Entropic segregation of short polymers to the surface of a polydisperse melt

Chain ends are known to have an entropic preference for the surface of a polymer melt, which in turn is expected to cause the short chains of a polydisperse melt to segregate to the surface. Here, we examine this entropic segregation for a bidisperse melt of short and long polymers, using self-consistent field theory (SCFT). The individual polymers are modeled by discrete monomers connected by freely-jointed bonds of statistical length a, and the field is adjusted so as to produce a specified surface profile of width xi. Semi-analytical expressions for the excess concentration of short polymers, delta phi(s)(z), the integrated excess, theta(s), and the entropic effect on the surface tension, gamma(en), are derived and tested against the numerical SCFT. The expressions exhibit universal dependences on the molecular-weight distribution with model-dependent coefficients. In general, the coefficients have to be evaluated numerically, but they can be approximated analytically once xi greater than or similar to a. We illustrate how this can be used to derive a simple expression for the interfacial tension between immiscible A- and B-type polydisperse homopolymers.