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.
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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 Ng, 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.
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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.
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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.
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