Influence of molecular weight and degree of crosslinking on the specific volume and glass temperature of polymers

Abstract

On the basis of simple assumptions, equations are derived for predicting the specific volume‐temperature‐molecular weight (v‐T‐M) relationships for a homologous series of polymers from the v‐T curves for the monomer and the polymer of infinite molecular weight. Analogous v‐T‐ρ relationships (where ρ is the degree of crosslinking) are similarly obtained. The result, that v decreases linearly with decreasing 1/M and with increasing ρ, conforms with the picture that either the removal of two chain ends (as M increases) or the introduction of a crosslinkage involves, between two polymer segments, the exchange of a van der Waals bond for a shorter covalent bond. The validity of these equations is illustrated by comparison with the observed data for polymers covering a wide range in M, T, and chemical type. For several polymer series the extrapolated value of v at 0°K (v0) is the same for all members of the series, indicating that at this temperature the average length of the van der Waals and covalent bonds between polymer segments are the same. Assuming that the form of the linear relationship observed for polystyrene between the specific volume (vg) at the glass temperature and the value (Tg) of the latter is valid for other polymer series, equations are derived which predict Tg as a function of M from the limiting value of the glass temperature for a chain of infinite length, and from the v‐T curves in the liquid state for the monomer and for the polymer of M = ∞. Analogous Tg‐ρ relationships are similarly obtained. According to these equations, a linear relationship between 1/Tg and 1/M should be obtained, which reduces at high M to a linear dependence of Tg on 1/M. Similarly, a linear dependence of Tg on ρ is predicted at low ρ. These predictions are in satisfactory agreement with data on polystyrene fractions and on crosslinked copolymers of styrene with divinylbenzene. The conclusion that Tg for polystyrenes represent a state of iso‐free volume irrespective of M is shown to be an approximation that is valid, within experimental error, only for large values of M.