Quantitative Interpretation of Simulated Polymer Mean-Square Displacements

TL;DR

This paper introduces a quantitative method for analyzing mean-square displacement curves of polymer chains, enabling precise identification of dynamic regimes and exponents without prior assumptions.

Contribution

It presents a general functional form approach that accurately describes $g(t)$ and its derivative across all times, improving analysis of polymer dynamics.

Findings

Accurately distinguishes between different dynamic regimes.

Precisely determines power-law exponents without assumptions.

Provides a unified framework for analyzing $g(t)$ curves.

Abstract

We propose a path for making quantitative analyses of mean-square displacement curves of polymer chains in the melt or in solution. The approach invokes a general functional form that accurately describes $g(t) \equiv \langle (\Delta x(t))^{2} \rangle$ for all times at which $g(t)$ was measured, and that gives values for the logarithmic derivative of $g(t)$ for the same times. By these means we can readily distinguish between regimes in which $g(t)$ follows a power law in time, does not follow a power law in time, or has an inflection point. In a power-law regime, the method accurately determines the exponent, without imposing any assumption as to the exponent's value.