Thermal fluctuations and x-ray scattering from free-standing smectic-A films

Temperature dependence of the Casimir-like force in free-standing smectic films

The thermal Casimir-like force in free-standing liquid crystal films close to the smectic-A-nematic transition temperature is computed using a quadratic functional approach. In the framework of a microscopic mean-field model of free-standing smectic-A films, the temperature dependence of the order parameter profiles is computed and later used to estimate 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, especially in thin films. This result 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.

Dynamics of fluctuations in smectic membranes

We present a comprehensive account of the dynamics of layer-displacement fluctuations in smectic liquid-crystal membranes as studied by x-ray photon correlation spectroscopy (XPCS) and neutron-spin echo (NSE). Combining these two techniques at fast relaxation times, three distinct relaxation regimes can be distinguished. For thin membranes, at the specular Bragg position oscillatory relaxation occurs, which transforms for thicker samples into exponential decay. Above a critical off-specular angle, in XPCS exponential relaxation is observed that does not depend on the scattering angle. This indicates relaxation times that are independent of the wavelength of the fluctuations. In this regime the relaxation of the fluctuations is dominated by the surface tension. Using NSE larger off-specular angles can be reached than by XPCS, for which the relaxation time decreases with the scattering angle. This regime is dominated by the bulk elasticity of the smectic membrane. The results are compared with theoretical models for the fluctuation behavior of smectic membranes, in which effects of the mosaic distribution and of the center of mass movement of the smectic membranes must be incorporated.

Field-driven crossover from attractive-to-repulsive Casimir-like force in smectic films

External fields have a profound effect on the fluctuations of strongly correlated fluids, such as a liquid crystal. Within a harmonic functional integral approach, we compute the fluctuation-induced force between the surfaces of a smectic liquid-crystal film under the presence of an ordering field. In particular, we show that for asymmetrically anchored films, the thermal Casimir interaction energy can be collapsed into a universal form crossing over from a repulsive to an attractive interaction as the film thickness is increased. We discuss the possible relevance of this field effect in nematic-smectic wetting transitions.

Smectic layer displacement fluctuations in solid substrate supported smectic-A films

In this paper we present results of calculations of static and dynamic characteristics of smectic layer displacement fluctuations in solid substrate supported smectic-A films with due regard for asymmetric profiles of the bending elastic constant K and the smectic layer compressibility B. We also take into account difference in properties of boundary surfaces of the film, namely, the surface tension of the free surface is taken to be finite whereas that of a film-substrate interface is assumed to be infinitely large. Profiles of the smectic layer displacement fluctuations and correlations between them are calculated for films formed of liquid crystalline compounds with the bulk smectic-A to nematic phase transition. The calculations are performed at temperatures much lower than that of the bulk phase transition and at maximum temperatures of existence of films of given thickness. The time dependent displacement-displacement correlation functions for thermal smectic layer displacement fluctuations and time dependent intensity-intensity correlation functions for diffuse x-ray scattering from the films are also calculated. It is shown that unlike free-standing smectic-A films, an effect of the temperature on dynamics of smectic layer displacement fluctuations in solid substrate supported smectic-A films can be observed in experiments on coherent x-ray dynamic scattering from not very thick films (N approximately 20) and at significantly smaller wave vector transfer component in the film plane.

Surface effects on the amplitude of fluctuation-induced interactions in smectic films

Within a quadratic functional integral approach, we investigate the role played by surface terms in the fluctuation-induced surface-surface interaction of free standing smectic liquid crystals. We show that the typical 1/l decay of the Casimir-type contribution to the free energy of a film with thickness l is replaced by a faster 1/l3 decay at a characteristic surface tension. An intermediate 1/l2 decay can also take place for specific surface parameters with unlike boundary conditions. In all the investigated cases, a repulsive long-range force appears only for mixed boundary conditions with strong anchoring at one surface and weak anchoring at the opposite one. Further, the amplitude of the thermal Casimir energy, besides being influenced by the applied surface tension, depicts a nonmonotonic dependence on the coupling between the outermost film layers, reflecting a crossover between strong and weak anchoring regimes.

Disjoining pressure in free-standing smectic-A films and its effect on their reflectivity

The results of calculations of a disjoining pressure and smectic layer spacings in free-standing smectic-A films (FSSAF's) heated above the temperature of disappearance of the smectic order in bulk liquid crystal samples are presented. An effect of the disjoining pressure on the optical reflectivity of FSSAF's having a different number of the smectic layers is investigated. The results of calculations are in agreement with results of experimental optical-reflectivity investigations of FSSAF's.