Dynamical Monte Carlo study of equilibrium polymers: Static properties

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 〈L〉 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/kBT=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 〈L〉∝φαexp(δE) where the exponents approach αd=δd=1/(1+γ)≈0.46 and αs=1/2[1+(γ−1)/(νd−1)]≈0.6,δs=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 p(s)≈sγ−1 exp(−s) where the scaling variable is s=γL/〈L〉. The very large size of these simulations allows also an accurate determination of the self-avoiding walk susceptibility exponent γ≈1.165±0.01. As chains overlap they enter the semidilute regime where the distribution becomes a pure exponential p(s)=exp(−s) with the scaling variable now s=L/〈L〉. In addition to the above results we measure the specific heat per monomer cv. We show that the average size of the micelles, as measured by the end-to-end distance and the radius of gyration, follows a crossover scaling that is, within numerical accuracy, identical to that of conventional monodisperse quenched polymers. Finite-size effects are discussed in detail.