Critical unmixing of polymer solutions

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Abstract
We present Monte Carlo simulations of semidilute solutions of long self-attracting chain polymers near their Ising type critical point. The polymers are modeled as monodisperse self-avoiding walks on the simple cubic lattice with attraction between nonbonded nearest neighbors. Chain lengths are up to N=2048, system sizes are up to 221 lattice sites and 2.8×105 monomers. These simulations used the recently introduced pruned-enriched Rosenbluth method, which proved extremely efficient, together with a histogram method for estimating finite size corrections. Our clearest result is that chains at the critical point are Gaussian for large N, having end-to-end distances R∼N. Also, the distance TΘ−Tc(N) [where TΘ=limN→∞Tc(N)] scales with the mean field exponent, TΘ−Tc(N)∼1/N. The critical density seems to scale with a nontrivial exponent similar to that observed in experiments. But we argue that this is due to large logarithmic corrections. These corrections are similar to the very large corrections to scaling seen in recent analyses of Θ polymers, and qualitatively predicted by the field theoretic renormalization group. The only serious deviation from this simple global picture concerns the N-dependence of the order parameter amplitudes, which disagrees with a minimalistic ansatz of de Gennes. But this might be due to problems with finite size scaling. We find that the finite size dependence of the density of states P(E,n) (where E is the total energy and n is the number of chains) is slightly but significantly different from that proposed recently by several authors.