Scaling law of the disjoining pressure reveals two dimensional structure of polymeric fluids

TL;DR

This paper introduces a new scaling relation for the disjoining pressure in confined polymer fluids, enabling determination of the polymer's radius of gyration exponent through simulations and suggesting experimental validation methods.

Contribution

It proposes the first scaling relation for disjoining pressure that directly yields the polymer's radius of gyration exponent, validated by computer simulations under theta solvent conditions.

Findings

The scaling exponent nu matches the expected 4/7 for 2D chains.

The scaling relation accurately predicts nu from confined polymer simulations.

Proposes experimental methods to test the scaling law.

Abstract

A scaling relation for the disjoining pressure of strongly confined polymer fluids is proposed for the first time, which yields directly the scaling exponent, nu, of the radius of gyration for polymers. To test the proposed scaling relation we performed extensive particle based, coarse grained computer simulations of polymers confined under theta solvent conditions and found that the value of nu agrees with the expected value for strictly two dimensional chains, nu = 4/7, which points towards the essential correctness of our scaling relation. New approaches are suggested for experimental tests of this scaling law. This work opens up the way to look for other scaling exponents that may reveal new physical regimes and it constitutes an efficient route to determine nu because the scaling exponent can be obtained with chains of a single polymerization degree by simply reducing the distance between the confining plates.