Molecular thermodynamic theory for polymer systems .1. A close-packed lattice model

A molecular thermodynamic theory for multicomponent polymer solutions and polymer blends is presented which is composed of two contributions: an equation of state and a close-packed lattice model served as a high-pressure limit. In this paper, we introduce a close-packed lattice model which is derived by using an effective chain-insertion probability for the entropy and a series expansion for the energy. The former is used to improve the mean-field Flory-Huggins entropy term. While the latter is adopted to account for interactions between more than two segments. For practical application, a double-lattice model is introduced to account for the specific oriented interactions which automatically gives a temperature dependence for the energy parameter. The coefficients in the model are determined by a few computer-simulation data and by referring to the rigorous Freed's theory. The agreement with computer-simulation results for spinodals and binodals is shown to be excellent, much better than the classical Flory-Huggins theory. Comparisons with calculated binodals and critical coordinates by the Freed's theory for binaries and ternaries coverd a wide range of chain length indicate that the two theories give almost the same results while the present work is much simpler and suitable for engineering use. Illustrative examples are presented for liquid-liquid equilibria of polymer solutions and polymer blends.