| Abstract: | Mesoscopic theories can be used in the field of materials science to derive local average properties of relevance to the engineer such as flux, pressure, average density or composition. In the following density functional theory will be described and applied to different systems of interest and in particular, to materials formed from complex liquids as characterized by atomic structure and the type of interaction between the individual particles. The calculation of the solid to liquid transition will be explained in detail as a prototype for other order disorder transitions. The theory of polymers in solution will be revisited and used to calculate phase separation in mixtures. An extension of the theory to include the orientation of rodlike, long molecules will be applied to liquid crystals. In the presence of an interface, the system properties depend strongly on position in space and can be predicted from parameters obtained in the bulk in a square gradient approximation for sufficiently smooth and small deviations from the uniform distribution. A phase transition is often used to prepare heterogeneous materials by nucleation and growth. It will be shown how the equilibrium theory can be extended to study the dynamics of nonequilibrium phenomena. |
