Distance dependence of angular correlations in dense polymer solutions

TL;DR

This study examines how angular correlations between bonds in dense polymer solutions decay with distance, revealing a universal 1/r^3 decay in a specific range and introducing a new length scale related to chain length.

Contribution

It combines perturbation theory with Monte Carlo simulations to analyze bond-bond correlations, including effects of density, finite chain length, and different polymer distributions.

Findings

Bond-bond correlation function decays as 1/r^3 in a specific regime.

Introduces a new length scale r* ~ N^{1/3} related to chain length.

Density effects and finite chain corrections are discussed.

Abstract

Angular correlations in dense solutions and melts of flexible polymer chains are investigated with respect to the distance $r$ between the bonds by comparing quantitative predictions of perturbation calculations with numerical data obtained by Monte Carlo simulation of the bond-fluctuation model. We consider both monodisperse systems and grand-canonical (Flory-distributed) equilibrium polymers. Density effects are discussed as well as finite chain length corrections. The intrachain bond-bond correlation function $P(r)$ is shown to decay as $P(r) \sim 1/r^3$ for $\xi \ll r \ll \r^*$ with $\xi$ being the screening length of the density fluctuations and $r^* \sim N^{1/3}$ a novel length scale increasing slowly with (mean) chain length $N$.