Application of a new structural theory to polymers. ii. transition states for amorphous polymers and copolymers

A recently developed nonequilibrium thermodynamic theory of continuum rheology is combined with a generalized definition of thermomechanical transitions, to produce a single equation for interrelating the basic variables (stress o, strain rate ε, pressure p, temperature T, and structure ?) at a transition. Specialization of ? to represent uncrosslinked polymers leads to incorporation of molecular weight M as a variable. New predictions are thus made for the glass transition T_g(M), T_g(p), T_g(ε) and others] and compared successfully with data. Particularly remarkable are the results that 1/T_g is a piecewise linear function of In M, and T is piecewise linear with p. Comparable results and confirmation with data arise when applying the theory to the liquid-liquid transition, T _ll (M). For random copolymers, application of a single mixing rule to the transition equation leads to a prediction of T_g as a function of composition and the T_gi for the homopolymers (components i). This relationship reduces, in various cases, to several familiar equations in which the parameters were simply empirical, thus providing an interpretation of those parameters and defining restrictions applicable to each case. Finally, an alternative interpretation of ? in terms of free volume allows the theory to be extended to other systems, including those with small molecules.