Free-standing Smectic Films Research Articles

Line tension and line entropy associated with the monolayer/trilayer boundary of smectic liquid crystal at the air-water interface.

Molecularly thin films of the smectic liquid crystal 4'-octyl-4-biphenylcarbonitrile (8CB) at the air-water interface phase separate into regions with different numbers of layers, in analogy with freestanding smectic liquid crystalline films. This paper reports the line tension associated with the boundary of coexisting trilayer and monolayer phases of in Langmuir films of 8CB at the air-water interface as a function of temperature and humidity and infers information on the boundary profile between the coexisting phases. Two complementary techniques are used to characterize the 8CB thin films: surface pressure-area isotherm and Brewster angle microscopy (BAM). We determine the line tension by stretching isolated domains from their equilibrium circular shape and analyzing the free relaxation with a hydrodynamic model. Then, we interpret the line tension vs temperature data in terms of an excess line entropy for the domain boundary, which requires careful consideration of the thermodynamics of inhomogeneous monolayer systems.

Coarsening of Quasi Two-Dimensional Emulsions Formed by Islands in Free-Standing Smectic Films.

We study the coarsening behavior of assemblies of islands on smectic A freely suspended films in ISS microgravity experiments. The islands can be regarded as liquid inclusions in a two-dimensional fluid in analogy to liquid droplets of the discontinuous phase of an emulsion. The coarsening is effectuated by two processes, predominantly by island coalescence, but to some extend also by Ostwald ripening, whereby large islands grow at the expense of surrounding smaller ones. A peculiarity of this system is that the continuous and the discontinuous phases consist of the same material. We determine the dynamics, analyze the self-similar aging of the island size distribution and discuss characteristic exponents of the mean island growth.

Circulating Marangoni flows within droplets in smectic films.

We present a theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free-standing smectic films (FSSFs). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition and oil lenses deposited on the surface of the smectic film. The realistic model for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops are derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air is determined in the frame of the perturbation theory. As a result, the analytical solutions for the stationary thermocapillary convection are obtained for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in drops are made. Both analytical and numerical simulations predict the axially symmetric circulatory convection motion determined by the Marangoni effect at the droplet-free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always exists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers. Possible experimental observations enabling the checking of our predictions are proposed.

Rapid thickness mapping of free-standing smectic films using colour information of reflected light II: real-time areal mapping using lookup table scheme

ABSTRACT In the previous paper [Liq Cryst. 2020; 48(6): 873–887], we demonstrated that the thickness of free-standing smectic films can be accurately determined from microscopic reflective images, solely utilising the colour information on the image. Even after full vectorisation of the computational code, however, it took ca. 0.1 ms per data point, leaving a big room of improvement to realise a true real-time 2D thickness mapping. Here, we show that the processing speed can be enhanced by a factor of 350 by using a lookup table scheme based on a modified hierarchical triangular partitioning of the colour space. A one-million-pixel image can now be captured and processed in 1 s, offering a clear path to a true video rate 2D thickness mapping.

Rapid thickness mapping of free-standing smectic films using colour information of reflected light

ABSTRACT A practical method to rapidly obtain the 2D thickness distribution in free-standing smectic films is developed based on the colour information of reflected image of the film. The red(R), green(G) and blue(B) colour coordinates from each pixel of a colour camera is normalised by the local intensity and is then quantitatively analysed in reference to the theoretical reflection spectra evaluated as a function of the film thickness. Results from the optical system employing a standard stereomicroscope can clearly discriminate a single-layer step over a wide range of thicknesses and provide thickness values with a precision better than 1 nm.

Surface and finite-size effects on N-Sm-A-Sm-C phase transitions in free-standing films.

The present study is devoted to the investigation of surface anchoring and finite-size effects on nematic-smectic-A-smectic-C (N-Sm-A-Sm-C) phase transitions in free-standing films. Using an extended version of the molecular theory for smectic-C liquid crystals, we analyze how surface anchoring and film thickness affect the thermal behavior of the order parameters in free-standing smectic films. In particular, we determine how the transition temperature depends on the surface ordering and film thickness. We show that the additional orientational order imposed by the surface anchoring may lead to a stabilization of order parameters in central layers, thus modifying the nature of the phase transitions. We compare our results with experimental findings for typical thermotropic compounds presenting a N-Sm-A-Sm-C phase sequence.

Coalescence of holes in two-dimensional free-standing smectic films.

We investigate in free-standing smectic films coalescence of holes (circular regions with thickness smaller than the surrounding film). This process can be considered as a two-dimensional analog of coalescence of bubbles in a three-dimensional fluid. A high speed video camera was used to study the evolution of domains at different stages of coalescence. Special attention was given to investigations of the dependence of the size of the bridge between two holes at the initial stage of coalescence, which was considered in numerous theoretical works and bears information on the coalescence mechanism. It is established that the scaling law is applicable for the description of the transformation of bridges for holes of different radius R. We found that in the regime corresponding to the experimental situation the length of the bridge H increases with the scaling law H/R=(t/τ_{R})^{1/2}. The characteristic time τ_{R} determined from the scaling law is larger than the theoretical time, which can be connected with dissipation of energy both in the film and inside the holes.

Coalescence of isotropic droplets in overheated free standing smectic films.

A theoretical study of the interaction and coalescence of isotropic droplets in overheated free-standing smectic films (FSSF) is presented. Experimentally it is clear that merging of such droplets is extremely rare. On the basis of the general thermodynamic approach to the stability of FSSF, we determined the energy gains and losses involved in the coalescence process. The main contributions to the critical work of drop coalescence are due to the gain related to the decrease of the surface energy of the merging drops, which is opposed by the entropic repulsions of elementary steps at the smectic interface between them. To quantify the evolution of the merging drops, we use a simple geometrical model in which the volume of the smectic material, rearranged in the process of coalescence, is described by an asymmetrical pyramid at the intersection of two drops. In this way, the critical work for drop coalescence and the corresponding energy barrier have been calculated. The probability of the thermal activation of the coalescence process was found to be negligibly small, indicating that droplet merging can be initiated by only an external stimulus. The dynamics of drop merging was calculated by equating the capillary force driving the coalescence, and the Stokes viscous force slowing it down. For the latter, an approximation of moving oblate spheroids permitting exact calculations was used. The time evolution of the height of the neck between the coalescing drops and that of their lateral size are in good agreement with experiments.

Dynamics of island-meniscus coalescence in free-standing smectic films.

In free-standing smectic films islands (regions of larger thickness than the film) can be considered as two-dimensional analogues of liquid droplets in a three-dimensional medium. The dynamics of droplet coalescence is an important but up to now incompletely solved problem in non-equilibrium mechanics. Here, we report on our investigations of island coalescence with the film meniscus. This phenomenon is analogous to the coalescence of a 3D droplet with a flat liquid surface. We found that the time evolution of island dimension is described by universal power-law dependencies for different stages of coalescence. Limited agreement with existing theory was found. In particular, in the final stage of coalescence the domain dynamics differs from theoretical predictions.

Coalescence of viscous two-dimensional smectic islands.

Freestanding smectic films give a unique possibility to study two-dimensional coalescence. We report experimental investigations in freestanding films and detailed analysis of coalescence of islands, circular regions of larger thickness than the surrounding film. The driving force of island coalescence is the dislocation tension on the boundary between the island and the film. The obtained experimental results enable one to perform complex analysis of two-dimensional coalescence in Stokes regime and compare it to theoretical predictions. The applicability of scaling arguments for the description of the peculiarities of domain dynamics is demonstrated. The whole process of coalescence is well described by the analytical solution adapted to our case of islands in freestanding smectic films.

Structural and optical properties of free-standing smectic films.

We have carried out a complex numerical study of the structural, thermodynamic and optical properties of the partially fluorinated 5-n -alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) free-standing smectic film in air under the action of the external electric field [Formula: see text]. Calculations, based upon the extended McMillan's mean-field theory with anisotropic forces, show a stepwise reduction of the value of the Helmholtz free energy and the reflectivity of the partially fluorinated smectic film in air, as the temperature is raised above the bulk smectic-A-isotropic transition value. It has been shown, by solving the self-consistent nonlinear equations for the orientational and translational order parameters, that the electric field [Formula: see text] may not only affect the layer-thinning transition sequences, but also change the first multilayer jump in the film thickness, whereas practically does not affect the reflectivity R(N) of the partially fluorinated N -layer smectic film in air. In the range of film thicknesses investigated, the reduction of the R(N) is, at least, qualitatively in agreement with the experimentally observed decrease of the optical reflectivity with the decrease of N.

Nucleation of filaments of the TGBA phase in free-standing films

ABSTRACTA model of filament nucleation in the twist grain boundary A (TGBA) phase in free-standing smectic films is proposed. It is based on a concept of finite blocks of parallel smectic layers forming a helical structure in the interior of a film. In our model, the blocks resemble twin-like domains in smectic-A liquid crystal. The blocks are mediated to surrounding smectic layers in film either continuously (coherent twin boundary) or discontinuously via dislocation loops wrapping up blocks. Edge components of dislocation loops form incoherent twin boundary. Screw components forming twist grain boundary connect neighbour blocks among themselves. Nucleation of TGBA filament in a film is treated using a simplified model based on isotropic smectic-A elastic theory. Discussion showed that filaments can be nucleated just below the transition temperature from the isotropic to the TGBA phase under slow temperature decrease. The nucleation of dislocation loops is possible due to low compression modulus of material which can be expected just below the transition temperature.

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.

Stripe instabilities in menisci of free-standing smectic films with a direct transition from smectic C to an isotropic or nematic phase

ABSTRACTRegular periodic stripe patterns that are found in the menisci of smectic C and C freely suspended films were described first by Meyer and Pershan (Solid State Commun. 13 (1973)) more than 40 years ago, but their physical origin is still under debate. Loudet et al. (Phys. Rev. Lett. 106 117, 802 (2011)) proposed a layer dilatation model to explain their formation. Our observation of such patterns in films with a direct transition from smectic C to a nematic or isotropic phase is in sharp conflict with that model. Moreover, we demonstrate the disappearance of the patterns at the transition from synclinic to anticlinic smectic C phases. An essentially different explanation of the physical mechanism of the stripe formation must be sought. We propose potential sources of the instability.

Translational diffusion across a free-standing smectic film above the bulk smectic-A-isotropic transition temperature.

Calculations of translational self-diffusion coefficient in free-standing smectic films during a series of layer-thinning transitions as the temperature is raised above the bulk smectic-A-isotropic transition have been carried out. A molecular model based upon the random walk theory is applied for calculating the translational diffusion coefficient (TDC) D_{∥} across the smectic film both in the bulk of the film, as well as in the vicinity of the bounding surfaces. Calculations of D_{∥} require the set of the orientational and translational order parameters (OPs) which have been obtained by using the extended McMillan approach with anisotropic forces. The effect of E on the orientational and translational OPs, as well as on the TDC of smectic films has been investigated. A reasonable agreement between the theoretically predicted and the experimentally obtained data on the TDC in the bulk of the partially fluorinated H10F5MOPP film has been obtained. We also found, in agreement with the experimentally observed behavior of D_{∥}(N)(N=25,13,11,10), that the translational diffusion coefficient in the bulk of the film gradually increases as the film thickness N is decreased.

Anomalous melting of overheated smectic films

ABSTRACTThe formation of droplets of a nematic phase in free-standing smectic films (FSSFs) overheated above the temperature of the bulk smectic–nematic transition is studied theoretically. Contrary to the bulk systems the film melting is strongly influenced by its confinement between two free surfaces. By using the general thermodynamic approach to the stability of FSSF, 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 necessary material for initial drops growth is provided by the thermally exited dislocation loops. The further drops growth occurs through merging of the droplets of different size under influence of the capillary forces. These forces arise due to gradients of the surface energy of the film around the drops. At smaller distances an additional interaction of the fluctuation origin appears (pseudo-Casimir), which also favour the drops coalescence. The scenarios of the drop size evolution and of the dynamics of the process are in good agreement with experiments.

Dynamics of layer-by-layer thinning of free-standing smectic films

A dynamic model has been proposed for describing the extrusion of a single layer of a liquid-crystal (LC) material into a meniscus from an N-layer circular free-standing smectic film (FSSF). In the framework of this model, the main mechanism responsible for the process of the thinning (extrusion) of the LC material from the N-layer FSSF is based on the appearance of a spatial pressure gradient directed along the radius of the circular FSSF. This gradient is formed due to the difference in the disjoining pressures on both sides of the front separating the N- and (N–1)-layer domains of the smectic film. The proposed model allows taking into account the influence of the meniscus on dynamic characteristics, such as the time required for the complete extrusion of a single layer from the N-layer FSSF and the velocity of propagation of the front separating the N- and (N–1)-layer domains in the process of the thinning of the smectic film formed by molecules of 5-n-alkyl-2-(4-n-(perfluoroalkyl-methyleneoxy))pentyl.

Squeezing-out dynamics in free-standing smectic films

We have carried out a theoretical study of the dynamics of the squeezing-out of one layer from the N-layer free-standing smectic film (FSSF) coupled with a meniscus, during the layer-thinning process. Squeezing-out is initiated by a thermally activated nucleation process in which a density fluctuation forms a small void in the center of the circular FSSF. The pressure gradient develops between the squeezed-out and nonsqueezed-out areas and is responsible for the driving out of one or several layer(s) from the N-layer smectic film. The dynamics of the boundary between these areas in the FSSF is studied by the use of the conservation laws for mass and linear momentum with accounting for the coupling between the meniscus and the smectic film. This coupling has a strong effect on the dynamics of the squeezing-out process and may significantly change the time which is needed to completely squeezed-out one or several layer(s) from the N-layer smectic film.

Optical reflectance in free-standing smectic films

We have carried out a numerical study of the structural, thermodynamic and optical properties of the partially fluorinated 5-n-alkyl-2-(4-n-(perfluoroalkyl-metheleneoxy)phenyl) free-standing smectic film in air under the action of the external electric field E. Calculations, based upon the extended McMillan′s mean-field theory with anisotropic forces, show a stepwise reduction of the value of the Helmholtz free energy and the reflectivity of the partially fluorinated smectic film in air, as the temperature is raised above the bulk smectic-A-isotropic transition value. It has been shown, by solving the self-consistent nonlinear equations for the orientational and translational order parameters, that the electric field E may not only affect the layer-thinning transition sequences, but also change the first multilayer jump in the film thickness, whereas practically does not affect the reflectivity of the partially fluorinated smectic film in air. The partially fluorinated LC compounds reveal a compression of a smectic layer spacing during the layer-thinning transitions which is supported by the negative values of the thermal expansion coefficient.

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.