Perimeter Length and Form Factor of Two-Dimensional Polymer Melts

TL;DR

This study uses molecular dynamics simulations to analyze the shape and perimeter fractality of two-dimensional polymer melts, revealing self-similar structures with specific fractal dimensions and distinctive scattering behaviors.

Contribution

The paper introduces a detailed analysis of perimeter length and form factor fractality in 2D polymer melts, highlighting their self-similar and fractal nature across scales.

Findings

Perimeter length scales as $L(N) \\sim R(N)^{5/4}$ with fractal dimension 5/4.

Chains exhibit self-similar structure down to a few monomers.

Form factor shows a non-monotonous behavior in the intermediate wavevector regime.

Abstract

Self-avoiding polymers in two-dimensional ($d=2$) melts are known to adopt compact configurations of typical size $R(N) \sim N^{1/d}$ with $N$ being the chain length. Using molecular dynamics simulations we show that the irregular shapes of these chains are characterized by a perimeter length $L(N) \sim R(N)^{\dpm}$ of fractal dimension $\dpm = d-\Theta_2 =5/4$ with $\Theta_2=3/4$ being a well-known contact exponent. Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all arc-lengths $s$ down to a few monomers. The Kratky representation of the intramolecular form factor $F(q)$ reveals a strong non-monotonous behavior with $q^2F(q) \sim 1/(qN^{1/d})^{\Theta_2}$ in the intermediate regime of the wavevector $q$. Measuring the scattering of labeled subchains %($s F(q) \sim L(s)$) the form factor may allow to test our predictions in real experiments.