Segregation of chain ends to the surface of a polymer melt

Self-consistent field theory (SCFT) is used to examine the surface of an incompressible polymer melt of freely jointed chains, each consisting of N discrete monomers connected by bonds of an arbitrary potential. As a result of entropic considerations, the end monomers tend to accumulate in a narrow region next to the surface (on the monomer scale), which causes a slight depletion of ends further into the melt (on the molecular scale). Due to the reduced configurational entropy available to polymers in the vicinity of a surface, we find an entropic contribution to the surface tension that increases with the degree of polymerization, N. While many quantities are dependent on the precise bond potential connecting the monomers, the excess of ends at the surface in the limit of infinite N, the functional form of the long-range depletion of ends, and the N dependence of the surface tension turn out to be universal.