The x dependence of the normalized basal spacing, d n (x), of pillared vermiculite (Vm) has been measured for the mixed-layer system [(CH3)4N + ] X [(CH3>3NH + lir Vm and compared with that of CsxRbix -Vm. Both systems exhibit a nonlinear d n (x) with approximate thresholds of x =0.2 and 0.5, respectively. A model which related d n (x) to layer rigidity and the binding energies of gallery and defect sites yields excellent fits to the basal spacing data and to monolayer simulations if collective effects are included. This model should be applicable to other types of lamellar solids.PACS numbers: 68.65.+g Lamellar solids constitute a class of materials which exhibit a variety of specific properties. These properties are in large part determined by the host-layer transverse rigidity which characterizes its response to out-of-plane distortions. 1 For example, graphite, whose monatomic amphoteric layers are "floppy" and thus collapse around intercalated guest species, does not sustain a microporous structure with large internal surface area. In contrast, layered alumino-silicate "clays," whose multiatomic fixed-charge layers are "rigid," are unique among lamellar solids in their ability to be pillared 2 by robust intercalated guest ions which occupy specific lattice sites in the interlayer galleries. 3 The resultant pillared clay is characterized by widely spaced host layers that are propped apart by sparsely distributed guest species whose intralayer separation can be many times their diameter. The enormous free volume of accessible interior space that is derived from such an open structure has significant practical implications in the fields of catalysis and selective adsorption (sieving).Although it is obvious that layer rigidity and pillaring, which is a special example of the more general phenomenon of intercalation, are interrelated, the pillaring mechanism has, to date, been poorly understood. For instance, none of the available elastic models account quantitatively for the full composition dependence of the the c-axis repeat distance of any intercalated layered solid. 4 " 6 It is not surprising that the rigid-layer versions of such models fail when applied to floppy or moderately rigid hosts such as graphite 5 and layer dichalcogenides. 5 But they are qualitatively inconsistent with data derived from clay hosts to which rigid-layer models should be most applicable. Accordingly, we report in this paper the first successful attempt to quantify and parametrize the relation between pillaring and layer rigidity. To accomplish this we have carried out x-ray and simulation studies of the JC dependence of the basal spacing, d(x), of mixed-layer vermiculite (Vm) clays A X B\-X -Vm, 0< x :< 1, where A and B are cations (assume that A is larger than B) that are judiciously chosen to elucidate the physics of pillaring. In a previous study 6 we exam-ined the Cs x Rbix -Vm system for which the alkali intercalate species are best characterized as "puny" pillars since their ionic diameters are only 3.34 and 2.92 A, respective...

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