The confinement free energies of non-ideal branched polymers and ideal unbranched polymers are the same

TL;DR

This paper demonstrates that the confinement free energy and density profile of non-ideal branched polymers are equivalent to those of ideal unbranched polymers under the same conditions, due to a balance between branching-induced condensation and excluded volume swelling.

Contribution

It establishes a theoretical equivalence between non-ideal branched and ideal unbranched polymers in confined environments using dimensional reduction.

Findings

Confinement free energies are identical for both polymer types.

Density profiles match between branched and unbranched polymers.

Branching effects are offset by excluded volume interactions.

Abstract

We use the method of dimensional reduction to show that a branching polymer with excluded volume interaction confined between two flat plates has, in the thermodynamic limit, a confinement free energy and density profile that is the same as that of an ideal linear polymer with the same number of monomers and the same monomer-plate interaction potential. Condensation due to branching is exactly compensated by swelling due to excluded volume interaction.