Glass temperature depression of polymer by use of mixed solvents: A colligative property

The entropy theory of glasses is used to determine the glass temperature depression by a multicomponent low molecular weight plasticizer (diluent). The glass temperature, Tg, is calculated as a function of pressure, P, the mole fractions, mi, of the plasticizers, and the degree of polymerization p. One finds, provided there is no phase separation, that to a good approximation, the initial glass temperature depression is a function of the total mole fraction of plasticizer. Moreover, the glass temperature depression for small plasticizer molecules is found to be nearly a universal function of the plasticizer mole fraction (it depends on no other plasticizer variable), and to vary inversely as the number of flexible bonds per monomer unit of the polymer. A useful approximation is found, ?dTg/dm1 = -3Tg, where m1 is the total mole fraction of diluent on a per monomer of polymer basis, and ? is the number of flexible bonds per monomer. Although these results agree with experimental data in the literature, a more definitive experimental test is needed