Theoretical Research in Statistical Mechanics

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Theoretical research will be conducted on complex fluids, fluids characterized by components which tend to self-assemble, and are therefore characterized by several different lengths. The first of these fluids to be investigated is the ternary mixture of oil, water and amphiphile which produces a uniform, structured fluid in which oil and water are solubilized but separated by sheets of amphiphile; a microemulsion. Among the properties to be studied are the behavior in a confined geometry, the low interfacial tension brought about between oil and water, the elastic properties of the amphiphile sheets, and the evolution of this phase into the sponge phase. The second complex fluid to be studied consists of polymers. The ability of a block copolymer in a ternary mixture to act as a compatibilizer of homopolymers will be examined. %%% Theoretical research will be conducted on two classes of complex fluids. These are fluids which have a number of interacting components which produce interesting, and often important, physical properties. Examples of complex fluids include liquid crystals, microemulsions, biopolymers and polymers. Besides offering fundamental challenges in condensed matter physics, these materials all have important practical applications.