Layer dynamics of freely standing smectic-A films

The dynamics of freely standing thermotropic smectic-[Formula Presented] films are studied in the isothermal, incompressible limit via a continuous hydrodynamic description. The role of permeation in the films, the structure of the hydrodynamic normal modes, and the form of the autocorrelation functions for the smectic layer and order-parameter fluctuations are discussed. We find two characteristic lengths [Formula Presented] and [Formula Presented] associated with the dynamic behavior of the system, where [Formula Presented] is the surface tension, d is the film thickness, B is the elastic constant for layer compression, [Formula Presented] is the layer sliding viscosity, and [Formula Presented] is the density of the liquid crystal. The crossover from filmlike to bulklike behavior is controlled by [Formula Presented] alone; the crossover from overdamped to underdamped dynamics when the in-plane length scale is large compared to [Formula Presented] is controlled by [Formula Presented] alone.