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 Θ 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.