Long Range Bond-Bond Correlations in Dense Polymer Solutions

TL;DR

This study reveals that in dense polymer solutions, bond-bond correlations decay as a power law with an exponent of 3/2, challenging previous exponential assumptions, and provides scaling insights across different densities.

Contribution

The paper demonstrates that bond-bond correlations in dense polymer solutions follow a power-law decay, supported by simulations and scaling arguments, contrasting with the exponential decay previously assumed.

Findings

Correlations decay as $s^{-3/2}$ in dense solutions.

Scaling of $C(s)$ depends on monomer density and blob size.

Simulation results align with theoretical scaling predictions.

Abstract

The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $\rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) \sim s^{-\omega}$ with $\omega=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) \approx g^{-\omega_0} (s/g)^{-\omega}$ with $\omega_0=2-2\nu=0.824$ ($\nu=0.588$ being Flory's exponent) is set by the number of monomers $g(\rho)$ contained in an excluded volume blob of size $\xi$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s \gg g$ caused by the connectivity of chains and the incompressibility of the melt. %