Spinodal shifts of a polymeric blend film on an interacting surface

We use the Gaussian chain model in half-space, to study surface interacting binary polymer blends for a system that is not laterally incompressible. We derive the partition function of the system to all orders of the surface interaction parameters and find the spinodal limits. Surface-spinodal lines are shifted from those of the bulk on changing the thickness of the film or surface interactions, due to the change of the average number of heterocontacts between the units of different kind. These heterocontacts generally decrease for opposite surface interactions of the two species and contribute to the stability of the blend while they increase for surface interactions of the same kind, leading to destabilization. We thus explain quantitatively the experimental observations of both positive and negative shifts of the spinodals of polymeric films. For large confinements, an increase of the stability of a film is seen. This agrees with what is found in polymer blends and mixtures of smaller molecules between two symmetrical surfaces by Monte Carlo techniques and mean and self-consistent field theories.