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Kirsten Harth, Alexey Eremin, Ralf Stannarius
Free-standing films of thermotropic smectic phases represent the simplest model for quasi-two-dimensional liquids. Owing to their layered structure, stable films from two to thousands of molecular layers in thickness can be prepared, with areas up to several square centimeters. Such films show many peculiarities. Macroscopic material properties like phase transitions may change their character with a reduction of the film thickness, new phases can be induced or bulk phases can be suppressed. In smectic C or C* films, distortions of the local tilt-azimuth (c-director) of the mesogens mediate elastic forces and torques. In these quasi-2D anisotropic fluids, the viscous coupling of orientational and flow fields can lead to complex pattern formation. Experiments are performed by means of polarising light microscopy. Images and videos are recorded with a CCD camera. In millimeter-sized films, drawn across a metal or glass frame, simple non-equilibrium states are prepared by means of external electric fields. It is shown that during the relaxation of these structures in the field off state, the distorted director field drives a macroscopic flow in the film plane. By deposition of small solid spheres or droplets of an immiscible fluid as tracers on the film plane, the flow field can be decorated and measured quantitatively [1]. The dynamic equations - the incompressible quasi Navier-Stokes equation and the torque balance equation for an order parameter - are solved with standard finite elements software (COMSOL) in order to describe the flow and director dynamics in 2D. Inclusions in free-standing smectic films (islands or micrometer sized particles / droplets) can be considered as simple and conveniently studied models of two-dimensional colloids [2]. As the films tend to minimise their free elastic energy, inclusions self-organise into pairs, chains or clusters - through interaction with the surrounding director field. Droplets can be generated either randomly on the film by heating the material close to the nematic transition point, they can also be deposited in a controlled way by picoliter dispensers. After generation, they interact with each other via the c-director field. These interactions may be described by topological charges in dipolar and quadrupolar arrangements. While the description of their interactions is rather complex in tree dimensions, the 2d-case can be described in exact analogy to electrodynamics. Another interesting aspect is the observation of droplets moving on oblique or vertical films under the action of gravity. Five viscosities and two elastic constants of the liquid crystal are involved in this simple motion. We present some simple calculated scenarios and compare them with experimental data. [1] R. Stannarius, Ch. Bohley, and A. Eremin, Phys. Rev. Lett. 97 97802 (2006) [2] Ch. Bohley and R. Stannarius, Soft Matter 4 683 (2008) |
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