Surface segregation and surface tension of polydisperse polymer melts.

The effect of polydispersity on surface segregation of a lower molecular weight polymer component in a higher molecular weight linear polymer melt host is investigated theoretically. We show that the integrated surface excess zM of a polymer component of molecular weight M satisfies a simple relation zM=2Ue(M/Mw-1)phiM, where Mw is the weight averaged molecular weight, phiM is the polymer volume fraction, and Ue is the attraction of polymer chain ends to the surface. Ue is principally of entropic origin, but also reflects any energetic preference of chain ends to the surface. We further show that the surface tension gammaM of a polydisperse melt of high molar mass components depends on the number average degree of polymerization Mn as, gammaM=gammainfinity+2UerhobRT/Mn. The parameter gammainfinity is the asymptotic surface tension of an infinitely long polymer of the same chemistry, rhob is the bulk density of the polymer, R is the universal gas constant, and T is the temperature. The predicted gammaM compare favorably with surface tension values obtained from self-consistent field theory simulations that include equation of state effects, which account for changes in polymer density with molecular weight. We also compare the predicted surface tension with available experimental data.

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.

Surface enrichment of branched polymers in linear hosts: effect of asymmetry in intersegmental interactions and density gradients.

Variable density lattice treatment of surface enrichment of f-arm star-branched chains in star/linear polymer blends is compared with results of an analytical response theory proposed by Wu and Fredrickson [Macromolecules 29, 7919 (1996)]. We find that differences in treating the intersegmental interactions in the small interfacial region near a free surface lead to significant differences in the potentials by which polymer chain ends are attracted towards the surface. Consideration of an asymmetric relationship between segment potentials and density changes in polystyrene at 450 K and 0.1 MPa, for example, gives typically a threefold to fourfold enhancement in composition of star molecules at a vacuum interface. When contributions from gradients in density are included in the analysis even greater levels of surface enhancement (fivefold to sixfold increases) are observed. By appropriately estimating the attraction of chain ends and repulsion of branch points at a free surface, we show that concentration profiles of branched polymers predicted in the lattice model are consistent with results obtained in the analytical response theory.