Layer dynamics of freely standing smectic-A films

The dynamics of freely standing thermotropic smectic-A films are studied in the isothermal, incompressible limit via a continuous hydrodynamic descrip tion. The role of permeation in the films, the structure of the hydrodynami c normal modes, and the form of the autocorrelation functions for the smect ic layer and order-parameter fluctuations are discussed. We find two charac teristic lengths l(d) = root alpha d/B and l(c) = root eta(3)(2)d/8 rho alp ha associated with the dynamic behavior of the system, where a is the surfa ce tension, d is the film thickness, B is the elastic constant for layer co mpression, eta(3) is the layer sliding viscosity, and rho is the density of the liquid crystal. The crossover from filmlike to bulklike behavior is co ntrolled by l(d) alone; the crossover from overdamped to underdamped dynami cs when the in-plane length scale is large compared to l(d) is controlled b y l(c) alone. PACS number(s): 61.30.Cz, 68.15.+e, 83.70.Jr.