Layer Rigidity and Collective Effects in Pillared Lamellar Solids

The x dependence of the normalized basal spacing, dₙ(x) of pillared vermiculite (Vm) has been measured for the mixed-layer system [(CH₃)₄N⁺]ₓ[(CH₃)₃NH⁺]_1-x-Vm and compared with that of CsₓRb_1-x-Vm. Both systems exhibit a nonlinear dₙ(x) with approximate thresholds of x0.2 and 0.5, respectively. A model which related dₙ(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.