Microscopic aspects of Stretched Exponential Relaxation (SER) in homogeneous molecular and network glasses and polymers

The “diffusion to traps” model quantitatively explains “magic” stretching fractions β(Tg) for a wide variety of relaxation experiments (nearly 50 altogether) on microscopically homogeneous electronic and molecular glasses and deeply supercooled liquids by assuming that quasi-particle excitations indexed by Breit–Wigner channels diffuse to randomly distributed sinks. Here the theme of earlier reviews, based on the observation that in the presence of short-range forces only d* = d = 3 is the actual spatial dimensionality, while for mixed short- and long-range forces, d* = fd = d/2, is applied to four new spectacular examples, where it turns out that SER is useful not only for purposes of quality control, but also for defining what is meant by a glass in novel contexts. The examples are three relaxation experiments that used different probes on different materials: luminescence in isoelectronic crystalline Zn(Se,Te) alloys, fibrous relaxation in orthoterphenyl (OTP) and related glasses and supercooled melts up to 1.15T g, and relaxation of binary chalcogen melts probed by spin-polarized neutrons (T as high as 1.5T g). The model also explains quantitatively the appearance of SER in a fourth “sociological” example, distributions of 600 million 20th century natural science citations, and the remarkable appearance of the same “magic” values of β = 3/5 and 3/7 seen in glasses. ► Glassy stretched exponential relaxation is the oldest unsolved problem in science. ► The curated data base bifurcates into two “magic” exponents β 1 = 3/5 and β 2 = 3/7. ► Diffusion to traps derives β 1 from short hops, β 2 from mixed short/long hops. ► Elastic relaxation can be used for quality control. ► 600 million 20th century citations bifurcated into β 1 = 3/5, 3/7 ( 1960).