Lattice cluster theory for dense, thin polymer films.

While the application of the lattice cluster theory (LCT) to study the miscibility of polymer blends has greatly expanded our understanding of the monomer scale molecular details influencing miscibility, the corresponding theory for inhomogeneous systems has not yet emerged because of considerable technical difficulties and much greater complexity. Here, we present a general formulation enabling the extension of the LCT to describe the thermodynamic properties of dense, thin polymer films using a high dimension, high temperature expansion. Whereas the leading order of the LCT for bulk polymer systems is essentially simple Flory-Huggins theory, the highly non-trivial leading order inhomogeneous LCT (ILCT) for a film with L layers already involves the numerical solution of 3(L - 1) coupled, highly nonlinear equations for the various density profiles in the film. The new theory incorporates the essential "transport" constraints of Helfand and focuses on the strict imposition of excluded volume constraints, appropriate to dense polymer systems, rather than the maintenance of chain connectivity as appropriate for lower densities and as implemented in self-consistent theories of polymer adsorption at interfaces. The ILCT is illustrated by presenting examples of the computed profiles of the density, the parallel and perpendicular bonds, and the chain ends for free standing and supported films as a function of average film density, chain length, temperature, interaction with support, and chain stiffness. The results generally agree with expected general trends. [ABSTRACT FROM AUTHOR]