INTRODUCTION TO MESOSCOPIC THEORY AND APPLICATIONS – Niels Bohr Institute - University of Copenhagen

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INTRODUCTION TO MESOSCOPIC THEORY AND APPLICATIONS

Polymers, micro-crystallinesolids, ferrofluids, liquidcrystals and solids with micro-cracks are typical examples for materials with an internal structure. They show complex macroscopic material behavior, because the internal structure can change under the action of external fields. For instance, polymer melts show non-Newtonian rheological properties, due to stretching and reorientation of the polymer chains. The reorientation of micro-crystallites under deformation leads to material behavior, depending on the loading history. In ferrofluids, the viscosity and other properties can be changed by a magnetic field. The interesting optical properties of liquid crystals, leading to many technical applications, are due to the orientational order of the non-spherical molecules. The so called mesoscopic theory deals with such complex materials within a continuum description. The idea is to enlarge the domain of the field quantities. The new mesoscopic fields are defined on an enlarged space, including some element of internal structure. The macroscopic properties are the result of an averaging procedure with a distribution function. The first example presented here is the alignment tensor theory of liquid crystals. Here, the additional degree of freedom is the orientation of a molecule, and the distr-bution function is an orientation distribution. The macroscopic parameters, describing the orientational order, are the alignment tensors - in the simplest case only one tensor of second order. A differential equation for this order parameter is derived. The wellknown Landau-theory of phase transitions is recovered as a special case of the more general equation of motion for the alignment tensor. In addition, the order-parameter dependence of viscosity coefficients can be predicted by the mesoscopic theory. The second example of application of the mesoscopic theory are ferro-magnetic materials, like ferro-fluids. Hereagain, we have an orientational degree of freedom, the orientation of magnetic moments of single ferromagnetic particles. The macroscopic magnetization is the average over all particle magnetic moments. The resulting diffe-ential equation for the magnetization is a generalized Debye-type equation.

Seminar by Christina Papenfuss, Technical University of Berlin