Thermodynamic properties of lattice polymers: Monte Carlo simulations and mean-field theories

Monte Carlo simulations of a lattice polymer melt are used to determine the thermodynamic properties of the system over a range of monomer volume fractions 0≤φ≤0.8 and effective temperatures 3.3≤T*≤∞. The simulations consider chains of length M=40 and M=100. The thermodynamic quantities analyzed are the chemical potential, the entropy, the specific heat, the isothermal compressibility, the internal energy, and the pressure. Canonical and grand canonical ensemble methods are employed as independent checks of the simulations for the chemical potential and the pressure. The predictions of Flory-Huggins (FH) theory, lattice cluster theory (LCT), and Guggenheim's random mixing and quasichemical approximations are compared with the simulations. The comparisons greatly extend prior demonstrations of very large errors in the simple FH approximation and show the major improvements provided by Guggenheim's approximations and the LCT.