Free Energy of Multiple Overlapping Chains

TL;DR

This paper investigates the limitations of pair additivity in modeling the free energy of overlapping polymer chains, revealing its inadequacy at high densities and proposing a refined scaling theory to better describe the system.

Contribution

It introduces a quantitative analysis of free energy costs for multiple overlapping chains and develops a revised scaling theory accounting for complex interactions and a star-polymer crossover.

Findings

Pair additivity becomes inadequate at high chain densities.

A new scaling theory better captures the free energy of overlapping chains.

Identification of an isotropic to star-polymer crossover at large chain numbers.

Abstract

How accurate is pair additivity in describing interactions between soft polymer-based nanoparticles? Using numerical simulations we compute the free energy cost required to overlap multiple chains in the same region of space, and provide a quantitative measure of the effectiveness of pair additivity as a function of chain number and length. Our data suggest that pair additivity can indeed become quite inadequate as the chain density in the overlapping region increases. We also show that even a scaling theory based on polymer confinement can only partially account for the complexity of the problem. In fact, we unveil and characterize an isotropic to star-polymer cross-over taking place for large number of chains, and propose a revised scaling theory that better captures the physics of the problem.