Critical unmixing of polymer solutions

Abstract

We present Monte Carlo simulations of semidilute solutions of long selfattracting 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 non-bonded nearest neighbors. Chain lengths are up to N = 2048, system sizes are up to 2 21 lattice sites and 2.8 × 10 5 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 most clear result is that chains at the critical point are Gaussian for large N , having end-to-end distances R ∼ √ N. Also the distance T Θ − T c (N ) (where T Θ = lim N →∞ T c (N )) scales with the mean field exponent, T Θ − T c (N ) ∼ 1/ √ N . The critical density seems to scale with a non-trivial 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.

Critical behavior of lattice polymers studied by Monte Carlo simulations

“…Both are in good agreement with previously reported values. 4,6 The high linearities in the figure confirm that x 3 ϭ0.5. Figure 4 shows a log-log plot of critical compositions as a function of chain length.…”

“…Experimental data 1 show that x 2 ϭ0.38Ϯ0.01. Recent simulation results [4][5][6] for reasonably long chains also give x 2 ϭ0.38Ϯ0.01; earlier simulation data gave much lower values for x 2 , but the chain lengths involved in those simulations were not long enough to be in the scaling regime. [7][8][9][10][11] Equation ͑3͒ describes the scaling behavior of the critical temperature as a function of chain length.…”

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

“…The precise nature of the trends for R E /σ ≫ 1 will be those for a long polymer in a poor solvent; see the simulation results of Refs. [2][3][4].…”

“…It is known that a Flory-Huggins free energy describes rather well the qualitative features of the phase separation of a long polymer and a poor solvent; see the comparison with computer simulation data in Refs. [2][3][4]. It is also known that purely entropic effects can result in the polymer effectively being in a poor solvent [5].…”

“…The phase separation of polymer and much smaller colloidal spheres will be qualitatively identical to that of a long polymer and a poor solvent. This phase separation has been extensively studied and is quite well understood [1][2][3][4]. The approximate theory we will develop is essentially a Flory-Huggins polymer-plus-solvent free energy with an effective solvent quality which depends on the concentration of the colloid.…”