VOLUME 60, NUMBER 21 PHYSICAL REVIEW LETTERS 23 MAY 1988 Layer Rigidity and Collective Effects in Pillared Lamellar Solids H. K m, ' W. Jin, S. Lee, P. Zhou, " T. J. Pinnavaia, ' S. D. Mahanti, and S. A. Solin Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824 (Received 18 November 1987) The x dependence of the normalized basal spacing, d„(x), of pillared vermiculite (Vm) has been mea- sured for the mixed-layer system [(CH&)4N+l„[(CH3)3NH+l~ — -Vm and compared with that of Cs„Rb~ — „-Vm. Both systems exhibit a nonlinear d„(x) with approximate thresholds of x=0.2 and 0.5, respectively. A model which related d, (x) to layer rigidity and the binding energies of gallery and de- fect sites yields excellent fits to the basal spacing data and to monolayer simulations if collective eff'ects 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. ' 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 lamel- lar solids in their ability to be pillared3 by robust inter- calated guest ions which occupy specific lattice sites in the interlayer galleries. 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 di- ameter. 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 phe- nomenon of intercalation, are interrelated, the pillaring mechanism has, to date, been poorly understood. For in- stance, 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. It is not surprising that the rigid-layer versions of such models fail when applied to floppy or moderately rigid hosts such as graphite and layer dichalcogenides. 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 ac- complish this we have carried out x-ray and simulation studies of the x dependence of the basal spacing, d(x), of mixed-layer vermiculite (Vm) clays A, B i —, -Vm, 0 ~ x ~ 1, where A and B are cations (assume that & is larger than B) that are judiciously chosen to elucidate the physics of pillaring. In a previous study we exam- ined the Cs„Rbi-„-Vm system for which the alkali in- tercalate species are best characterized as "puny" pillars since their ionic diameters are only 3.34 and 2.92 A. , re- spectively. Here we focus on the more robust mixed pil- lar system tetramethyl ammonium-trimethyl ammoni- um-vermiculite with eff'ective diameters of 4. 8 and 4.0 A. , respectively. We find that the pillaring process is a collective phenomenon which introduces an intrinsic non- linearity in d(x). While our results are deduced for clay intercalation compounds (CIC's) they should also be applicable to other lamellar solids. Vermiculite is a trioctahedral 2:1 layered silicate. Its layers are formed from a sheet of edge-connected octahe- dra (M"' =Mg, Al, Fe) which is bound to two sheets of corner-connected tetrahedra (M' =Si, Al) as shown in the inset of Fig. 1. The layers of oxygen atoms which terminate the clay layers are arranged in a kagome lat- tice whose hexagonal pockets form a triangular lattice of gallery sites which here are constrained by the require- ment of overall charge neutrality to be occupied by the gallery exchange cation. This occupation imposes a la- teral registration of adjacent clay layers as indicated in the inset of Fig. l. To synthesize the specimens studied here, the Mg + gallery cations which link the layers of natural Llano vermiculite were exchanged for (CH3 ) 3NH + ions with ethylenediaminetetraacetate as a complexant. Subsequent exposure of pure [(CH3)3NH+]-Vm to the proper amount of (CH3)4N+ yielded a solid-solution pillared CIC [(CH3)4N'l, [(CH, )3NH ]i — „-Vm. Self-supporting sedimented films exhibited a mosaic spread of = 5' with the layers parallel to the substrate. The x dependence of the (001) x-ray difraction pat- terns of [(CH3)4N ], [(CH3)3NH+]i —, --Vm is shown in Fig. 1. The starred reflections in that figure are from a small concentration of an impurity phase whose 14. 477-A basal spacing is x independent as evidenced by the vertical line in Fig. 1. The patterns in Fig. 1 can be well accounted for by a structure-factor calculation for a 25-layer stack. We have also attempted to fit the pat- 2168 1988 The American Physical Society