The calorimetric glass transition. A simple model

Abstract

The approximate discontinuity, ΔC, in the dynamic specific heat of glasses at the calorimetric glass-transition temperature. T_g, is calculated from first principles. The existence of a ‘glass transition’ is a result of the strong temperature dependence of the α-relaxation peaks, as argued by Goetze. The experimental frequency is related to the temperature sweep rate, dT/dt, and compared with the frequency of the α-peak, Ω_c, and a general self-consistent equation for T _σ is given. The proportionality of ω_c and the d.c. conductivity is a fundamental consequence of percolation theory, and is independent of the Coulomb interaction, as this proportionality is observed even in those glasses where interactions can be neglected. An analytical calculation of the jump, ΔC in the dynamic heat capacity in the so-called Fermi (electronic) glass is given and is by analogy extended to traditional glasses. Since the relaxation structure in supercooled liquids is identical to that of glasses, it is suggested that the important physical change between liquids and glasses occurs at higher temperatures than T_g, and is related to the onset in the applicability of percolation theories as opposed to effective medium theories.