Polydisperse polymers near a solid surface: Analytical mean-field theory.

A linearized mean-field theory is presented, which provides algebraic expressions for the segment density profiles and surface tension of polydisperse polymers near a flat surface. The main finding is that surface properties of polydisperse polymers in solution are well-described by the average degree of polymerization N̄, independent of the shape or variance σ2 of the chain length distribution. Polymers with longer chain lengths are found to preferentially adsorb at the surface in the weak adsorption regime. Analytical expressions are derived for the adsorbed amount and surface tension. The results are in quantitative agreement with numerical self-consistent field computations, as long as the ratio σ2/N̄3 is small compared to the static structure factor of Gaussian chains. The analytical expressions are shown to be valid for polymer solutions and for polymer melts. For the case of polymer melts, we show that our theoretical predictions are in agreement with experimental results.