Statistical thermodynamics predictions of the solubility parameter

The Simha and Somcynsky (S-S) lattice-hole theory has been shown to represent accurately the pressure-volume-temperature (PVT) surface of chain molecular melts and their mixtures. The characteristic scaling parameters, P*, T* and V*, extracted from equation of state (eos) measurements, are known for a large number of polymers. On this basis it is possible to compute the configurational internal energy density and thus the solubility parameter 6 as a function of temperature and pressure, delta = delta (T, P). In the first part of this paper it is shown that the theory leads to an energy approximately proportional to the first power of density, that is of the van der Waals type, as found for low molar mass fluids by Hildebrand. We continue with a computation of delta for a series of polymer melts at two levels of temperature, namely T = 25degreesC and T = T-g + 300 K. Next, the results are compared with those listed in reference publications, all at ambient pressure. The theoretical values extrapolated from the melt to 25 degreesC were systematically higher than those listed. However, good correlation is obtained with the high-temperature calculations for a large variety of polymers. Arguments for this low-high temperature correlation are presented in terms of corresponding levels of molecular mobility and packing in solution and in bulk. (C) 2004 Society of Chemical Industry.