Relaxation kinetics of glasses and glass-forming melts

Abstract

Relaxation is a process of prime importance for the properties of amorphous solids. First we give a new approach describing quantitatively this process under isothermal conditions. It is shown that, in line with experimental evidence, the response function is not a simple exponential. Solving an appropriately defined non-linear differential equation describing the relaxation in terms of the variable x we obtain a modified response function in the form M(t)≡ 1− exp(−bx) 1− exp(−bx in ) = exp − t τ that decays exponentially with time t, where τ e is the equilibrium relaxation time. We find a quantitative dependence between the parameter b, from the above expression, and the thermodynamic `fragility' of the system. Thus it follows that the nature of relaxation, fragility, and rigidity of glasses are generically related manifestations of the same physical nature. The advantages and limitations of the stretched exponent relaxation function (often known as Kohlrausch–Williams–Watts (KWW) function) are reexamined. The present approach predicts a new form of the relaxation function to which the stretched exponent is only a suitable approximation. It is a usual procedure to extract from experimental data the parameter, τ K, controlling the kinetics of the process according to the KWW function. We demonstrate the relationship between τ K and the relaxation time, τ e, of a system close to equilibrium.