Surface migration of branched molecules: analysis of energetic and entropic factors

We have introduced energetic factors into the response theory developed by Wu and Fredrickson [Macromolecules 29, 7919 (1996)] to predict the enrichment of branched molecules due to architectural effects at surfaces. This development simultaneously increases the utility of the theory for guiding experimental investigations, and makes possible a rigorous assessment of theoretical predictions in careful studies of isotopically labeled linear/branched species binary blends at surfaces. For example, the introduction of energetic factors allows us to predict the existence of a crossover molecular weight, below which an energetically unfavorable species at a surface can be enriched entirely due to architecture. For binary blends of linear chains, the degree of polymerization (Kuhn) of the energetically unfavorable species at the crossover point is r(c) approximately =2U(e)/DeltaU(s). Here, U(e) is the attraction of chain ends towards the surface and DeltaU(s) is the difference in the interaction potential of main chain segments to the surface due to chemical differences and/or isotopic labeling. We also show that surface segregation of an additive in a host polymer due to architectural effects alone is significantly enhanced as the spinodal temperature of a branched/linear blend is approached. Detailed comparisons of the modified response theory with lattice simulations are used to evaluate the theory and to determine the limits of its applicability.