Elastic interactions and stability of clay-filled lamellar phases

High aspect ratio clay particles dispersed in a lamellar matrix composed of a block copolymer or a lyotropic smectic are expected to orient with the lamellae. Under such conditions, the smectic medium transmits elastic forces among particles in addition to the usual forces produced by dispersion and electrostatic interactions. S;Ve compute these elastic forces and explore their influence on the thermodynamics of lamellar-clay dispersions. It turns out that the large aspect ratio of the clay implies a long range of interaction at the two particle level. Consequently, virial expansions break down at very low loadings of particles. We examine the thermodynamic behavior of assemblies of flexible and rigid clay plates in both dilute and semidilute concentration regimes. Our results should have implications for the design of nanocomposites formulated with block copolymers and lyotropic liquid crystals.