Universal amplitude in density-force relations for polymer chains in confined geometries: Massive field theory approach

TL;DR

This paper investigates the universal density-force relations for confined polymer chains using massive field theory, providing analytical results for various geometries and validating them with simulations.

Contribution

It introduces a massive field theory approach to derive universal amplitude ratios and density profiles for polymers in confined geometries, extending prior theoretical understanding.

Findings

Derived universal amplitude ratio $B_{real}$ in d=3

Calculated monomer density profiles for ideal and real polymers

Validated results with Monte Carlo simulations

Abstract

The universal density-force relation is analyzed and the correspondent universal amplitude ratio $B_{real}$ is obtained using the massive field theory approach in fixed space dimensions d=3 up to one-loop order. The layer monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall are obtained. Besides, taking into account the Derjaguin approximation the layer monomer density profiles for dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The last mentioned situation is analyzed for both cases when wall and particle are repulsive and for the mixed case of repulsive wall and inert particle. The obtained results are in good agreement with previous theoretical results and with the results of Monte Carlo simulations.