  We present a lattice formulation of a dynamic self-consistent field (DSCF)
theory that is capable of resolving interfacial structure, dynamics and
rheology in inhomogeneous, compressible melts and blends of unentangled
homopolymer chains. The joint probability distribution of all the Kuhn segments
in the fluid, interacting with adjacent segments and walls, is approximated by
a product of one-body probabilities for free segments interacting solely with
an external potential field that is determined self-consistently. The effect of
flow on ideal chain conformations is modeled with FENE-P dumbbells, and related
to stepping probabilities in a random walk. Free segment and stepping
probabilities generate statistical weights for chain conformations in a
self-consistent field, and determine local volume fractions of chain segments.
Flux balance across unit lattice cells yields mean-field transport equations
for the evolution of free segment probabilities and of momentum densities on
the Kuhn length scale. Diffusive and viscous contributions to the fluxes arise
from segmental hops modeled as a Markov process, with transition rates
reflecting changes in segmental interaction, kinetic energy, and entropic
contributions to the free energy under flow.
