Scale-free center-of-mass displacement correlations in dense polymer solutions and melts without topological constraints and momentum conservation: A bond-fluctuation model study

TL;DR

This study uses Monte Carlo simulations to analyze the center-of-mass displacement correlations in dense polymer solutions and melts, revealing universal algebraic decay behaviors driven by chain connectivity and melt incompressibility.

Contribution

It demonstrates a universal form of the COM displacement correlation function in dense polymer melts without topological constraints, highlighting the role of chain connectivity and incompressibility.

Findings

COM displacement correlation decays as t^{-5/4} for short times

Universal function f(x) describes the correlation decay across different chain lengths

Correlated chain and subchain motion arise from connectivity and incompressibility

Abstract

By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints we examine the center-of-mass (COM) dynamics of polymer melts in $d=3$ dimensions. Our analysis focuses on the COM displacement correlation function $\CN(t) \approx \partial_t^2 \MSDcmN(t)/2$, measuring the curvature of the COM mean-square displacement $\MSDcmN(t)$. We demonstrate that $\CN(t) \approx -(\RN/\TN)^2 (\rhostar/\rho) \ f(x=t/\TN)$ with $N$ being the chain length ($16 \le N \le 8192$), $\RN\sim N^{1/2}$ the typical chain size, $\TN\sim N^2$ the longest chain relaxation time, $\rho$ the monomer density, $\rhostar \approx N/\RN^d$ the self-density and $f(x)$ a universal function decaying asymptotically as $f(x) \sim x^{-\omega}$ with $\omega = (d+2) \times \alpha$ where $\alpha = 1/4$ for $x \ll 1$ and $\alpha = 1/2$ for $x \gg 1$. We argue that the algebraic decay $N \CN(t) \sim - t^{-5/4}$ for $t \ll \TN$ results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.