First-order Landau-de Gennes model for layer thinning in presmectic free-standing films

Structural, Optical and Dynamic Properties of Thin Smectic Films

The problem of predicting structural and dynamic behavior associated with thin smectic films, both deposited on a solid surface or stretched over an opening, when the temperature is slowly increased above the bulk transition temperature towards either the nematic or isotropic phases, remains an interesting one in the physics of condensed matter. A useful route in studies of structural and optical properties of thin smectic films is provided by a combination of statistical–mechanical theories, hydrodynamics of liquid crystal phases, and optical and calorimetric techniques. We believe that this review shows some useful routes not only for the further examining of the validity of a theoretical description of thin smectic films, both deposited on a solid surface or stretched over an opening, but also for analyzing their structural, optical, and dynamic properties.

Squeezing-out dynamics in free-standing smectic films

We have carried out a theoretical study of the dynamics of the removal of one smectic layer from the N-layer free-standing smectic film during the layer-thinning process. Squeezing-out is initiated by a thermally activated nucleation process in which a density fluctuation forms a small hole. The dynamics of the bounding area during the layer-thinning transition N → N - 1, when the nucleation occurs in the center of the circular smectic film and the squeezed-out area increases up to the edge of the circular smectic area, is studied by the use of the conservation laws for mass and linear momentum. The disjoining pressure is the main factor that is responsible for the driving out of one smectic layer from the N-layer smectic film.

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.

Transition Helmholtz free energy, entropy, and heat capacity of free-standing smectic films in water: a mean-field treatment

Using the extended McMillan's mean field approach with anisotropic forces a study of both the structural and thermodynamic properties of free-standing smectic film (FSSF) in water on heating to the isotropic temperature is carried out numerically. By solving the self-consistent nonlinear equations for the order parameters, we obtained that the smectic-A-isotropic (AI) transition occurs through the series of layer-thinning transitions causing the films to thin in the stepwise manner as the temperature is increased above the bulk smectic-A-isotropic temperature TAI(bulk). With enhanced pair interactions in the bounding layers, the smectic-isotropic transition corresponds to smectic melting of the central layers. The effects of surface "enhanced" pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy and entropy, as well as the temperature dependence of the heat capacity of FSSFs, have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained - by means of optical microscopy and ellipsometry techniques - data of the temperature when the thin decylcyanobiphenyl smectic film immersing in water ruptures has been obtained.

Surface tension and disjoining pressure of free-standing smectic films above the bulk smectic-A-isotropic transition temperature

We have carried out a numerical study of both the structural and thermodynamic properties of free-standing smectic films for the case of enhanced pair interaction in the bounding layers. Calculations, based upon the extended McMillan's mean-field theory with anisotropic forces, show that the layer-thinning transitions are characterized by abrupt drops to lower values, both for a disjoining pressure and a fluctuation-induced long-range interaction between the smectic film surfaces, and then continues to increase with a larger positive slope. Reasonable agreement between the theoretically predicted and the experimentally obtained data on the surface tension of the partially fluorinated 5-n-alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) film has been obtained.

Theoretical model of the frequency and temperature dependence of the complex non-linear dielectric effect in the isotropic phase above the isotropic-smectic-A phase transition

Using the Landau model, the temperature and frequency dependence of the complex non-linear dielectric effect in the isotropic phase above the isotropic-smectic-A phase transition is calculated. Comparing the results of the calculations with existing data, we finally conclude that the model provides a description of the isotropic-smectic-A transition that takes all experimentally known features of the non-linear dielectric effect in the isotropic phase into account in a qualitatively correct way.

Transition entropy, Helmholtz free energy, and heat capacity of free-standing smectic films above the bulk smectic-A-isotropic transition temperature: a mean-field treatment

We have carried out a numerical study of both the structural and thermodynamic properties of free-standing smectic films (FSSFs) for two cases of enhanced pair interactions in the bounding layers. Calculations, based upon the extended McMillan's approach with anisotropic forces, shows a stepwise reduction of the value of the heat capacity as the temperature is raised above the bulk smectic A-isotropic transition. The effects of surface "enhanced" pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy, and entropy of FSSFs have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained--by means of calorimetric techniques--data on the heat capacity of the partially fluorinated 5-n-alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) (H10F5MOPP) films has been obtained.

Field-induced layer thinning transition on free-standing smectic films

Strongly anchored free-standing smectic films usually present a stepwise reduction of the number of layers when the temperature is raised above the smectic-isotropic bulk transition temperature. Here, we demonstrate that a field-induced layer thinning transition can take place in smectic films with a negative dielectric anisotropy even below the bulk transition temperature. Using an extended McMillan's model, we provide the phase diagram of this layering transition and show that, when the field is raised above the bulk transition field, the film thickness reduction is well described by a power law with an exponent that depends on the temperature and the aspect ratio of the liquid-crystal molecule.

Inclusions in free standing smectic liquid crystal films

Colloidal inclusions in thin free standing liquid crystal films are ideal model systems for 2D anisotropic dispersions. Different types of self-organization in chain and lattice structures have been observed. The orientational elasticity of the anisotropic matrix and capillary forces are the dominating interaction mechanisms between solid or liquid inclusions, the director field, and dislocations of the films. We give an overview of the progress in this field, focussing on different inclusion types and their interactions in thermotropic smectic films.

Homeotropic surface anchoring and the layer-thinning transition in free-standing films

In this work, we investigate the interplay between surface anchoring and finite-size effects on the smectic-isotropic transition in free-standing smectic films. Using an extended McMillan model, we study how a homeotropic anchoring stabilizes the smectic order above the bulk transition temperature. In particular, we determine how the transition temperature depends on the surface ordering and film thickness. We identify a characteristic anchoring for which the transition temperature does not depend on the film thickness. For strong surface ordering, we found that the thickness dependence of the transition temperature can be well represented by a power-law relation. The power-law exponent exhibits a weak dependence on the range of film thicknesses, as well as on the molecular alkyl tail length. Our results reproduce the main experimental findings concerning the layer-thinning transitions in free-standing smectic films.