Casimir-like force in free-standing smectic films close to Smectic A Nematic phse transition
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
It is well known that a thermal Casimir-like force emerges in highly correlated classical systems due to thermal fluctuations. It is particularly important in liquid crystal where the long range character of this interaction has been shown to be relevant to several interesting phenomena, such as wetting and unbinding of fluid membranes. Free-standing smectic films are formed by a stack of smectic ayers confined by a surrounding gas. The effective coupling between the film and the gas is mimicked by a surface tension term which reduces surface fluctuations of the smectic order and provides the characteristic quasi-long range order with logarithmically diverging fluctuations. As a result, the fluctuation-induced interactions decay as $1/l^2$, where $l$ is the film thickness. This effective interaction between surfaces of free-standing films has a longer range than the usual van der Walls interaction. In this work, the thermal Casimir-like in free-standing liquid crystal films close to smectic-A nemactic transition temperature is computed using a quadratic functional integral approach. In the framework of a microscopic mean-field model of free-standing films, the temperature dependence of the order parameter profiles is computed and later used estimated the elastic coupling variability in the vicinity of first- and second order bulk smectic-A nematic phase transitions. The strong nonuniformity of the coupling constant profiles promotes a significant increase of the fluctuation-induced force over three orders of magnitude, specially in thin films. This results reinforces the possible predominance of the thermal Casimir force as compared to the standard van der Waals interaction in thin smectic-A liquid crystal films.