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

Abstract

a b s t r a c tThe "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.

Study of carrier recombination transient characteristics in MOCVD grown GaN dependent on layer thickness

“…5) displayed on the logarithm time scale (ln(−ln(U(t)/U(0))) versus ln(t)). 34,35 A rather good linearity of the normalized MW-PC signals approximated by a stretch-exponent is obtained (Fig. 5(a)) over a wide range of running time (form ns to ms) within a transient.…”

“…A linearization of these residual MW-PC (after subtraction of the PL inherent component) transients is only possible using the stretched exponent approximation. 10,34,35 This approximation yields to a description of excess carrier density variations in time expressed as n ex (t) = n ex (t = 0)exp[−(t/τ se ) α ], where α is a fractional index which is associated with material disorder characteristics. 10,34,35 Fractional index is evaluated from a linear fit of the double logarithm of the normalized transients (Fig.…”

“…This slope correlated with α can be associated with the fractal index. 25,34,35 The approach of α to unity implies a reduction of the disorder of material. Thereby, the crystalline structure slightly straightens up with enlargement of the thickness of GaN epi-layer over 15 μm.…”

Ab initio study of Si doping effects in Pd–Ni–P bulk metallic glass

“…These changes in coordinations due to the shoving effect, can be responsible for the improved glass formation ability, as has been put forward by Phillips rigidity theory [32][33][34][35]11,12,[36][37][38].…”

Statistics of modifier distributions in mixed network glasses

“…This relaxation follows a stretched exponential decay, exp [−(t/τ ) β ], where τ is the relaxation time and β is the dimensionless stretching exponent given by Here, d* is the effective dimensionality of the relaxation channels. [81][82][83][84] Figure 7 shows the evolution of the modifier speciation during relaxation, considering a stretching exponent of β = 3/7, which arises from d* = 3/2 and is characteristic of structural relaxation in homogeneous glasses dominated by long-range relaxation pathways. [85][86][87][88][89] As the glass structure relaxes to a lower fictive temperature, the modifiers reconfigure to a correspondingly lower enthalpy state.…”