Model of layer-by-layer thinning transition in thin films

Free-standing smectic liquid-crystal films exhibit an interesting phenomenon of layer-by-layer thinning transition where, instead of abrupt rupture of the film at or below Sm-A-isotropic transition temperature T-c, discrete jumps in film thickness are observed when temperature is increased, and the film eventually breaks at a temperature above the bulk value T-c [4]. Starting with a molecular pair interaction potential of the McMillan form and deriving therefrom a single effective potential, the behavior of thin films with changing temperature is studied. The film thickness experimentally found [4] to exhibit a clear functional relationship to temperatures of layer transitions, h(t) = l(0)t(-v), can be explained qualitatively, its exact form depending strongly on the parameters of the potential. Fluctuation profile of the order parameters within smectic layers is considered showing a critical behavior in the vicinity of the transition.