FLUCTUATIONS IN A CRYSTALLINE MONOLAYER ON A LIQUID

The structure factor of a crystalline monolayer on the surface of a li quid is calculated. It is shown that in the first approximation the fi nite rigidity of the monolayer maintains the power-law profile of quas i-Bragg peaks typical for two-dimensional systems but leads to a reduc tion of the X-ray scattering intensity. It is found that this effectiv e Debye-Waller factor has very strong dependence on the length h of th e chains composing the monolayer. Namely, it is proportional to exp(-h (3)/xi a(2)), where xi is a chain persistence length and a is a charac teristic atomic scale. We have also studied the spectrum of modes wher e the motion of the liquid is localised near the film. It turns out th at for thick films there are three propagating sound-like modes: the t ransverse sound with a velocity which becomes zero if the wave vector q is directed along the normal to the film (z-axis); the conventional longitudinal sound with the almost isotropic velocity (determined main ly by the compressibility of the film); and the mode analogous to the second sound in smectics. For thin films the last mode transforms into the fast pure relaxational one. For tilted or heretic layers there is also an orientational diffusion mode. This mode strongly influences t he viscosity of the system. The fluctuation contribution in the viscos ity coefficients is proportional to (T/Gamma)ln(qa), where Gamma is th e orientational diffusion coefficient. Transverse and longitudinal sou nd are transformed into overdamped modes with the following dispersion law omega proportional to (root 3 - i)q(4/3).