A New Activity Model for Polymer Solutions in the Frame of Lattice Theory

A simplified activity model for polymer solutions is derived from the Gibbs-Helmholtz relation, in conjunction with the lattice theory in this work. The model includes not only combinatorial and residual terms but also a free-volume (FV) term. The calculated results differ significantly between the model equations with and without taking the FV effect into consideration. The validity of this new method is demonstrated by comparing the calculated activities from the proposed model equation with those by the Entropic-FV (EFV), UNIFACFV, and UNIFAC methods. The overall average absolute deviation (AAD) of solvent activities in 34 polymer solutions was 7.58% for the EFV method, 5.32% for the UNIFAC-FV method, 22.00% for the UNIFAC method, and 3.48% for the proposed model. It is shown that the new model can yield improved results over the other models and is able to predict the phase behavior for polymer solutions over a wide range of molecular weights, temperatures, and densities.