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

Abstract

Abstract.: 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 ξ. Semi-analytical expressions for the excess concentration of short polymers, δϕs(z) , the integrated excess, θs , and the entropic effect on the surface tension, γen, 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 ξ≳ 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. Graphical abstract: [Figure not available: see fulltext.].