Effect of architecture in the surface segregation of polymer blends

We examine the surface segregation behavior of binary polymer blends with architecturally asymmetric components. Particular attention is given to molten blends containing linear and branched polymers composed of the same type of monomer. If the branches are sufficiently long and the branch points (joints) dilute, we argue that the surface enrichment behavior has universal features that are independent of the chemical identity of monomers. We identify entropic and enthalpic contributions to the surface potentials acting on end, joint, and middle monomers of each species and show that these can be incorporated into a linear response formalism for the prediction of surface enrichment. Applications to linear-comb and linear-star mixtures are explicitly demonstrated, and scaling relations for the integrated surface enrichment and enrichment length scale are identified. We also identify a topological. enrichment mechanism for blends that contain loops, e.g. linear-ring mixtures. Surprisingly, a dilute amount of ring polymer added to a linear melt is found at a surface at precisely twice the bulk concentration, independent of ring length. This is argued to be a natural consequence of the reflecting boundary conditions that are imposed on polymer propagators for nearly incompressible melts at impenetrable surfaces.