Linear nonequilibrium thermodynamic theory of glass transition kinetics

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Abstract
A phenomenological nonequilibrium thermodynamic theory of the glass transition is presented in a linear approximation and applied to glass transition kinetics. A linear relationship between ordering parameters and affinities is diagonalized so that each new affinity is proportional to the nonequilibrium portion of a corresponding single ordering parameter. It is shown that fictive temperatures defined for each of these new parameters can themselves serve as ordering parameters, and that the experimental fictive temperatures represent averaged ordering parameter values. A further transformation is made to uncouple the equations of motion, obtaining exponentially relaxing ordering parameters and affinities. The nonequilibrium portions of the dependent thermodynamic variables take the form of convolutions between linear response functions and the time derivatives of the independent variables. It is shown for the first time that the coefficients of expansion of the response functions into exponetials are not independent, but that coefficients for the entire set of 24 functions characterizing S, T, V, and P, with different dependent–independent variable pair combinations, can be expressed in terms of the coefficients for two properly chosen response functions.