular modeling here.

Alternatively, individual SiO₄ tetrahedra could be handled by a complexing agent, perhaps analogously to the biological mechanisms in diatoms. Artificial macrocyclic molecules with catechol moieties have been designed for highly selective complexation of small hard cations (Raymond & Garrett, 1988); and perhaps such moieties could be included in a mechanosynthetic handler. Si-complexes using modified catechols have been described recently (Hahn et al., 1995ab).

6. Building Blocks and Silicate MNT.

As traditional chemical synthesis can make small, atomically perfect objects (i.e., molecules) in reasonable yield, it seems attractive for early MNT development to use molecules as building blocks rather than individual atoms. Not only is there less material to move, but molecules should be easier to handle due to their lesser relative thermal and zero-point motion.

Krummenacker (1994) notes that an issue with the "building-block" approach is that it is difficult to avoid "zeolitic" structures; i.e., structures containing molecule-scale voids. Although this may be an issue in some applications, void-bearing structures are a synthetic goal in much tectosilicate chemistry, as has been emphasized. Furthermore, although Krummenacker (1994) dismissed "most" silicon-bearing molecules as too reactive, this does not apply silicate-based building blocks. Indeed, a building-block approach is especially attractive for tectosilicates and related tetrahedral frameworks since an extensive literature exists on conceptual building blocks. Zeolite structures, for example, are commonly described in terms of the linkages of "secondary building units" (SBUs) consisting of small clusters and polyhedra. Although it is no longer widely thought that such units reflect real atomic clusters that originally polymerized during crystallization, as noted above, their geometric utility, however, is not in dispute.

In this section the structures that could be built with certain highly symmetric silicate building blocks will be surveyed briefly. For the preliminary investigation here, these blocks will have the following constraints:

• Only 3D 4-nets are considered; i.e., no more than 4 bonds can meet at a node. This of course is basic to the tetrahedral coordination of the atoms.
• Only highly symmetric blocks will be considered, and as far as possible only structures in which all blocks have the same orientation. Hence, for assembly ideally only pure translation (motion along the Cartesian axes x, y, z) is required, although in some cases rotations about the z axis are required. In no case, however, are rotations around non-vertical axes needed. Not only is this likely to considerably simplify early mechanosynthetic approaches, but it also may simplify potential approaches based on self-assembly of the building units.
• All 4-vertices shared must be shared. (One minor exception is treated in passing.)
• All building blocks have identical frameworks and contain identical T-atoms, assumed to be Si.

In addition, the following axis conventions will be used: x and y lie in the horizontal plane, whereas z is perpendicular to the plane and also along the axis of prismatic building blocks.

Presumably all these constraints could be relaxed with more sophisticated assembly techniques. A mechanosynthetic assembler could intersperse atoms with higher coordination at certain nodes, or build an "interrupted" framework, with (say) activating groups at a subset of notes instead of the full number of linkages. Indeed, many useful structures probably require such variations; after all, a major point of MNT synthesis is to build molecular structures inaccessible by current techniques. Even with less versatile techniques such as self-assembly, building blocks with complementary shapes (e.g., Davis, 1994) or partly substituted with alternative T-atoms (e.g., Al) could form a much wider variety of structures . However, outlining a uniform building-block approach seems a useful first step.

The blocks will be described below and the structures obtained from them related to published topological descriptions of 4-nets. Any occurrences of the building blocks as separate ionic or molecular entities will also be described, as this is likely to be relevant to their synthesis.

Terminology of such blocks can rapidly get ambiguous, particularly when the same "silicate skeleton" is referred to indifferently as an anion, a siloxane, or a polysilicic acid, as it then becomes unclear if the groups (e.g., oxygen atoms) at the unshared vertices are to be count as part of the block. Therefore, the abbreviations described below (3R, D4R, etc.) will refer to the linked silicate skeleton only. For example, 3R, the unit consisting a ring of three silicons, has the formula Si₃O₃. Here each silicon has two unused bonds. Thus the corresponding "tricyclosilicic acid" is Si₃O₃(OH)₆ and can be written 3R(OH)₆, the anionic (fully deprotonated) form is 3RO₆^-6, and the alkoxysilane is 3R(OR)₆. Hexamethylcyclotrisiloxane can be written 3R(CH₃)₆, showing that the tetrahedral coordination has been completed with Si-C rather than Si-O bonds. The unit 3RO₆^-6 will also be called the 3R anion, 3Ra. Similarly, the double 4-ring structure, D4R, is Si₈O₁₂; since each silicon already has three bonds, the "silicic acid" form is D4R(OH)₈, the anion is D4RO₈^-8 (= Si₈O₂₀^-8 = D4Ra), the alkoxy form is D4R(OR)₈, "cubosiloxane" is H₈D4R, and so on.

6.1 Vertex- and Edge-Linked Blocks.

For simplicity yet flexibility, the building blocks first considered will be rings of silicate tetrahedra, termed nR with n the number of tetrahedral atoms in the ring (Figure 1a-d). (Note that since the linking oxygens are not counted, the number of atoms in the ring is 2n; cf. Figure 2.) Depending on the number of tetrahedra they contain, such rings can be linked by vertices or by edges into 3D structures. The rings lie in alternating layers with the lower vertex (or edge) of one ring linked to a ring in the layer below and the upper vertex (or edge) to a ring in the layer above. Note that such linkage occurs through a disiloxy link, formed (for example) via condensation of silanol groups at separate unshared vertices on each ring

Rings can also be "stacked" one atop another to yield prisms of conceptually arbitrary multiplicity, and then these prisms can be linked via edges or vertices. For obvious reasons, the prism consisting of 2 layers is also called a "double ring" (Figure 1e-h). By convention, such double-ring structures are called DnR, with n the number of tetrahedral atoms in one of the component rings. Linkage of DnR units will also be treated specifically below.

Prisms consisting of 3 or more stacked rings will not be treated specifically, but the conceptual extension to such prisms is straightforward. However, such triple rings have apparently not been found in silicates, as oligomeric oxyanions in solution, or in siloxanes. It furthermore appears that 4-nets based on such elongate prisms have not been formally described.

To yield a crystal structure, the rings or prisms obviously must be capable of linking into an overall trigonal, tetragonal, or hexagonal configuration. In conjunction with the constraint that no vertex must remain unshared, this means that only the 3-ring, 4-ring, 6-ring, and 8-ring based structures are possible building blocks (Figure 1a-h). Furthermore, rings with n>4 must share edges rather than vertices because of steric constraints.

Figure 1. Cyclic silicate building blocks. (a-d), single-ring blocks: (a) 3-ring, 3R. (b) 4-ring, 4R. (c) 6-ring, 6R. (d) 8-ring, 8R. (e-h), double-ring blocks: (e) double-3-ring, D3R. (f) double-4-ring, D4R. (g) double-6-ring, D6R. (h) double-8-ring, D8R. D6R is currently known as an independent unit only formally, in the milarite-group minerals, where it is part of a 3D ordered tetrahedral network; D8R is unknown as an independent entity. All the others are known as oligomeric oxyanions or siloxane frameworks.

Figure 2. Relation of the formal geometry of the building-block tetrahedral framework to the actual distribution of Si and O atoms, using the 3R unit (Si3O3) as an example. Small black circles are Si; larger open circles are O. The unshared tetrahedral oxygens are dotted, as they may be replaced with other groups as in a cyclotrisiloxane.

6.1.1 Vertex sharing: 3-rings and 4-rings.

6.1.1.1 3R and D3R.

Vertex-linking single three-ring units leads to net #94 of Smith (1979), which was also described by Wells (1977, Figs. 9.15a and 9.16) (Figure 3a). This net can be formally derived from a 3·12² 2D net by replacing the links between the triangles with a zigzag chain. The rings, unfortunately, are not translationally equivalent but require rotation about the z axis, which would make mechanosynthetic assembly more complicated.

The structure based on vertex-linking D3R units (a trigonal prism) is topologically equivalent to net #64 of Smith (1978), which is derived by perpendicular linkages from a 3·12² 2D network (Figure 3b). Net #64 can also obviously be formally derived from net #94 above by replacing the rings with double-rings. Such an operation is commonly called a s-(sigma)-transformation (e.g., Smith & Bennett, 1981).

Neither net #94 nor #64 is apparently the basis of any known crystal structure, probably because silicate 3-rings are strongly strained. Nonetheless, if these structures can be built, they are likely to be particularly useful for molecular sieve applications, as they have 12-ring channels parallel to the z-axis (Smith, 1979). Indeed, the nonexistence of 3-rings in zeolites is one motivation for the building-block approach (Harrison & Kannengiesser, 1996).

Despite the strain, the 3-ring oxyanion (Si₃O₉^-6 = 3RO₆^-6 = 3Ra) is known in several crystalline silicates (Liebau, 1985, Table 7.3, p. 98, & 10.9, p. 192). 3Ra has also been inferred to exist in solution, typically from ²⁹Si NMR studies. It is a minor species in solutions of sodium and potassium silicates (e.g., Harris et al., 1982; Harris & Knight, 1983a). McCormick et al. (1987), for example, inferred a maximum concentration of 3Ra of only ~3% of total dissolved silicate in sodium silicate solutions, at an atom ratio of Na:Si = 1:1 and 3 M total Si. In contrast, Harris & Knight (1982) found 3Ra to be much more important in solutions in which the cation was tetraethylammonium (TEA), especially as the temperature was raised.

3R is also well known in cyclosiloxanes (e.g., Noll, 1968, p. 4) and is favored for ring-opening polymerizations because it opens easily due to the strain (e.g., Kendrick et al., 1989).

The trigonal prism D3R, though also strongly strained, exists as the independent D3Ra (Si₆O₁₅^-6) oxyanion in several synthetic silicates, as follows: [Ni(H₂NC₂H₄NH₂)₃]₃[Si₆O₁₅]·26H₂O (Smolin, 1970; 1982); (N(C₂H₅)₄)₆[Si₆O₁₅]·57H₂O (Hoebbel et al., 1980), and ((CH₃)₃SiO)₆Si₆O₉ (Hoebbel et al., 1987).

D3Ra also exists as a minor species in concentrated aqueous alkali silicate solutions. Again, such studies rely on inferences from ²⁹Si NMR study (Harris et al., 1982; Harris & Knight, 1983b), sometimes in conjunction with other techniques (e.g., electrochemistry: Sjöberg et al., 1985b; ¹⁷O NMR, Kinrade, 1996). McCormick et al. (1987) reported a maximum concentration of only ~1% of dissolved silicate in concentration sodium silicate solution (Na:Si = 2:1, 3 mol % Si). D3Ra is much more prominent in tetraalkylammonium solutions, constituting up to 60% of total silicate in TEA at high pH (Groenen et al., 1986). Hoebbel et al. (1980) reported D3Ra to be the dominant ion in TEA solutions when TEA:Si >1. With TEA:Si = 1:1, Harris & Knight (1982) found D3Ra more prominent at low temperature, but they inferred 3Ra to be more important at room temperature

Substituted spherosiloxanes based on D3R have also been synthesized, as described below.

Figure 3. Tetrahedral 3D frameworks (4-nets) generated by linkage of simple building blocks, I. Vertex-linked blocks (3- and 4-rings). (a) Net #94 (Smith, 1979), viewed down the z axis; (b) Net #64 (Smith, 1978), viewed down the z axis; (c) Net #3 (Smith, 1977, 1979), viewed down the z axis; (d) Net #3 viewed along the x or y axis; (e) Net #46 (Smith, 1978). In (a) and (c), rings labeled A and B are offset by 1/2 of the vertical repeat distance. The dashed link connecting the vertices represents two corner links, to the rings above and below. In (b), (d), and (e), closed (open) circles represent perpendicular links into (out of) the plane of the page that connect to the net on the next level. Note that (e) has cubic symmetry and thus looks identical along all three Cartesian axes. The slightly distorted net in (d) is obviously topologically equivalent to a symmetric hexagonal net.

4R and D4R.

Vertex-linking single 4-rings, 4R, yields 4-net #3 of Smith (1977, 1979; Figure 3c,d), which is also described in Wells (1977, Figs. 9.15c, 9.17). It is the basis of the framework of monoclinic CaAl₂Si₂O₈ (Smith, 1977).

The double 4-ring, D4R, obviously has cubic symmetry (Table 1), and the structure built from it is topologically equivalent to net #46 of Smith (1978; Figure 3e), which is derived by perpendicular linkages from a 2D 4·8² net. It can also be formally derived from net #3 above by s-transformation of the 4R units.

This net is evidently not the basis of a known crystal structure; however, Davis (1994) has proposed its construction by the condensation of functionalized D4R units. Although the structure of zeolite Linde A, described below, can also be formally built from D4R, the units are not related by translational symmetry and hence the structure is different.

Single 4-rings also occur as the Si₄O₁₂^-8 (4Ra) oxyanion in a number of crystalline silicates (Liebau, 1985, Table 7.3, p. 98, & 10.9, p. 192; synthetic Ca₈[Si₄O₁₂]Cl₈, Goodwin & Kenney, 1990ab). As with D3Ra, it is also found in alkali silicate solutions as a minor constituent (Harris et al., 1982; Harris et al., 1983b; Sjöberg et al., 1985b; Kinrade, 1996). McCormick et al. (1987) found that its proportion reached a maximum of ~1% when Na:Si = 2:1 at 3 M Si. According to Hoebbel et al. (1980), 4Ra is a minor species in TEA solutions when TEA:Si >1.

The 4R is also well-known as a cyclosiloxane framework (e.g., Steinfink et al., 1955).

The D4R prism is well known as an independent entity and seems to be a particularly stable unit. D4Ra is a very minor constituent in alkali silicate solutions (Harris et al., 1982; Harris & Knight, 1983b, Kinrade, 1996). McCormick et al. (1987) reported it constituted only ~0.1% of the dissolved silicate at the maximum (Na:Si = 2:1, 3 M total Si). However, as described in detail below, D4Ra is the dominant species in tetramethylammonium (TMA) solutions (Harris & Knight, 1982), and is always a major species in tetraalkylammonium (TAA) solutions (Hoebbel et al., 1980; Groenen et al., 1986; Kinrade et al., 1998a). D4Ra is particularly favored in the presence of organic co-solvents such as dimethyl sulfoxide (DMSO) or methanol (Hasegawa et al., 1989; Hendricks et al., 1991b; Kinrade et al., 1998b).

Furthermore, D4R is also known as a siloxane framework, as is discussed in detail below. Finally, D4Ra occurs as an ion in crystalline silicates (Liebau, 1985, Table 7.4, p. 99; & 10.10, p. 194; Hoebbel et al., 1980; Smolin, 1982; Wiebcke & Hoebbel, 1992).

TABLE 1. SILICATE BUILDING BLOCKS:

Table 1. Explanation of headings: Name, name of building unit. Formula: The formal formula of the oligomeric skeleton only; unshared oxygens at each vertex are not included. For polygonal units, the general formula is thus Si_nO_n, where n is the number of vertices. The formula of the corresponding oxyanion (2 unshared oxygens at each vertex) is Si_nO_3n^2n-. For polyhedral blocks, the general formula is Si_nO_1.5n; the corresponding oxyanion formula (1 unshared oxygen at each vertex) is Si_nO_2.5n^n-. Faces (indices): the number of faces on a polyhedral block; e.g., 4⁶ means 6 symmetry-equivalent square faces exist. (This number is undefined for a simple polygonal-ring building block and so is left blank.) If faces exist, their Miller indices are listed underneath; all symmetry-equivalent faces are not shown. Vertices: Number of vertices of the building block, which equals the number of Si atoms. Symmetry: The Schoenflies (spectroscopic) symmetry designation is shown. The International (crystallographic) symbol is also shown if it exists.

6.1.2 Edge sharing: 6-rings and 8-rings.

6R and D6R.

A literally infinite set of structures is possible (Smith & Bennett, 1981), because of different stacking possibilities. The possibilities can be envisioned by considering 4-nets derived from the 4·6·12 2D net (Smith, 1978, 1979), where the hexagons represent 6-rings in two successive layers. If the rings in the third layer lie directly above those in the first, 12-ring channels run through the structure parallel to z. This corresponds to Smith's (1979) 4-net #95 and describes the framework of the zeolite cancrinite (Figure 4a). If the rings in the first layer are designated A and those in the second B, the stacking of cancrinite can then be described as ABABAB....

Alternatively, the rings in the third layer can be positioned over neither those in the first or second layers, but instead directly over the open 12-rings in the first layer. In this case there obviously are no through-going channels. This structure corresponds to that of sodalite (4-net #108 of Smith & Bennett, 1981; Figure 4b) ; extending the terminology above, the stacking can be described as ABCABCABC.... (The sodalite structure can alternatively be viewed in terms of space-filling polyhedra, as described in section 6.2.1.)

These two alternative positions for the third layer are analogous to the difference between hexagonal closest packing and cubic closest packing, respectively, of identical spheres. Hence, just as with spheres an infinite number of more complicated polytypes is possible by varying the stacking sequence. Smith & Bennett (1981) tabulate some of the simpler possibilities and note that several correspond to known zeolite structures; e.g., the synthetic zeolite Losod corresponds to ABCB....

In addition, s-transformations can be carried out to convert the 6-rings into D6R prisms. Smith's (1978) net #82 corresponds to carrying out s-transformations on the cancrinite structure (net #95), and is the basis of the structure of the zeolite gmelinite (Figure 4c). It can be described as AABBAABB... .

Similarly, s-transforming the hexagons in the sodalite structure (#108) yields Smith's (1978) net #83, which is the basis of the chabazite structure and has the stacking sequence AABBCCAABBCC... .

Of course, mixed structures consisting of both single and double 6-rings can be envisioned, and some have been found in real structures; the zeolite erionite, for example, has the stacking sequence AABAAC (Smith & Bennett, 1981; net #119).

Quite a number of crystalline silicates contain the Si₆O₁₈^-12 oxyanion, 6Ra (Liebau, 1985, Tables 7.3, p 98, & 10.9, p. 192-3; Na₄Ca₄[Si₆O₁₈], Ohsato et al., 1986). In several cases, however, the occurrence is purely formal, because other tetrahedrally coordinated, strongly bound cations exist in the crystal structure. Hence, such a structure is better viewed as a 3D framework in which tetrahedral cations (Si and others) are ordered (Zoltai, 1960). In particular, the Be atoms in beryl (Be₃Al₂[Si₆O₁₈]), which occupy tetrahedral sites, can be considered part of such a 3D framework.

The existence of 6Ra in aqueous solutions is disputed. McCormick et al. (1987) claimed its presence in sodium silicate solutions, with a maximum of ~0.2% of total silicate at Si:Na = 3:1 and 3 M total Si. Knight et al. (1989), however, saw no evidence of its existence in concentrated potassium silicate solutions.

The D6R prism structure is also formally present as a polysilicate oxyanion (Si₁₂O₃₀^-12 = D6Ra) in the milarite-group minerals (Liebau, 1985, Tables 7.4, p. 99, & 10.10, p. 194; Hawthorne et al., 1991, and refs. therein; Winter et al., 1995). As with beryl, however, the structure is better considered as an ordered tetrahedral framework that includes other tetrahedral atoms (Brown & Gibbs, 1969; Hawthorne et al., 1991).

If D6Ra occurs in aqueous solution, it is at a very low level. McCormick et al. (1987) thought it was possibly present in concentrated sodium silicate solution. It was not detected by ²⁹Si NMR in concentrated potassium silicate solution, but there was so much overlap with other species that it was probably undetectable (Knight et al., 1989). D6Ra was thought to be present at low concentration by Hoebbel et al. (1980) in TEA solutions when TEA:Si <1. Most recently, Kinrade et al. (1998a) suggested that the species interpreted as reflecting higher double-ring structures are instead clathrated molecules closely related to D4Ra.

8R and D8R.

Edge-linking of single 8-rings yields Smith's (1979) net #93, which does not correspond to a known crystal structure (Figure 4d). Edge-linking D8R prisms yields a tetragonal structure topologically equivalent to net #17 of Smith (1978), which is derived by perpendicular linkage from a 2D 4·8² net (Figure 4e). Analogously to the discussions above, it can also be derived from net #93 by s-transformation. The structure of the zeolite merlinoite is based on this 4-net.

Neither 8Ra nor D8Ra has been reported in aqueous solution; evidently such large rings are too "floppy" to be stable to any degree. The D8R unit has also not been reported to be the basis of a siloxane, but the 8R methylsiloxane has been known for decades (Hunter et al., 1946).

8Ra (Si₈O₂₄^-16) occurs in muirite (Khan & Baur, 1971); D8Ra, however, has not been reported as a polysilicate oxyanion.

Figure 4. Tetrahedral 3D frameworks (4-nets) generated by linkage of simple building blocks, II. Edge-linked blocks (6- and 8-rings). All nets viewed down z axis. (a) Net #95 (Smith, 1979); (b) Net #108 (Smith & Bennett, 1981); (c) Net #82 (Smith, 1978); (d) Net #93 (Smith, 1979); (e) Net #17 (Smith, 1978). In (a) and (d), rings labeled A and B are offset by 1/2 of the vertical repeat distance; in (b), the rings labeled A, B, and C are offset by 1/3 of the repeat distance, respectively. Dashed links in (a) and (b) have the same significance as in Fig. 3, as do the open and closed circles in (c) and (e).

6.2 Face-Linking Blocks.

A perhaps even more obvious way to build structures from smaller blocks is by the linking of congruent faces of adjacent polyhedra. Although there is an abundant literature on the filling of space by the packing of polyhedra (e.g., Coxeter, 1963, Ch. IV; Wells, 1977, pp. 233 ff.; Smith, 1982), and a number of known structures can be described simply by translations of face-shared "polyhedral building blocks" (e.g., Liebau, 1985, pp. 145 ff.), this is less relevant to the present problem, because face-sharing implies that the atoms making up the polyhedral face must also shared between the polyhedra. Intact polyhedral building blocks, however, cannot share atoms; instead, the faces of adjacent polyhedra must be linked by perpendicular bonds. Geometrically, the building-blocks thus become joined by n-prisms between the n-faces of adjacent polyhedra.

Less work has been done on developing 4-networks by such offset polyhedra, although some has been carried out (e.g., Smith & Bennett, 1981; Hawthorne & Smith, 1986; Smith, 1988). In particular, the constraint that every vertex must become a 4-node, coupled with the requirement that all vertices be connected, proves to be stringent indeed. For one thing, it implies that there must be exactly one unused face between any two of the linking n prisms. However, determining all polyhedra that can meet this constraint lies well beyond the scope of this paper.

For the three highly symmetric building blocks considered here, however, the possibilities are sufficiently limited that they may be readily determined by inspection. All building blocks have O_h (m3m) symmetry (Table 1; Figures 5a; 6; 8a). The Miller indices of the faces on each polyhedron are given, as they are a useful guide to the potential ways in which the polyhedra can be stacked. For example, existence of a (111) face implies that a "tetrahedral" connection of the polyhedra may be possible, because rays from the center through the vertices of a regular tetrahedron inscribed in a cube are perpendicular to (111). For another example, the existence of faces parallel to (100), (010), and (001) implies that stacking of the polyhedra parallel to the coordinate axes may be possible. (Note that no attempt is made to specify all sets of symmetry-equivalent indices; e.g., with O_h symmetry, (111) also implies the existence of equivalent (111), (111), etc., faces.)

Unfortunately, none of these blocks has been synthesized as an independent entity, although all occur as formal "building units" in known tectosilicates.

6.2.1 Sodalite cage (truncated octahedron, to).

This figure is derived by truncating the vertices of a regular octahedron so that the originally triangular faces become regular hexagons (Figure 5a). It has squares in "diamond" orientation (i.e., with their diagonals parallel to the Cartesian axes) parallel to (100), while the hexagonal faces are parallel to (111). The unit is often called the "sodalite cage", because the alumino-tectosilicate sodalite consists of a cubic array of truncated octahedra sharing their square faces. (As noted above, the sodalite structure may also be described in terms of linked 6-rings.) The to is an Archimedean solid; that is, although different polygonal faces exist all vertices are equivalent.

Connecting the square faces of the to yields the structure of zeolite Linde Type A (Figure 5b) (Smith & Bennett, 1981). As noted above, this structure can also be built from D4R units: the prisms connecting the diamonds on the sodalite cages are obviously D4Rs, and the connecting links between their vertices outline a sodalite cage. This is a different structure than described previously, however. In the Linde A structure the D4Rs lie along each Cartesian axis, but they are rotated 45° around each axis. Hence the D4Rs are not related merely by a rotation about the z axis, and so this structure cannot be built from D4Rs under the assembly assumptions made herein.

All hexagons in the sodalite cage cannot be connected by offset prisms, as this would yield more than 4 segments at a node. Hence, alternate hexagonal faces, at positions corresponding to the vertices of a tetrahedron, must be connected. There are two ways of doing so, which correspond to alternative 60° rotations of one to with respect to the next around an axis perpendicular to the linking hexagonal prism. Putting the square faces of one to across from the hexagonal faces of the next (trans-configuration), which corresponds to keeping all tos in the same relative configuration, yields the faujasite structure uniquely (Figure 5c). The structure is akin to that of diamond, with the tetrahedrally connected to units corresponding to the carbon atoms. The faujasite structure has large channels and voids and thus is useful in catalysis and as a molecular sieve, especially in its high-silica modifications (zeolites X and Y). By contrast, connecting tos in cis configuration (squares and hexagons of adjacent tos facing each other) does not yield a regular 3D net, although inserting cis-configuration connections between some layers "yields an infinite polytypic series" (Smith, 1988). For example, the "hexagonal" polymorph of the faujasite structure consists of alternate layers of such cis-linkages (Thomas et al., 1981; Fig. 5d); this geometry is analogous to the hexagonal diamond polymorph, lonsdaleite. Faujasite crystals can also be twinned by the occasional insertion of a cis layer, as obviously a mirror plane bisects the connecting 6-prism between the tos (Fig. 5d). Unfortunately, however, inserting cis connections requires relative rotation of the tos, not just simple translation.

Figure 5. Tetrahedral 3D frameworks (4-nets) generated by linkage of simple building blocks, III. Face-linkage of the truncated octahedron (to) block (sodalite cage). (a) Framework of the to. (b) Structure of zeolite Linde Type A, formed by connecting square faces. (c) Structure of faujasite, formed by trans-connection (square opposite hexagon) of alternate hexagonal faces. Note that all tos are in the same orientation. Compare the trans connection at the arrows with the cis connection in (d) below. This structure is cubic and analogous to diamond. (d) Structure of "hexagonal" faujasite, with successive layers of cis-linkages (arrows). Note that at a cis linkage the adjacent tos are rotated 60° with respect to each other. Note also that planes of cis linkages are mirror planes. This is how the faujasite structure can be twinned by inserting a plane of cis linkages.

6.2.2 Truncated rhombic dodecahedron (trd).

Like the truncated octahedron, this is an isometric polyhedron whose faces consist only of squares and regular hexagons (Figure 6a). However, it is not an Archimedean solid because there are two types of vertex: one at which a square meets two hexagons, and one where three hexagons meet. The squares have sides parallel to the coordinate axes (100), whereas the hexagonal faces are on (110). All squares and all hexagons are thus symmetrically equivalent.

The trd yields a space-filling structure if packed hexagon to hexagon, with cubical voids remaining between the square faces of adjacent polyhedra. This is the basis of the structure of the aluminophosphate molecular sieve AlPO₄-16 and is also closely related to the zunyite structure (Bennett & Kirchner, 1991). As with sodalite and the sodalite cage, however, this is irrelevant to the purposes here as atoms are shared between adjacent polyhedra. (However, Davis (1994) has noted that this structure could be built by complementary building blocks, one a D4R unit and the other a D4R(SiO₃R)₈ unit.)

Linking trd units in what is perhaps the most obvious way, at the square faces, yields a structure with cubic symmetry that violates the requirement that all vertices must become 4-nodes, as the vertex between the three hexagonal faces remains unlinked. Similarly, linking alternate hexagons in "tetrahedral" configuration also yields an interrupted framework, as two vertexes on each square face then remain unused. Nonetheless, such structures might be very useful for catalysis or similar applications, if functional groups could be attached to the unused vertexes. Indeed, this might be one of the easiest ways to build an interrupted framework structure. So far as the author is aware, however, both these structures are unknown.

The only way to link trds so that all vertices become 4-nodes is as follows. Arbitrarily select orthogonal axes passing through each opposite pair of square faces as x, y, and z. Now link each hexagonal face perpendicular to the xy plane (i.e., those at (110), (110), (110), and (110)) to an adjacent trd. This yields a 2D array of trd units in which all linkages are at 45° to the Cartesian axes (Figure 7). Such arrays can then be stacked by linking them through the square faces above and below (i.e., at (001) and (001)) to give a 3D structure with large channels running along the z axis. Obviously this vertical linkage lowers the symmetry of the entire structure to tetragonal. This structure is apparently unknown as well.

Figure 6. Tetrahedral 3D frameworks (4-nets) generated by linkage of simple building blocks, IVa. (a) The truncated rhombic dodecahedron (trd); (b) The great rhombododecahedron (truncated cuboctahedron, tco).

Figure 7. Tetrahedral 3D frameworks (4-nets) generated by linkage of simple building blocks, IVb. Linkage of trd units so that all vertices become 4-nodes. View down z axis. These x-y- arrays can be stacked via linkage at the square faces above and below to yield a 4-net with tetragonal symmetry.

6.2.3 Great rhombododecahedron (truncated cuboctahedron, tco).

This large building unit has octagonal faces on (100), hexagonal faces on (111), and squares on (110) (Figure 6b). Like the to it is an Archimedean solid. Linking the square faces merely yields the Linde A structure again (Smith, 1988). Connecting all the hexagonal faces of parallel tco units yields the zeolite Mobil ZK-5, whereas linking the large octagonal faces of parallel tcos yields zeolite rho (Smith, 1988). Both these synthetic zeolites find use in catalysis.

7. Assembly Issues.

As Krummenacker (1994) notes, making covalent bonds between molecular "building block" precursors requires that there be enough room for the "leaving groups" formed upon making the bond to exit. In the case of condensation of a disiloxy bond from silanols, this group is just H₂O, which should hardly present a steric problem when making open silicate frameworks. Direct condensation of an Si-O-R group with Si-O-H, however, yields an alcohol (ROH) as the leaving group, and thus R = methyl would minimize any space problems. Hence, methoxides may be better raw materials despite their higher toxicity. A larger problem may be removing any "scaffolding" necessary to support the blocks during assembly. If this scaffolding remains incorporated in the structure, it could perhaps be burned out later, as with the templating molecules in current zeolite syntheses. In the long run, however, such removal is both inelegant and energy-intensive.

The blocks could be moved into place with a molecular assembler such as sketched out in section 5. As noted, most structures described above require only x, y, z translations for their construction, and at most only a rotation around the z axis is needed.

At least for indefinitely repeating structures (i.e., crystals), self-assembly approaches are also worth investigating. Indeed, the hydrothermal syntheses of zeolites and related molecular sieves can be considered an empirical self-assembly technique (Davis et al., 1994). Even though progress in understanding zeolite crystallization at an atomic level is being made (e.g., Burggraf & Davis, 1986; Szostak, 1989, Ch. 3; Burkett & Davis, 1994), as noted, there remain fundamental disputes. Obviously, an enormous number of variables are involved, and even though some effects can be rationalized qualitatively, we are a long way from any comprehensive understanding.

It seems there are many avenues where molecular modeling would be useful, to investigate possible fits and (conceivably) possible reaction mechanisms. Lewis et al. (1995, 1996, 1997) have made an impressive start toward this goal, with computer software that has successfully modeled templating agents in high-silica gels on the basis of their weak interactions with silicate species. Nonetheless, full ab initio molecular design of syntheses remains a distant goal.

In an empirical approach to molecular design, Zones et al. (1992) designed and synthesized a structure-directing agent, a molecule incorporating two ammonium moieties on a rigid, 3D aromatic framework, to synthesize a novel large-pore zeolite. Davis and coworkers (e.g., Lobo et al., 1994; Lobo & Davis, 1995; Kubota & Davis, 1996) have emphasized the importance of the size and rigidity of the organic template in determining its selectivity for crystallizing particular structures. They also emphasize that more than one discrete charge center, as in substituted diammonium cations, is more effective than a molecule with a single diffuse charge. They further find that intermediate hydrophobicity is needed: hydrophobic molecules form aggregates, whereas hydrophilic molecules do not have a large structure-directing effect on water molecules.

Davis (1994) further outlined methods by which functionalized building blocks could yield new silica structures by self-assembly. He focused on D4R units with complementary moieties that could crosslink in a controlled way, but his approach should be feasible for many of the building blocks discussed above. This author (Davis, 1996) also emphasized the need to understand better the kinetics of the crystallization.

New experimental approaches should also be valuable in broadening the data base, and in determining important variables, particularly with respect to kinetics. One is non-aqueous solvents: Hong et al. (1997), for example, used ethylene glycol as both solvent and structure-directing agent. Different counter ions are another possibility. Van de Goor et al. (1995) synthesized a clathracil using the organic complex cobalticenium as a structure-directing agent. As described below, too, aqueous solutions containing large cationic complexes precipitate unusual silicate structures (Smolin, 1970; Smolin, 1982; Wiebcke & Hoebbel, 1992). Such approaches, however, will also probably require lower temperature syntheses, as even the relatively low temperatures required during conventional hydrothermal syntheses are sufficient to destroy most complexes (van de Goor, 1995).

As was mentioned, silicon and siloxane alkoxides are under increasing investigation as raw materials for silicate synthesis because of the greater control they potentially offer at the molecular level. Although current efforts with using "building blocks" in sol-gel synthesis have not led to large-scale molecular order, it seems that this approach may worth extending. Designing templating molecules (not necessarily cations) that fit complementarily with particular oligomeric alkoxide building blocks, for example, might allow crystalline self-assembly. A recent study that used thiol-functionalized alkoxides to build self-assembled layers on an Au surface could be a step in this direction (Wang et al., 1998).

A striking example of using self-assembly is the recent work on building mesoporous silica structures, in which the silica, though non-crystalline, supports uniform voids and channels several nanometers across (e.g., Beck et al., 1992; Bagshaw et al., 1995; Fyfe & Fu, 1995; Tanev & Pinnavaia, 1995; Fowler et al., 1997; Romero et al., 1997; Zhao et al., 1998ab). In these systems, the organic templates, typically surfactants, self-assemble into supramolecular structures that then guide the precipitation of the silica (e.g., Fowler et al., 1997; Huo et al., 1994). This contrasts with zeolite synthesis, in which the organic and silicate species are thought to interact nearly one-on-one (Davis et al., 1994). Although such mesoporous silicas currently are glassy, adroit choice of templates helps the self-organization, and may lead ultimately to higher crystallinity. This seems indeed much like biological silica-deposition systems, in which precipitation of glassy silica is constrained by organic layers.

7.1 Building-Block Synthesis.

None of the syntheses suggested above, whether based on mechanosynthesis or self-assembly, is possible without a supply of molecular building blocks. Hence, convenient, high-yield syntheses of potential building blocks are a serious issue, particularly because the larger the building block, the more difficult it is, in general, to synthesize. As mentioned the to, trd, and gco blocks have not even been isolated as independent entities.

7.1.1 Selection from aqueous solution.

As described, many small oligomeric silicate oxyanions, including double-ring structures, exist in moderately concentrated alkaline silicate solutions, and the distribution of particular ionic species is both a function of pH and of the counterions (e.g., Kinrade & Pole, 1992). Lowering pH obviously favors polymerization. Larger cations favor larger oligomers, apparently because ion-pairing shields them from hydrolysis (McCormick et al., 1989; Hendricks et al., 1991a).

Most strikingly, as mentioned above, tetraalkylammonium (TAA) solutions strongly favor small ring structures (Hoebbel et al., 1980; Harris & Knight, 1982; Groenen et al., 1986). The D3Ra is favored in TEA solutions at high pH, but D4Ra is always also present. It is dominant in TMA solutions, particularly in the presence of organic co-solvents such as DMSO ((CH₃)₂SO) and CH₃OH. In a 50% MeOH TMA solution with total SiO₂ concentration of 1 M and a TMA:Si mole ratio of 1, essentially all dissolved silicate is present as D4Ra (Hendricks et al., 1991b). Hasegawa & Sakka (1989) and Wiebke & Hoebbel (1992) crystallized silicates containing intact D4Ra from aqueous TMA solutions.

Hasegawa and coworkers synthesized D4Ra in such methanolic solutions as a "building block". In some cases (Hasegawa et al., 1994; Hasegawa & Nakane, 1996) they polymerized the D4Ra units directly by adding dichlorodimethylsilane; in other cases (Hasegawa et al., 1987; Hasegawa & Motojima, 1992) they extracted the D4R units by a variation of trimethylsilylation (Lentz, 1964). By replacing one of the methyl groups with a vinyl (CHCH₂) group, these workers obtained a functionalized "building block" that could be polymerized, as described above. Similarly, Hoebbel et al. (1990, 1994) extracted functionalized D4R units, which were capable of condensation and polymerization, by substituted silylation.

The preference of oligomeric structures in TAA solutions is in part a simple consequence of mass action, as the lessened water activity will disfavor the hydrolysis of disiloxy bonds. Organic co-solvents, by further lowering H₂O activity, obviously enhance this effect. Hendricks et al. (1991b) showed, however, that mass action could not account for all the stabilization, and attributed part of the effect to the structuring of water molecules by the organic moiety. Furthermore, for larger TAA molecules smaller 3Ra and 4Ra cyclic oligomers were even more favored. They attributed this to "ionic crowding"; the tendency to minimize electrostatic energy will favor smaller oligomeric oxyanions because they can be distributed more evenly through the solution and thus better cancel the diffuse charges on the large cations.

Kinrade et al. (1998a) particularly attributed the enhancement of the cage structures D3Ra and D4Ra in TMA and TEA solutions to their shielding by the cations, owing to both hydrophobicity and ion pairing. Smolin (1982), in a review of his group's work, describes a series of water-soluble silicates that include the cationic complexes of ethylenediamine (1,2 ethanediamine) complexes with Ni⁺⁺, Cu⁺⁺, and Co⁺⁺, as well as TMA and TEA. These silicates crystallize with the D3Ra and D4Ra oxyanions, which he also attributes to their shielding by the large cations. Gerke et al. (1982) also attempted to determine the effect of cations by crystallizing silicates from aqueous solutions containing the large organic cations tetrabutylammonium and tetrabutylphosphonium.

Clearly, the D4Ra unit is isolable and extractable even with present-day chemical techniques. Using other oligomers, however, probably will require molecular mechanisms that select them out specifically from a solution containing a mixture, perhaps by the steric fit approaches sketched in Section 5. This may allow molecular construction directly from aqueous solution.

7.1.2 Oligomeric oxyanions in crystals.

As noted above, most of the cyclosilicate building blocks exist, at least formally, as oxyanions in crystalline silicates. Indeed, a great many oligomeric silicate oxyanions exist, not just the cyclic forms. This suggests another approach to synthesis: the extraction of oxyanions having a desired geometry from a crystal in which they occur. Hence, the synthesis of crystalline silicates having desired anionic structures may also be a useful goal. The survey in Liebau (1985) shows that there is considerably greater variety in silicate structures than is represented by common mineral types, which are dominated by common elements such as Ca, Mg, Fe, Na, and K. Rare minerals, as well as synthetic compounds, have a considerably greater variety of cations available, and this causes a wide variety of different anion structures to occur, as the polymeric oxyanions in silicates evidently reflect an energy compromise with the packing dictated by the cations (Liebau, 1985, Ch. 10). For example, although chain anions are normally favored over rings due to within-ring repulsion, strong electrostatic interactions with the cations can cancel this effect (Liebau, 1985, p.191). Furthermore, the presence of co-anions, especially large anions such as Cl^- and CO3⁼, also tends to lead to cyclic or oligomeric silicate polyanions (Liebau, 1985, p. 187).

The variety of cations available in synthesis includes large organic cations, such as substituted ammonium cations or metal complexes (e.g., Smolin, 1982); transition metals such as Zn, Cu, and Ni, as well as second- and third-row elements; large, "soft" (i.e., polarizable) cations, such as Pb⁺⁺, which can develop asymmetric electronic structures; and "hard" cations with geochemically unusual ion radius/charge ratios, such as lanthanides and heavy alkali and alkaline-earth metals (e.g., Ba, Cs). In natural systems, such cations are generally not abundant enough to form silicate phases, and even when locally abundant enough to form separate phases, the phases usually are not silicates. For example, Zn, Cu, and other transition metals, as well as soft cations like Pb, typically form sulfides in natural systems because of their considerably greater affinity for sulfur over oxygen, and because sulfur is a relatively common element. (This is also why these metals are currently recovered from sulfide ore minerals, as remarked in the previous paper.) A wider variety of co-anions is also conceivable in synthesis, although few have apparently been tried. Very large anions with low charge-to-size ratios, such as ClO₄^- or PF₆^-, for example, have evidently not been tried.

An example of the effect of large organic cations is provided by such water-soluble silicates as [Ni(H₂NC₂H₄NH₂)₃]₃[Si₆O₁₅]·26H₂O (Smolin, 1970; 1982), (N(C₂H₅)₄)₆[Si₆O₁₅]·57H₂O (Hoebbel et al., 1980), and [N(CH₃)₄]₁₆[Si₈O₂₀][OH]₈·116H₂O (Wiebcke & Hoebbel, 1992), which contain intact D3Ra and D4Ra units. The propensity of geochemically unusual metal ions to force cyclic structures is illustrated by such compounds as margarosanite, Ca₂Pb[Si₃O₉], a cyclotrisilicate; synthetic Pb₈[Si₄O₁₂]O₄, a cyclotetrasilicate; and synthetic Na₈Sn[Si₆O₁₈], a cyclohexasilicate (Liebau, 1985, p. 98). The effect of co-anions is illustrated by synthetic Ca₈[Si₄O₁₂]Cl₈, a cyclotetrasilicate (Goodwin & Kenney, 1990ab) and scawtite (Ca₇[Si₆O₁₈][CO₃]·2H₂O, a cyclohexasilicate. Both effects are apparent in muirite (Ba₁₀(Ca,Mn,Ti)₄[Si₈O₂₄](Cl,O,OH)₁₂·4H₂O, the only known cyclooctasilicate. Moore et al. (1981) comment on the lone-pair effect of Pb(II) in hyalotekite (Pb₂Ba₂Ca₂[B₂(Si_1.5Be_0.5)Si₈O₂₈]F); the unused 6s² electron pair, whose distribution is distorted easily by electrostatic forces, causes asymmetric bonds. One might also (say) speculate that a "crown" effect might occur in which the fit of a cation inside a cyclosilicate ring might favor particular cyclic structures.

Obviously, although such observations suggest how a particular structure might be favored, they remain highly qualitative. This seems another area in which detailed modeling might yield new insights.

Of course, once a silicate having a desired anionic structure is located or synthesized, extracting that structure intact presents another problem. The trimethylsilylation method shows that in many cases the anionic structure can be largely preserved, if the structure can be solubilized. Trimethylsilylation, however, still requires reduced Si and thus remains energy-intensive. As described in the previous paper, in a series of papers and patents Kenney and coworkers (Goodwin & Kenney, 1988, 1989, 1990ab; Kenney & Goodwin, 1988; Harrington & Kenney, 1992) have demonstrated the extraction of the silicate "backbone" from a variety of silicates by gentle dissolution in acidified alcohol instead. The product(s) are siloxyalkoxides, which can be considered esters of various hypothetical polymeric silicic acids. For example, the synthetic cyclotetrasilicate Ca₈[Si₄O₁₂]Cl₈ yields the ethoxy derivative Si₄O₄(OC₂H₅)₄; i.e., ethanol has condensed with the silicate oxyanion [Si₄O₁₂], in the presence of acid, to yield an ester of the hypothetical tetracyclosilicic acid Si₄O₄(OH)₈. The reaction is the reverse of the hydrolysis employed in the sol-gel hydrolysis of alkoxides, and is forced to run "backwards" by employing "scarce-water" conditions. Similarly, the "tube" silicate K₂CuSi₄O₁₀ yields a "tube alkoxide" by esterification of the infinite quadruple chain anion (Harrington & Kenney, 1992).

Despite the mild conditions, the silicate structure is not always preserved, however. Pseudowollastonite, Ca₃[Si₃O₉], can be used but the 3-rings open up during the esterification to yield linear trisiloxy alkoxides, presumably due to the release of strain in the 3-ring. With dioptase (Cu₆[Si₆O₁₈]·6H₂O), or synthetic Na₄Ca₄[Si₆O₁₈], both of which are soluble in dilute HCl and contain 6Ra units, the 6-ring is not preserved on esterification. It becomes crosslinked with disiloxy bonds to yield a pair of isomers ([5·5·1] and [5·5·3]) of (C₂H₅O)₁₀Si₆O₇.

This procedure also requires that the starting silicate be reasonably soluble in the dilute acid solution. The nature of the cations affects solubility; Harrington & Kenney (1992) comment, for example, that Cu and Zn silicates are generally vulnerable to acidified alcohol attack. Silicates containing large organic cations, as described above, also are soluble; indeed, they are generally precipitated from aqueous solutions. Large co-anions such as Cl and CO₃ also tend to make the structure soluble.

Nonetheless, many silicates with formal polysilicic ions are essentially insoluble. Commonly such silicates are framework structures in the Zoltai classification; i.e., the formal silicate polyanions are linked by non-silicate tetrahedra. Milarite-group minerals, for example, with their ordered tetrahedral framework containing D6Ra as a formal sub-unit, are insoluble in HCl. Zunyite, which contains a formal, highly branched SiO₄(SiO₃)₄ oligomer, is also highly insoluble and is better viewed as an interrupted framework structure. In such cases dissolution with more active agents such as base or complexing agents such as catechol may be useful. Although this may disrupt the polyanions as well, such experiments have evidently not been tried.

7.1.3 Spherosiloxanes, cyclosiloxanes, and silsesquioxanes.

As briefly mentioned in the previous paper, siloxanes are traditionally derived from partly substituted silicon chlorides. The usual starting material is dichlorodimethylsilane, SiCl₂(CH₃)₂, because replacement of the chlorines with oxygen links leads directly to cyclic and linear polymers, the usual ones of technological interest (e.g., Noll, 1968, p. 190 ff.; Saam, 1990). Methyl cyclosiloxanes have been known for decades (Hunter et al., 1946), and cyclosiloxanes are traditionally a starting material for manufacture of linear siloxane polymers by ring-opening polymerization (e.g., Kendrick et al., 1989). Cyclosiloxanes have been functionalized by substituting different side groups to vary the properties of the resulting polymers; recently, for example, tetracyclosiloxane was functionalized by ferrocene moieties (Casado et al, 1995). As sketched above, functionalized cyclosiloxanes have also been used as starting materials in hybrid inorganic-organic polymers. Klemperer et al. (1986) also used hexamethoxycyclotrisiloxane (3R(OCH₃)₆) as a starting oligomeric material for sol-gel synthesis.

Silsesquioxanes have traditionally been less valuable, as chains are the usual synthetic goal. However, the synthesis and properties of oligomeric silsesquioxanes has also become a focus of increasing interest in the last few years. Feher and coworkers (e.g., Feher & Budzichowski, 1989, Feher et al., 1989; Feher et al., 1992; Feher & Budzichowski, 1995) have devised syntheses for polyhedral forms containing three silanol groups in a triangular array at a "missing corner" of the polyhedron. This proves to be a useful model for catalysis directed by metal ions adsorbed at silanol groups, as on a silica surface. Moreover, the silanols act as useful functional groups for further reaction; the corner can be "capped", for example, by condensation with another moiety. This echoes the stepwise assembly of desired molecules that characterizes organic chemistry.

This group has also devised a high-yield synthesis for substituted D3R siloxanes, and Behbahani et al. (1994) reported a study of (C₆H₁₁)₆Si₆O₉.

Agaskar, Klemperer, and coworkers (Day et al., 1985; Agaskar, 1989, 1990, 1991, 1992ab; Agaskar & Klemperer, 1995) have developed syntheses for various hydridospherosiloxanes and substituted spherosiloxanes. One functionalization they term "spherosilicates," in which the hydrogens on the siloxane core are replaced with oxytrimethylsilyl (OSi(CH₃)₃) groups. Obviously, these are the same structures as obtained from the corresponding anionic form by trimethylsilylation. These authors also found that D4R is the only group readily synthesized in high yield, again based on extraction by trimethylsilylation from methanolic TMA solution. The other spherosilicates must be synthesized from the analogous siloxane, which is considerably more difficult.

Calzaferri and coworkers (e.g., Calzaferri & Imhof, 1992; Herren et al., 1991; Bürgi et al., 1993; Calzaferri et al., 1996) have investigated different synthetic approaches to preparing substituted spherosiloxanes, particularly with unsymmetrical substitution. They also found that the D4R unit is the most synthetically accessible, although they have also done some work on D5R structures. In addition, this group has modeled the vibrational modes of silicate structures using force-field models, as mentioned above.

Finally, Dittmar et al. (1995) reported the synthesis of substituted cubosiloxanes, and Harrison & Kannengiesser (1996) report syntheses of functionalized D3R and D4R methoxides, including small polymeric units consisting of two double-ring units linked together. Several groups (Hong et al., 1997; Jaffres & Morris, 1998) are also investigating using D4R as a core in dendrimers.

Most of the spherosiloxane syntheses are still based on trichlorosilane or substituted trichlorosilanes (RSiCl₃, R = H, organic side chain) as the starting material. Even though trichlorosilanes are largely unwanted by-products of dichlorosilane synthesis, however, their manufacture is nonetheless highly energy-intensive. Therefore, ultimately a large-scale siloxane-based approach to silicate MNT will also need to address synthesizing the building blocks in a more energy-efficient manner.

7.1.4 Large units.

A problem apparent in the above survey is that the large units are by far the most difficult to make, yet would be the most useful! Though many routes are available to the D4R structure, probably because of both kinetic (Kinrade et al., 1998ab) and electronic (Calzaferri & Hoffmann, 1991) factors, larger structures are disfavored. Bornhauser & Calzaferri (1996) carried out calculations of the vibrational modes of the hypothetical spherosiloxanes H₂₀Si₂₀O₃₀ (I_h symmetry; a spherosiloxane analog of the hypothetical fullerene "dodecahedrane"), and H₂₄Si₂₄O₃₆ (O_h) an isolated sodalite cage, but noted that both structures are "not yet known as isolated molecules."

Moreover, the largest double-ring structure that has been synthesized as a spherosiloxane molecule is D5R; all larger known spherosiloxanes have more compact shapes with faces differing little in multiplicity. For example, the known isomer of H₁₂Si₁₂O₁₈ has 4⁴5⁴ faces and D_2d symmetry, whereas the D6R isomer is unknown as a molecular entity (Törnroos et al., 1995; an early report (Barry et al., 1955) is evidently in error). Rikowski & Marsmann (1997) demonstrated catalyzed cage-rearrangement of R₈D4R to larger units, but the Si₁₂O₁₆ isomer is again not the D6R type. Evidently, large differences in face multiplicity are disfavored.

All this indicates that, if the building-block approach is to be practical for large units such as 6- or 8-rings or the polyhedra proposed in Section 6, alternative synthetic pathways must be found. As such polyhedra (as well as many others) are known in zeolites, and 6- and 8-rings are known in other crystalline silicates, they obviously can form spontaneously under the proper conditions. Perhaps a "templating" approach would again be useful: large co-solutes (cations or neutral molecules) might provide scaffolding around which units could spontaneously organize, analogously to the way metal ions are commonly used in the synthesis of macrocycles (e.g., McMurry et al., 1989). Progress with the mechanistic modeling of zeolite crystallization is also likely to be helpful in these issues, as are further experimental studies to determine the molecular basis of framework crystallization.

8. Conclusions.

Silicates, the most abundant chemical compounds on this and any rocky planet, show promise as a basis for molecular nanotechnology. The open framework structures that arise naturally as a result of 3D polymerization of Si-O bonds lend themselves naturally to a great many practical uses of near-term interest such as catalysis, ion exchange and separation, and supports for novel electronic and optical materials. Furthermore, substituting other tetrahedrally coordinated atoms (Al, Ge, B, Zn, Be, etc.) for Si vastly broadens the variety and utility of potential structures. Silicate modeling is also sufficiently advanced that structures of potential interest can be investigated.

Although an enormous database has been accumulated on the synthesis of silicate structures, it remains largely empirical. Much progress has been made in elucidating the molecular mechanisms by which structure-directing agents work in zeolite self-assembly, but major controversies remain, and ab initio design, much less synthesis, of arbitrary structures remains a distant goal. Syntheses based on alkoxide hydrolysis seem promising, because of the low temperatures and prospect of better molecular control over the building units. Conventional sol-gel syntheses, however, merely yield glasses; no long-range molecular order is present, even if a degree of short-range ordering exists.

The fact that many useful silicate structures are open frameworks indicates that a building- block approach to assembly is particularly promising. Although true molecular mechanosynthesis seems remote at this point, at least for macroscopic materials, manipulation of oligomeric silicate units with conventional AFM probes seems an obvious step to test the selectivity and manipulability of different functionalizations, as well as the degree to which disiloxy bonds can be formed by direct assembly. The molecular mechanisms by which biosystems handle silica also merit much further study.

Building-blocks approaches may even be accessible by self-assembly techniques, as suggested by work such as that of Davis (1994), in which complementary functionalizations on building blocks direct their assembly in certain ways. Certainly the tradition of self-assembly in zeolite synthesis encourages such approaches.

The synthesis of small building blocks seems relatively straightforward, as many are known as oxyanions or siloxane skeletons. Separating oligomers from each other, in particular out of aqueous solution, is likely to require some sort of molecular recognition, however. Furthermore, synthesis of the large building blocks, which would even be more useful for constructing interesting structures, seems a major issue. No large block is now known as an independent molecular entity. Perhaps templated assembly, as is common in organic synthesis, will be useful here as well.

Acknowledgments

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