Phase equilibria of lattice polymers from histogram reweighting Monte Carlo simulations

Histogram reweighting Monte Carlo simulations were used to obtain polymer/solvent phase diagrams for lattice homopolymers of chain lengths up to r = 1000 monomers. The simulation technique was based on performing a series of grand canonical Monte Carlo calculations for a small number of state points and combining the results to obtain the phase behavior of a system over a range of temperatures and densities. Critical parameters were determined from mixed-field finite-size scaling concepts by matching the order parameter distribution near the critical point to the distribution for the three-dimensional Ising universality class. Calculations for the simple cubic lattice (coordination number z = 6) and for a high coordination number version of the same lattice (z = 26) were performed for chain lengths significantly longer than those in previous simulation studies. The critical temperature was found to scale with a chain length following the Flory-Huggins functional form. For the z = 6 lattice, the extrapolated infinite chain length critical temperature is 3.71 +/- 0.01, in excellent agreement with previous calculations of the temperature at which the osmotic second virial coefficient is zero and the mean end-to-end distance proportional to the number of bonds. This confirms that the three alternative definitions of the Theta temperature are equivalent in the limit of long chains. The critical volume fraction scales with a chain length with an exponent equal to 0.38 +/- 0.01, in agreement with experimental data but in disagreement with polymer solution theories. The width of the coexistence curve prefactor was tentatively found to scale with a chain length with an exponent of 0.20 +/- 0.03 for z = 6 and 0.22 +/- 0.03 for z = 26. These values are near the lower range of values obtained from experimental data.