Modelling of microstructure in mesophases

Abstract

Small-molecule liquid crystals show textures which are readily studied at low magnification in the optical polarizing microscope. In polymeric liquid crystals, however, the textures are often much finer, taxing the microscope's resolution. Nevertheless, studies of microstructure in such polymers have been made and it is apparent that they can differ widely both from small-molecule liquid crystals and, indeed, from polymer to polymer. This paper sets out to account for these variations by exploring the effect on microstructure of the marked differences between the magnitudes of the splay, twist and bend elastic constants which are a characteristic of many liquid crystalline polymers. We report a computer model which simulates the development of microstructure for different ratios of the elastic constants. When these are approximately equal, textures characteristic of small-molecule liquid crystals result, such as those involving escape into the third dimension with the degeneration of line defects into points. When the splay energy is high in comparison with bend and twist, as is the case for many thermotropic liquid crystalline copolyesters, escape does not occur and half integral disclination lines predominate. For simulations involving planar boundary conditions, layered microstructures result, frequently with little matching of the orientation from layer to layer. Within the layers the trajectory of the orienting units is sinuous. This simulated microstructure resembles textures observed in thermotropic copolyesters, studied both in this laboratory and elsewhere. The computer model uses a lattice approach which is similar in some respects to that developed by Lebwohl and Lasher. It should not be thought of as a molecular scale model, however, but rather as one based on assemblies of molecules which share a common director.