Effect of Diluents on Tg

The effect of adding a low-molecular-weight substance to a polymer is to lower its glass transition temperature. The effect is well known, and is exploited in practice to obtain flexible products of poly(vinyl chloride) by adding relatively nonvolatile diluents such as dibutyl phthalate or tricresyl phosphate as plasticizers to the polymer. 

Since the free volume of a low-molecular-weight liquid is very large compared to that of a polymer at the same temperature and pressure, the addition of even a small amount of diluent has a large effect on the total free volume in the polymer phase, which is reflected in a signiflcant drop in Tg. 

Empirically Tg of a polymer-diluent mixture could be expressed in terras of the glass transition temperature of the pure polymer 9V and that of the pure diluent Tgd by 

A relation between Tg and composition of a polymer-diluent mixture can be derived [47] in a relatively straightforward manner from the free-volume concept by postulating that the free volumes of the polymer and diluent are additive in the mixture, and that the free volume fraction has a critical value fg, which is the same for the pure polymer, the diluent and their mixtures at their respective glass temperatures. The composition of polymer-diluent mixtures is conveniently expressed in terms of the volume fractions of polymer cj)p and diluent (f d. 

According to the free-volume theory, as we have seen earlier, the free-volume fraction / in a polymer at a temperature T above Tg can be expressed in a linear form [cf. Eq. (2.33)]  

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