Thermodynamics of the glassy state with multiple order parameters

Abstract

Experimental data, both old and more recent, indicate the need for more than a single order parameter for adequate description of glassy materials. The thermodynamics of the glassy state with multiple order parameters, previously discussed by others, has been examined and developed further systematically. The result shows that the Prigogine-Defay ratio can be defined at every point on the (T,p) plane near the glass transition line and is generally greater than unity. One has to define a number of glass transition lines (Tg versus p), depending on which of the order parameters are assumed frozen-in at the glass transition. Even for a definition of the glass transition line operationally in terms of the relaxation time, one has to specify not only the time scale of the experiment but also the particular property observed and the mode by which the system is disturbed from equilibrium. A one-dimensional lattice gas model is utilized to obtain an expression for the Gibbs free energy as a function of T, p, and two order parameters, and this is then used to illustrate and test out the concepts and the thermodynamic relations derived here.