Polymer chains in confined geometries: Massive field theory approach

TL;DR

This paper uses a massive field theory approach to analyze how long polymer chains behave confined between different wall types, revealing that excluded volume interactions weaken depletion forces compared to ideal chains.

Contribution

It applies the massive field theory in three dimensions to study polymer depletion forces with various wall interactions, including a modified renormalization scheme for inert walls.

Findings

Depletion forces are weaker for chains with excluded volume interactions.

Results agree qualitatively with experiments and simulations.

Modified renormalization scheme is developed for inert walls.

Abstract

The massive field theory approach in fixed space dimensions $d=3$ is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls and for the mixed case of one inert and one repulsive wall. The well known correspondence between the field theoretical $\phi^4$ O(n)-vector model in the limit $n\to 0$ and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. Our investigations include modification of renormalization scheme for the case of two inert walls. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains, because the EVI effectively reduces the depletion effect near the walls. Our results are in qualitative agreement with previous theoretical investigations, experimental results and with results of Monte Carlo simulations.