Dynamic self-consistent
field theory of polymer fluids:
Beyond singlet-level
mean-field, Markovian transport and Wiener walks
Department of Engineering Science and Physics, College of Staten Island and the Graduate Center, City University of New York, New York, USA
Electronic address:
shnidman@mail.csi.cuny.edu
The authors group has recently developed a dynamic self-consistent field (DSCF) theory on a lattice [M. Mihajlovic, T. S. Lo and Y. Shnidman, Phys. Rev. E 72, 041801 (2005)] for modeling the time evolution of composition, mass and momentum densities, and of chain conformation statistics in inhomogeneous polymer fluids under shear. It assumed a singlet-level dynamic mean-field approximation, a Markovian model for diffusive and viscous transport, and an anisotropic Wiener random walk for generating chain conformation in a self-consistent potential relating anisotropic stepping probabilities to the gradient of the velocity by means of an elastic dumbbell model. The theory above was applied to unentangled polymer blends that are sheared in a planar channel, and compared with a molecular dynamics study of the same systems [T. S. Lo et al., Phys. Rev. E 72, 040801(R) (2005).]. We will discuss a reformulation of the DSCF theory to make it applicable to entangled polymer fluids under shear, incorporating (a) non-Markovian mean field time evolution of occupancy probabilities for oriented pairs of adjacent sites coupled to the gradient of the velocity, and (b) a stochastic process generating chain conformation statistics that transcends the anisotropic Wiener random walk in a singlet-level self-consistent potential.