We review the important general dynamic and thermodynamic properties of structural glass-forming substances and classify them into 12 different categories. Our understanding of glass-forming substances is incomplete until all these properties have been explained. The dynamic properties considered include those relating to the high frequency fast relaxation, the Johari–Goldstein β-relaxation, and the slow structural α-relaxation. Practically all the important relaxation and diffusion processes in the time region extending from 10−13 to 106 s have been discussed. We show from experimental data that the properties in different categories bear some relations to each other. Some issues that impede progress of our understanding of the behavior of glass-forming substances are accentuated by formulating them as questions. Answers to these questions by future experimental and theoretical investigations will improve our understanding. Specific suggestions for future research efforts that can provide some answers to these questions are also made. Within the same property in each category, by examining a large number of glass-formers, a pattern of variation is found which correlates with the departure of the structural relaxation of the glass-former from exponential decay or the quantity, (1−β), where β is the fractional exponent in the Kohlrausch expression, exp[−(t/τ)β]. These patterns, as well as their correlations with (1−β), suggest that the salient dynamic properties (or phenomenology) of glass-forming substances are all governed by the non-exponential nature of the structural relaxation, i.e., the quantity (1−β). Therefore, a theory or model capable of relating the structural relaxation time τ to (1−β) has the potential of explaining many of the salient dynamic properties of glass-forming substances.

Dynamic and thermodynamic properties of glass-forming substances

A general equation for the susceptibility of disordered systems is proposed. It is based on the experimental observation of power laws at frequencies far from the peak frequency of the imaginary part of the frequency dependent relaxation function, the susceptibility. The obtained general expression contains the equations of other proposed relaxation functions as special cases and, thus, it might be considered as a generalization of these. From this general equation we derive an equation specially adapted for the α relaxation in glass-forming materials. This equation contains only three fit parameters and it is thus very suitable for fitting real experimental data. It is shown that this equation is a good frequency domain representation of the time domain Kohlrausch–Williams–Watts stretched exponential. From the general equation we also derive a four-parameter “universal” equation that describes most types of responses and even inverted response data, i.e., response peaks more stretched on the low frequency side than on the (as is normal) high frequency side. The physical significance of the different parameters is qualitatively discussed and the proposed functions are shown to satisfactorily describe typical experimental data.

General susceptibility functions for relaxations in disordered systems

Some secondary or β relaxations in glass-forming materials involve molecular motions that bear strong resemblance to the primitive α relaxations of the coupling model, although the two are not identical. For these β relaxations, at the glass transition temperature Tg the relaxation time τβ(Tg) is expected to be shorter than but not too different in order of magnitude from τ0(Tg), the primitive α-relaxation time at Tg. The latter can be calculated by the coupling model from the relaxation time τα(Tg), the exponent (1−n) of the Kohlrausch–Williams–Watts (KWW) correlation function exp[−(t/τα)1−n], and the experimental crossover time, tc≈2 ps, of the α relaxation. From experimental data of β and α relaxations in a variety of glass-forming materials, it is found that τβ(Tg) and τ0(Tg) are close to each other in order of magnitude as anticipated. The results indicate these β relaxations indeed bear some close relation to the corresponding primitive α relaxation, although they are not the same process. Since the...

Relation between some secondary relaxations and the α relaxations in glass-forming materials according to the coupling model

Dynamic heterogeneity is an active field of glass-transition research. The length scale of this heterogeneity is called the characteristic length. It can be calculated from complex heat capacity curves in the equilibrium liquid or from dynamic calorimetry curves corrected with regard to nonequilibrium. No molecular parameters or microscopic models are necessary for obtaining the length. We report the characteristic length near glass temperature for about 30 glass formers including small-molecule liquids, polymers, silicate glasses, a metallic glass, a liquid crystal, and a plastic crystal. The lengths are between 1.0 and 3.5 nm with certain cumulations between 1.0 and 2.0 nm and between 2.5 and 3.5 nm. To try a correlation to other properties, we find that at least two should be included, e.g., Angell's fragility and the distance of Tg from the crossover temperature, Tc.

Characteristic Length of Dynamic Glass Transition near Tg for a Wide Assortment of Glass-Forming Substances

Here we propose a simple physical model that may universally describe glass-transition phenomena from the strong to the fragile limit. Our model is based on the idea that there always exist two competing orderings in any liquids, (i) density ordering leading to crystallization and (ii) bond ordering favoring a local symmetry that is usually not consistent with the crystallographic symmetry. The former tries to maximize local density, while the latter tries to maximize the quality of bonds with neighboring molecules. For the phenomenological description of these competing ordering effects [(i) and (ii)] hidden in many-body interactions, we introduce density and bond order parameters, respectively. This leads to the following picture of a liquid structure: Locally favored structures with finite, but long lifetimes are randomly distributed in a sea of normal-liquid structures. Even simple liquids suffer from random disorder effects of thermodynamic origin. We argue that locally favored structures act as impu...

Two-order-parameter description of liquids. I. A general model of glass transition covering its strong to fragile limit

Neutron time-of-flight data of polybutadiene and polyisoprene in a wide temperature range around the glass transition are reported. The anharmonic part of the spectra is evaluated using a recently developed time domain Fourier transform technique. The results corroborate the recent finding of two different time domains in the dynamics, one above a crossover time of about 2 ps and the other below it. Two different interpretations of the short time behavior are considered, namely a fast Debye regime of the \ensuremath{\alpha} relaxation and a vibrational softening of the boson peak.

R. Zorn

Papers

Neutron scattering study of the picosecond dynamics of polybutadiene and polyisoprene.