Influence of the lattice site size in cell model theories on the prediction of thermodynamic properties of polymers and their mixtures

Abstract

Model calculations with the equation of state theories of Prigogine and Simha et al. were performed to investigate the influence of the lattice site size on the predicted thermodynamic properties. In these theories, as well as in some other equation of state theories, this quantity can be chosen arbitrarily, but it turns out that some properties of the theories depend appreciably on that choice. The theory of Simha et al. contains an equilibrium condition which serves to determine the fraction of occupied lattice sites. This condition contains the quantity 3 c/r, where 3 c is the number of degrees of freedom per chain, and r the number of segments per chain. It is common practice to set this quantity equal to unity, thus fixing the lattice site size. In the present work, it is also investigated how different choices for the lattice site size alter the description of pressure-volume-temperature (PVT) data of polymers. It turns out that for the theory of Simha et al., the reduction parameters of the polymers strongly depend on this choice, but the description of PVT behaviour and the prediction of free volume is almost independent of this choice. The prediction of phase behaviour of binary blends, however, can completely change when different choices for this quantity are made. It turns out that this change occurs in a way very similar to that of the Prigogine theory, in spite of the fact that the reduction parameters of the latter do not change. It seems that only the ratio of the lattice site volumes is important, not, however, their absolute size.