Hamiltonian modelling of liquid crystal polymers and blends

Abstract

Mathematical models of polymeric liquid crystal (PLC) are expected to be useful for developing applications, for gaining an understanding, and for guiding future investigations. The practical usefulness of models is usually measured by the extent to which they provide a setting for organizing results of the experimental observations of our particular interest, by the extent they allow us to extract from the experimental results pertinent material characteristics, and by the extent they can be used to predict flows arising in the course of industrial processing operations. By understanding the physical processes involved, we usually mean establishing relations between microscopic (molecular) properties and the macroscopic properties of our direct interest. It is very unlikely that all the above expectations can be satisfied by a single model. We have probably the best chance to satisfy the expectations with a family of mutually compatible and complementary models, each formulated on a different level of description. The main objective of this chapter is to show how the models in such a family are constructed. Our aim is to present a method - a do-it-yourself prescription. Particular models are introduced only as illustrations. In section 3.2, we present the method and illustrate its use on the well-known models (including Doi’s model). In section 3.3, we introduce a new computer-friendly model suitable for molecular simulation.In section 3.4, we use the method to model rheological properties of blends.