The long term goal of our research is to be able to predict the macroscopic equilibrium and transport properties of condensed phase systems such as complex fluids using the methods of statistical mechanics. Specific topics of current interest include dynamics of polymeric fluids, influence of nonuniform flow on the properties of colloidal and polymeric fluids, and phase transitions in liquid crystalline polymers.
One of the unique features of polymer dynamics is the strong dependence of the transport coefficients on the degree of polymerization, N. Similar to what is observed in critical phenomena, the transport coefficients obey scaling laws, e.g., the diffusion coefficient, D, scales as N-g, where g is a scaling exponent. The strong dependence of the transport properties on the degree of polymerization is attributed to the fact that two polymer molecules cannot cross each other. Current understanding of polymer dynamics is based on a phenomenological "reptation" theory which assumes that the polymer chains move like snakes. This theory provides estimates for the scaling exponents but not for the "prefactors" and therefore does not make predictions for the actual values of the transport coefficients. Our research will concentrate on a fundamental statistical mechanical description of polymer dynamics. In addition to providing an understanding of the microscopic origin of the scaling laws, our theory will allow us to calculate the corresponding prefactors and to obtain estimates for the magnitudes of the transport coefficients.
Nonuniform flow can induce profound changes in the macroscopic properties of complex fluids. For example, the transport coefficients are strongly shear-rate dependent, and the equilibrium phase boundaries can be shifted by shear flow. These phenomena fall beyond the realm of equilibrium statistical mechanics, and there is no standard or well-established procedure to describe them. Our research will aim at developing such a procedure by studying a series of specific problems of increasing complexity. We will begin with investigation of the non-equilibrium structure of colloidal and polymeric fluids, then study transport phenomena in steady states, and finally move on to the phase behavior under nonuniform flow.
Our understanding of the phase behavior of lyotropic polymeric liquid crystals is, at present, incomplete. Existing theories of the nematic transition in flexible polymers include only the second virial coefficient and are therefore not applicable to experimental systems which are very dense. We propose to develop a theory for the phase behavior of dense liquid crystalline polymeric systems. By a few-chain Monte Carlo simulation we will calculate higher virial coefficients and incorporate them into the present theory. We will also try to include approximately all of the virial coefficients by replacing the real interaction potential with an effective solvation potential.