“Elastic” fluctuation-induced effects in smectic wetting films

Abstract

The Li-Kardar field theory approach is generalized to wetting smectic films and the “elastic” fluctuation-induced interaction is obtained between the external flat bounding surface and distorted IA (isotropic liquid-smectic A) interface acting as an “internal” (bulk) boundary of the wetting smectic film under the assumption that the IA interface is essentially “softer” than the surface smectic layer. This field theory approach allows calculating the fluctuation-induced corrections in Hamiltonians of the so-called “correlated” liquids confined by two surfaces, in the case where one of the bounding surfaces is “rough” and with different types of surface smectic layer anchoring. We obtain that in practice, the account of thermal displacements of the smectic layers in a wetting smectic film reduces to the addition of two contributions to the IA interface Hamiltonian. The first, so-called local contribution describes the long-range thermal “elastic” repulsion of the fluctuating IA interface from the flat bounding surface. The second, so-called nonlocal contribution is connected with the occurrence of an “elastic” fluctuation-induced correction to the stiffness of the IA interface. An analytic expression for this correction is obtained.