A new formula for the entropy of mixing in polymer systems and free volume

Abstract

The famous equations of Flory-Huggins for the entropy of mixing with one highmolecular component are of great importance for polymer physics. But Gujrati stated in 1980 [12] that these equations cannot be exact. This is why we derived a new formula for the dependence of the entropy from the fraction of vacant sites in a quasi-lattice. It differs significantly from that of Huggins and still more from that of Flory in the case of low free volume. The equations of Flory-Huggins are correct with reference to low polymer content only.

If our formula for entropy is used instead of that of Huggins an important result of the theory of Gibbs-DiMarzio is called in question. The increase of thermal expansion at the glass transition cannot be explained by an increase of vacant sites. A growth of the number of unoccupied sites according to the thermodynamic equilibrium condition would bring about a far too great thermal expansion coefficient. From estimations of the energy of interaction between polymer molecules, which can be found in literature, it follows that the increase of entropy is far too small to enable the formation of vacant sites above the glass transition. It is unambiguously shown that the free volume, commonly regarded to be the decisive quantity with respect to glass transition, cannot consist of holes as considered in the quasi-lattice model and in many theoretical treatments.