STRETCHED EXPONENTIAL RELAXATION IN MOLECULAR AND ELECTRONIC GLASSES

Stretched exponential relaxation, exp[-(t/tau)(beta)], fits many relax ation processes in disordered and quenched electronic and molecular sy stems, 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 descr ibed in the context of dispersive transport, where beta is treated as an adjustable parameter, but in almost all cases it is generally assum ed 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 molecula r relaxation beta(T-g) can be understood, providing that one separates extrinsic and intrinsic effects, and that the intrinsic effects are d ominated by two magic numbers, beta(SR) = 3/5 for short-range forces, and beta(K) = 3/7 for long-range Coulomb forces, as originally observe d by Kohlrausch for the decay of residual charge on a Leyden jar. Our mathematical model treats relaxation kinetics using The Lifshitz-Kac-L uttinger diffusion to traps depletion model in a configuration space o f effective dimensionality, the latter being determined using axiomati c set theory and Phillips-Thorpe constraint theory. The experiments di scussed include ns neutron scattering experiments, particularly those based on neutron spin echoes which measure S(Q, t) directly, and the t raditional linear response measurements which span the range from mu s to s, as collected and analysed phenomenologically by Angell, Ngai, B ohmer and others. The electronic materials discussed include a-Si:H, g ranular C-60, semiconductor nanocrystallites, charge density waves in TaS3, spin glasses, and vortex glasses in high-temperature semiconduct ors. The molecular materials discussed include polymers, network glass es, electrolytes and alcohols, Van der Waals supercooled liquids and g lasses, 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 simila r to 5%. The extrinsic cases are identified by explicit structural sig natures which are discussed at length. The discussion also includes re cent molecular dynamical simulations for metallic glasses, spin glasse s, quasicrystals and polymers which have achieved the intermediate rel axed Kohlrausch state and which have obtained values of beta in excell ent agreement with the prediction of the microscopic theory.