Effect of chain stiffness on the entropic segregation of chain ends to the surface of a polymer melt

Abstract

Entropic segregation of chain ends to the surface of a monodisperse polymer melt and its effect on surface tension is examined using self-consistent field theory (SCFT). In order to assess the dependence on chain stiffness, the SCFT is solved for worm-like chains. Our focus is still on relatively flexible polymers, where the persistence length of the polymer, \ell_p, is comparable to the width of the surface profile, \xi, but still much smaller than the total contour length of the polymer, \ell_c. Even this small degree of rigidity causes a substantial increase in the level of segregation, relative to that of totally flexible Gaussian chains. Nevertheless, the long-range depletion that balances the surface excess still exhibits the same universal shape derived for Gaussian chains. Furthermore, the excess continues to reduce the surface tension by one unit of k_BT per chain end, which results in the usual N^{-1} reduction in surface tension observed by experiments. This enhanced segregation will also extend to polydisperse melts, causing the molecular-weight distribution at the surface to shift towards smaller N_n relative to the bulk. This provides a partial explanation for recent quantitive differences between experiments and SCFT calculations for flexible polymers.