Computational confirmation of scaling predictions for equilibrium polymers

TL;DR

This study uses extensive simulations to confirm theoretical predictions about how the mean chain length of equilibrium polymers scales with concentration and energy, revealing detailed size distributions and critical exponents.

Contribution

The paper provides the first large-scale simulation validation of scaling laws for equilibrium polymers, including size distributions and critical exponents, in dilute and semi-dilute regimes.

Findings

Mean-chain length scales as predicted by theory with specific exponents.

Size distributions transition from exponential to Schultz-Zimm type.

Accurate measurement of the self-avoiding walk susceptibility exponent b3 = 1.165 b1 0.01.

Abstract

We report the results of extensive Dynamic Monte Carlo simulations of systems of self-assembled Equilibrium Polymers without rings in good solvent. Confirming recent theoretical predictions, the mean-chain length is found to scale as $\Lav = \Lstar (\phi/\phistar)^\alpha \propto \phi^\alpha \exp(\delta E)$ with exponents $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$ and $\alpha_s = [1+(\gamma-1)/(\nu d -1)]/2 \approx 0.60, \delta_s=1/2$ in the dilute and semi-dilute limits respectively. The average size of the micelles, as measured by the end-to-end distance and the radius of gyration, follows a very similar crossover scaling to that of conventional quenched polymer chains. In the semi-dilute regime, the chain size distribution is found to be exponential, crossing over to a Schultz-Zimm type distribution in the dilute limit. The very large size of our simulations (which involve mean chain lengths up to 5000, even at high polymer densities) allows also an accurate determination of the self-avoiding walk susceptibility exponent $\gamma = 1.165 \pm 0.01$.