Jacques Rault 
Physical Aging of Glasses [PDF ebook] 
The VFT Approach

Metallic, organic and mineral glasses evolve similarly with the time and approach an equilibrium state. This physical aging, a basic feature of the glassy state, is very important for a practical point of view. The aging time and the conditions of glass preparation are important parameters, as temperature, stress and strain levels, which affect the mechanical properties at short and long times. The kinetics of physical aging, volume, enthalpy and mechanical properties (modulus, yield stress, creep, stress relaxation), are explained in the framework of the modified Vogel-Fulcher-Tamann (VFT) law giving the relaxation time. The model is based on the dependence of the cooperativity index (Kohlrausch exponent) n of the cooperative motions (alpha motions in polymers) on the volume. Below the glass temperature the relaxation time is function of T and of the volume. In the glass state the relaxation time depend on the time of measurement and on the aging time. The relaxation equations are given and solved numerically in various experimental conditions a) isothermal and non isothermal aging at constant pressure, b) varying pressure at constant temperature. The so called Tg transitions observed by dilatomery and calorimetry are predicted by the VFT relaxation equations and compared to the Deborah glass temperatures. The non exponential and non linear relaxations of the volume of glassy polymers, found by Struik, Kovacs, etc.., depend on the viscoelastic parameters of the liquid (C1 and C2) and on the expansion coefficients of the liquid and solid phases, there is no adjustable parameter. The calculated solutions of the relaxation equations are compared to the KWW functions (stretched and compressed exponentials), the stabilization domain of glasses is defined and compared to the experimental results. The glass formers materials present the well-known volume, enthalpy and creep memory effects (Struik), the amplitude and the memory time of these effects are given as function of the thermal history of the glass. The evolution of the mechanical properties of glassy polymers are dependent on the aging time and on the stress and strain level, the individual beta motions (and then the cooperative motions) been activated by the shear component of the stress tensor. The similar non linear evolution of volume and creep is thoroughly analyzed in this model, the modified VFT law explains the dependences of the yield stress, creep compliance and stress relaxation modulus with aging time, temperature and stress or strain rate. The mechanical properties can be described also by the ansatz KWW function; the relaxation time and the Kohlrausch exponent deduced from that function is found to vary inversely with the different parameters this is a direct consequence of the modified VFT law. It is shown that the long term creep behavior can be predicted by the model.