On the theoretical determination of the Prigogine-Defay ratio in glass transition.

In a recent analysis [J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511 (2006)] it was shown for the first time that--in contrast to earlier belief arising from the works of Prigogine and Defay [Chemical Thermodynamics (Longman, London, 1954), Chap. 19; The first French edition of this book was published in 1950] and Davies and Jones [Adv. Phys. 2, 370 (1953); and Proc. R. Soc. London, Ser. A 217, 26 (1953)]--a satisfactory theoretical interpretation of the experimentally observed values of the so-called Prigogine-Defay ratio Π, being a combination of jumps of thermodynamic coefficients at glass transition, can be given employing only one structural order parameter. According to this analysis, this ratio has to be, in full agreement with experimental findings, larger than one (Π > 1). Its particular value depends both on the thermodynamic properties of the system under consideration and on cooling and heating rates. Based on above-mentioned analysis, latter dependence on cooling rates has been studied in detail in another own preceding paper [T. V. Tropin, J. W. P. Schmelzer, and C. Schick, J. Non-Cryst. Solids 357, 1303 (2011)]. In the present analysis, an alternative general method of determination of the Prigogine-Defay ratio is outlined, allowing one to determine this ratio having at ones disposal the generalized equation of state of the glass-forming melts under consideration and, in particular, the knowledge of the equilibrium properties of the melts in the glass transformation range. Employing, as an illustration of the method, a particular model for the description of glass-forming melts, theoretical estimates are given for this ratio being, again, in good agreement with experimental data.