Adsorption of polymer chains at surfaces: Scaling and Monte Carlo analyses

Publisher Website
Google Scholar
Abstract
The influence of a hard wall on the configurations of long flexible polymer chains near the wall is studied, in the presence of a short‐range attractive force between monomers and the wall. Particular attention is paid to the region around the temperature Ta below which the polymer becomes adsorbed to the wall, i.e., where the typical polymer linear dimensions perpendicular to the wall become independent of chain length. Both ideal noninteracting chains and chains with excluded volume interactions are treated. Polymer linear dimensions parallel and perpendicular to the wall and their probability distributions are studied, as well as the behavior of the monomer fraction at the surface and a distance z in the interior. The relation of polymer statistics to the problem of correlation functions in the n‐vector model of magnetism in the limit n→0 is exploited to express both the exponents describing the various power laws and the crossover scaling functions near Ta in terms of results for the analogous problem of the critical behavior of magnets with a free surface. The predictions of this scaling theory are confirmed by Monte Carlo studies of self‐avoiding walks on the tetrahedral lattice with a free surface, and estimates for the exponents involved are presented. A new sampling technique with a bias in favor of adsorbed polymer configurations is developed.