Eur. Phys. J. E (2017) 40: 85
https://doi.org/10.1140/epje/i2017-11575-7

Regular Article

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

¹ Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada
² Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario, Canada
³ Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario, Canada

^* e-mail: mwmatsen@uwaterloo.ca

Received: 3 August 2017
Accepted: 19 September 2017
Published online: 6 October 2017

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 . Semi-analytical expressions for the excess concentration of short polymers, , the integrated excess, , and the entropic effect on the surface tension, , 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 . We illustrate how this can be used to derive a simple expression for the interfacial tension between immiscible A- and B-type polydisperse homopolymers.