Note: Scale-free center-of-mass displacement correlations in polymer films without topological constraints and momentum conservation

TL;DR

This study uses computational simulations to reveal scale-free, long-range correlations in the center-of-mass displacements of polymer chains in thin films, showing a negative algebraic decay and logarithmic corrections.

Contribution

It demonstrates the existence of scale-free correlated forces in polymer films without topological constraints, extending understanding of polymer dynamics in confined geometries.

Findings

Negative algebraic decay of correlation function C_N(t) as -1/(Nt)

Logarithmic correction to mean square displacement h_N(t)

Scale-free colored forces influence polymer chain dynamics

Abstract

We present here computational work on the center-of-mass displacements in thin polymer films of finite width without topological constraints and without momentum conservation obtained using a well-known lattice Monte Carlo algorithm with chain lengths ranging up to N=8192. Computing directly the center-of-mass displacement correlation function C_N(t) allows to make manifest the existence of scale-free colored forces acting on a reference chain. As suggested by the scaling arguments put forward in a recent work on three-dimensional melts, we obtain a negative algebraic decay C_N(t) \sim -1/(Nt) for times t << T_N with T_N being the chain relaxation time. This implies a logarithmic correction to the related center-of-mass mean square-displacement h_N(t) as has been checked directly.