In a previous study we modified a double lattice model by introducing a new interaction parameter, which improved the mathematical approximation defect, and gave a new expression for the Helmholtz energy of mixing. In the model the universal constants C-beta and C-gamma in the primary lattice were determined by comparing them with literature Monte Carlo simulation data, which is the only case for r(1) = 1 and r(2) = 100 (case I). In this study we introduce new universal constants, C-beta and C-gamma, as a function of the chain length of a polymer in a solvent (case II) by comparing them with other literature simulation data for various polymer chain lengths. The proposed model is compared with polymer-solvent systems. In an upper critical solution temperature phase behavior the theoretical results of case II were improved over those of case I. However, in a lower critical solution temperature phase behavior those of case I were not very sensitive to C-beta and C-gamma.