Dynamical Monte Carlo Study of Equilibrium Polymers : Static Properties

Abstract

We report results of extensive Dynamical Monte Carlo investigations on self-assembled Equilibrium Polymers (EP) without loops in good solvent. (This is thought to provide a good model of giant surfactant micelles.) Using a novel algorithm we are able to describe efficiently both static and dynamic properties of systems in which the mean chain length $\Lav$ is effectively comparable to that of laboratory experiments (up to 5000 monomers, even at high polymer densities). We sample up to scission energies of $E/k_BT=15$ over nearly three orders of magnitude in monomer density $ϕ$, and present a detailed crossover study ranging from swollen EP chains in the dilute regime up to dense molten systems. Confirming recent theoretical predictions, the mean-chain length is found to scale as $\Lav \propto ϕ^α\exp(δE)$ where the exponents approach $α_d=δ_d=1/(1+γ) \approx 0.46$ and $α_s = 1/2 [1+(γ-1)/(νd -1)] \approx 0.6, δ_s=1/2$ in the dilute and semidilute limits respectively. The chain length distribution is qualitatively well described in the dilute limit by the Schulz-Zimm distribution $\cN(s)\approx s^{γ-1} \exp(-s)$ where the scaling variable is $s=γL/\Lav$. The very large size of these simulations allows also an accurate determination of the self-avoiding walk susceptibility exponent $γ\approx 1.165 \pm 0.01$. ....... Finite-size effects are discussed in detail.