Nucleation and growth of droplets in the overheated free-standing smectic films

We present a theoretical explanation for the formation of nematic droplets in free-standing smectic films (FSSF) overheated above the temperature of the bulk smectic - nematic transition. The conditions for the formation of the nematic droplets in smectic films are studied on the basis of the general thermodynamic approach to the stability of FSSF. It is shown that the formation of droplets in overheated FSSF is only possible in the presence of a certain amount of thermally generated dislocation loops. We determined the gain in the free energy related with the formation of the nematic droplets, the value of the critical work and the critical size of the drops. The initial increase of the drops size is due to release of material from the growing dislocation loops. At the second stage the drops growth occurs through coalescence of the smaller drops with the larger ones. The droplets attract each other by means of capillary forces arising due to gradients of the surface energy in the area between them. Drops size evolution, the dynamics of their growth and merging are in good agreement with experiments

Benard–Marangoni convection within isotropic droplets in overheated free standing smectic films

We study theoretically internal flows in isotropic droplets formed in horizontal free-standing smectic films (FSSF) overheated above the bulk smectic-isotropic transition. The convection is due to vertical temperature gradient in the film and is driven by the surface tension variations at the drop interfaces. Using a conventional linear instability theory, we have found analytically the conditions under which the mechanical equilibrium within isotropic droplets in FSSFs becomes unstable relative to the thermocapillary convection. An explicit expression for the Marangoni number characterizing the onset of the convection as a function of the wave vector of in-plane instability and parameters of heat transfer is obtained. The cellular instability in FSSF with isotropic droplets behaving as a normal fluid (surface tension is a decreasing function of temperature) is possible for both directions of thermal gradient across the film: from bottom to top and conversely. We propose possible experimental observations enabling to check our predictions

Thinning and thickening of free-standing smectic films revisited

We present a theoretical explanation of the remarkable thickness instabilities that occur in free-standing smectic films (FSSF) upon changing the external conditions: i) upon heating the film above the bulk smectic disordering temperature, generally the film does not rupture but instead shows successive layer-by-layer thinning transitions; ii) thickening of FSSF, which occurs within the thermal range of the smectic phase upon local heating. All observations reported so far can be explained on the basis of the Landau-de Gennes theory of the smectic state in combination with nucleation theory. In overheated smectic films (thinning) or locally heated FSSF (thickening) an additional normal tensile force appears due to a change of the mean density of the film. In the case of an overheated FSSF the free energy has oscillatory character, and upon heating the balance of tensile and elastic forces breaks down spontaneously. This leads to thinning of the film, which proceeds via thermal nucleation and growing of dislocation loops in the middle plane of the film. The expression for the envelope of the points of thinning as well as estimates of the dynamics of growth of dislocation loops, are in good agreement with experiments. Local heating of a FSSF within the smectic temperature range induces thermal expansion, which shifts the system to a metastable state. This favors nucleation and growth of dislocation loops of excess smectic layers in the middle plane of the film. The activation energy of such dislocation loops attains values below the threshold energy and decreases upon further heating. This leads to local film thickening by many tens of layers. Realization of this scenario depends crucially on the energy dissipated locally in the film. Estimates of the thickness of the growing “island” in the film and of the velocity of the dislocation loop growth are in reasonable agreement with experiments

Layer-by-layer crystallization and the role of fluctuations in free standing smectic films

Specular x-ray reflectivity has been used to study the changes in the thermal fluctuation behavior of eight layer freely suspended N−(4−n−butoxybenzilidene)−4−n−octylaniline (4O.8) films during the process of successive layer-by-layer crystallizations. Each of these steps is preceded by the formation of an intermediate layer structure with in-plane hexatic ordering. We find an unusually large reduction of the fluctuations after the emergence of only the first hexatic toplayer. The fluctuation profiles over the film are in all cases quenched at the surfaces though less so after each crystallization step. This behavior supports theoretical arguments that hexatic order is reduced by out-of-plane smectic layer fluctuations