Thinning transitions in free-standing liquid-crystal films as the successive formation of dislocation loops

Flows Excited by Shear Stress in Freestanding Symmetric Smectic C Films

The purpose of this paper is to show some useful routes in describing the shear-driving flows in a freely suspended symmetric smectic C film stretched between two circular frames, the rest outer and rotating inner frames. Our calculations, based on a corresponding extension of the Eriksen–Leslie theory, show that the shear-driving flow in the film, excited by a rotating inner circular frame, causes a twisting rotation of the c^-director around the normal to smectic layers. It is found that the shear flow excited by the rotating frame in a positive sense (counterclockwise) causes a twisting rotation of the c^-director in a negative sense (clockwise) around the normal to smectic film. It is also shown that the twisting of the c^-director’s field has a jumping nature when a large reorientation is carried out in a short space of time. It was also shown that the twisting dynamics of the c^-director field strongly depends on the curvature of the inner rotating frame.

Self similarity of liquid droplet coalescence in a quasi-2D free-standing liquid-crystal film

Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biological systems. The process of merging of liquid objects has been studied during the past years experimentally and theoretically in different geometries. We introduce a unique system that allows a quasi two-dimensional description of the coalescence process: Micrometer-sized flat droplets in freely suspended smectic liquid-crystal films. We find that the bridge connecting the droplets grows linearly in time during the initial stage of coalescence, both with respect to its height and lateral width. We also verify self-similar dynamics of the bridge during the first stage of coalescence. We compare our results with a model based on the thin sheet equations. Our experiments confirm that the most important geometrical parameter influencing the coalescence rate is the contact angle of the droplets.

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.

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.

Orientational relaxation in free-standing smectic C film driven by rotating circular frame

The pecularities in the cˆ-director reorientation in free-standing smectic C film without of defects and stretched between two circular frames, the rest outer and rotating inner, have been investigated theoretically based on the hydrodynamic theory including the cˆ-director motion and with accounting for backflow. Since the orientation of the cˆ-director is fixed at the rims of the smectic film, the shear flow induced by rotating frame winds up of the cˆ-director field. It is found that the higher shearing flow produces the greater twisting rotation of the cˆ-director around the normal to the smectic film directed in the opposite sense with respect to the direction of the angular velocity. Calculations also show that the relaxation dynamics of the cˆ-director field depends crucially on the curvature of the inner rotating frame.

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.

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.

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.

Surface triple points and multiple-layer transitions observed by tuning the surface field at smectic liquid-crystal-water interfaces

We present an ellipsometric study of the interface between a smectic liquid crystal and water in the presence of a nonionic surfactant. The surfactant concentration serves as a handle to tune the surface field. For sufficiently large surfactant concentrations, a smectic phase is present at the interface in the temperature range above the smectic-A-isotropic bulk transition; when the bulk transition is approached, the thickness of this surface phase grows via a series of layer-by-layer transitions at which single smectic layers are formed. At lower surfactant concentrations, transitions appear at which the thickness of the surface phase jumps by multiple smectic layers, thereby implying the existence of triple points at which surface phases with different smectic layer numbers coexist. This is the first experimental demonstration of such surface triple points which are predicted by theoretical models.

Collapse dynamics of smectic-A bubbles

The collapse dynamics of smectic-A bubbles are analyzed experimentally and theoretically. Each bubble is expanded from a flat film stretched at the end of a hollow cylinder and deflated through a pressure release by means of a capillary tube. Its total collapse time can be varied between 0.1s and 20s by suitably choosing the length and the internal diameter of the capillary. This experiment allowed us to show that the collapse takes place in two steps: an initial one, which lasts a fraction of a second, where the meniscus destabilizes and fills up with focal conics, followed by a much longer period during which the bubble collapses and exchanges material with the meniscus. By measuring simultaneously the Laplace pressure and the internal pressure inside the bubble, we were able to fully characterize the shear-thinning behavior of the smectic phase within the meniscus. We emphasize that this method is generic and could be applied as well to other systems such as soap bubbles, on condition that inertial effects are negligible.

Interaction of surfaces in smectic membranes and their instability near thinning transitions

We report measurements of the interaction between surfaces of the presmectic membrane above the temperature of transition to the phase without layer ordering. Investigations were performed employing cholesteric droplets embedded in the membrane in the temperature range of thinning transitions. Upon heating, the difference between the membrane tension and surface tension of the bulk sample decreases sufficiently, which leads to membrane instability. After the thinning transition, the membrane returns to a stable state with a larger value of surface interaction.

Light-induced layer by layer thickening in photosensitive liquid crystal membranes

Photosensitive smectic membranes of pure liquid crystal (LC) were studied under white light illumination. A thickness increase is observed in the illuminated film area. Appropriate light and thermal conditions lead to a thickening layer by layer process. This unusual phenomenon is opposite to the well-known step-by-step thinning transitions under heating. We give a phenomenological interpretation for thickening based on layer transport of LC matter towards the illuminated area.

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

A Landau theory for surface enhanced ordering in free-standing smectic-A films is described, based on a generalization of de Gennes's "presmectic" model to systems which undergo a first-order smectic-isotropic transition in bulk. As found in related work on phase transitions in thin films, the system exhibits three phases, an isotropic liquid, a bulk-like ordered (smectic-A) phase, and a surface-ordered ("quasismectic") phase. Over much of its range, the temperature-thickness boundary between the bulk-ordered and surface-ordered phases is effectively characterized by a power-law relation similar to those observed for layer-thinning transitions in overheated free-standing smectic-A films.

Dislocation loops in overheated free-standing smectic films

Static and dynamic phenomena in overheated free-standing smectic-A films are studied theoretically. The work is based on a generalization, introduced recently by the authors, of de Gennes' theory for a confined presmectic liquid. In this approach, smectic ordering in an overheated film is caused by an intrinsic surface contribution to the film free energy and vanishes at some temperature depending on the number of layers. Here the theory is further generalized to study the dynamics of films with planar inhomogeneities. A static application is to determine the profile of the film meniscus and the meniscus contact angle, the results being compared with those of a recent study employing de Gennes' original theory. The dynamical generalization of the theory is based on a time-dependent Ginzburg-Landau approach. This is used to compare two modes for layer-thinning transitions in overheated free-standing films, namely, "uniform thinning" versus nucleation of dislocation loops. It is concluded that the nucleation mechanism dominates provided there is a sufficiently large pressure difference arising from meniscus curvature. Properties such as the line tension and velocity of a moving dislocation line are evaluated self-consistently by the theory.

When boundaries dominate: dislocation dynamics in smectic films

We discuss the influence of dissipation at a system boundary (film-meniscus interface) on the dynamics of dislocation loops inside a smectic film. This dissipation induces a strong coupling between dislocations-effectively independent of their separation-leading to their nontrivial dynamics. Because of these dynamics, the effective "dynamical" radius of nucleation can be 10 times larger than the usual static critical radius.

Landau-de Gennes theory of surface-enhanced ordering in smectic films

A Landau theory for surface-enhanced ordering in smectic-A free-standing films is described, based on a generalization of de Gennes' model for a "presmectic" fluid confined between two walls. According to the theory, smectic ordering in free-standing films heated above the bulk smectic melting temperature is due to an intrinsic surface contribution rather than an external field. The theory yields a persistent finite-size effect, in that the film melting temperatures do not tend to the bulk transition temperature in the limit of infinite film thickness. It also predicts that a continuous transition from (N+1)- to N-layer films is impossible without an external field. The theory closely fits existing experimental data on layer-thinning transitions in compounds which exhibit a bulk smectic-A to nematic phase transition. Possible origins of the intrinsic surface contribution are discussed.

Disjoining pressure and thinning transitions in smectic-A liquid crystal films

The contact angle between a free standing film of a smectic-A liquid crystal and its meniscus is different from zero. It increases independently of the meniscus size when the film thickness decreases. This angle provides a very precise measurement of the film tension and of the interactions between the two free surfaces. This interaction is attractive and can be qualitatively explained within the framework of the de Gennes theory of the presmectic state. According to this model, the attraction is caused by an increase of the smectic order parameter at the free surface. This phenomenon also explains the metastability of very thin smectic films above the bulk smectic-A-nematic phase transition. The temperatures T(N) of spontaneous thinning from N layers to N-1 layers is measured in the smectic phase of the liquid crystal 8CB (octylcyanobiphenyl).

Formation of string defects at thinning transitions in smectic-C* free-standing films

The layer thinning transitions in freely suspended smectic-C* films have been investigated. The defect structure formed by stringlike lines was observed just before the thinning transitions. The string defects disappear after the thinning transition and appear again near the temperature of the next thinning transition. These results clearly indicate that thin free-standing films at the thinning transitions are slightly below the melting temperature of the interior layers.

Kinetics of layer-thinning transitions in overheated smectic films

The kinetic behavior of dislocation loops in overheated free-standing smectic-A films is reported. The loops open at velocities that are much faster than those seen in nonoverheated films. The velocities increase dramatically as a function of temperature and vary slightly as a function of film thickness. The behavior of dislocation loops induced with a pulsed resistive wire heater is identical to that of the loops giving rise to the layer-thinning transition. In addition, the interaction between two simultaneously nucleated dislocation loops is analyzed. The observed interactions give evidence that thinning occurs in the interior of the film. The results support a model for the layer-by-layer thinning transition based on the nucleation of dislocation loops.