Stretched exponential relaxation in molecular and electronic glasses

Stretched exponential relaxation, exp[-(t/tau)(beta)], fits many relaxation processes in disordered and quenched electronic and molecular systems, but it is widely believed that this function has no microscopic basis, especially in the case of molecular relaxation. For electronic relaxation the appearance of the stretched exponential is often described in the context of dispersive transport, where beta is treated as an adjustable parameter, but in almost all cases it is generally assumed that no microscopic meaning can be assigned to 0 < beta(T) < 1 even at T = T-g, a glass transition temperature. We show that for molecular relaxation beta(T-g) can be understood, providing that one separates extrinsic and intrinsic effects, and that the intrinsic effects are dominated by two magic numbers, beta(SR) = 3/5 for short-range forces, and beta(K) = 3/7 for long-range Coulomb forces, as originally observed by Kohlrausch for the decay of residual charge on a Leyden jar. Our mathematical model treats relaxation kinetics using The Lifshitz-Kac-Luttinger diffusion to traps depletion model in a configuration space of effective dimensionality, the latter being determined using axiomatic set theory and Phillips-Thorpe constraint theory. The experiments discussed include ns neutron scattering experiments, particularly those based on neutron spin echoes which measure S(Q, t) directly, and the traditional linear response measurements which span the range from mu s to s, as collected and analysed phenomenologically by Angell, Ngai, Bohmer and others. The electronic materials discussed include a-Si:H, granular C-60, semiconductor nanocrystallites, charge density waves in TaS3, spin glasses, and vortex glasses in high-temperature semiconductors. The molecular materials discussed include polymers, network glasses, electrolytes and alcohols, Van der Waals supercooled liquids and glasses, orientational glasses, water, fused salts, and heme proteins. In the intrinsic cases the theory of beta(T-g) is often accurate to 2%, which is often better than the quoted experimental accuracies similar to 5%. The extrinsic cases are identified by explicit structural signatures which are discussed at length. The discussion also includes recent molecular dynamical simulations for metallic glasses, spin glasses, quasicrystals and polymers which have achieved the intermediate relaxed Kohlrausch state and which have obtained values of beta in excellent agreement with the prediction of the microscopic theory.