Selected aspects of recent progress in the study of supercooled liquids and glasses are presented in this review. As an introduction for nonspecialists, several basic features of the dynamics and thermodynamics of supercooled liquids and glasses are described. Among these are nonexponential relaxation functions, non-Arrhenius temperature dependences, and the Kauzmann temperature. Various theoretical models which attempt to explain these basic features are presented next. These models are conveniently categorized according to the temperature regimes deemed important by their authors. The major portion of this review is given to a summary of current experimental and computational research. The utility of mode coupling theory is addressed. Evidence is discussed for new relaxation mechanisms and new time and length scales in supercooled liquids. Relaxations in the glassy state and significance of the “boson peak” are also addressed.

Supercooled Liquids and Glasses

Jump relaxation in solid electrolytes

Perspective on the glass transition

Stretched exponential relaxation, , 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 is treated as an adjustable parameter, but in almost all cases it is generally assumed that no microscopic meaning can be assigned to even at , a glass transition temperature. We show that for molecular relaxation can be understood, providing that one separates extrinsic and intrinsic effects, and that the intrinsic effects are dominated by two magic numbers, for short-range forces, and 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 to s, as collected and analysed phenomenologically by Angell, Ngai, Bohmer and others. The electronic materials discussed include a-Si:H, granular , semiconductor nanocrystallites, charge density waves in , 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 is often accurate to 2%, which is often better than the quoted experimental accuracies . 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 in excellent agreement with the prediction of the microscopic theory.

https://iopscience.iop.org/article/10.1088/0034-4885/59/9/003/pdf

Stretched exponential relaxation in molecular and electronic glasses

Molecular Dynamics

Neutron spin-echo measurements have been performed on the ionic system ${\mathrm{Ca}}_{0.4}$${\mathrm{K}}_{0.6}$(${\mathrm{NO}}_{3}$${)}_{1.4}$ around the glass transition temperature ${\mathrm{T}}_{0}$, in order to determine the time dependence of the density correlation function ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{q}}$(t), which plays a central role in recent theories. Above ${\mathrm{T}}_{0}$ the results reveal that ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{q}}$(t) contains two distinct ``slow'' components, the slower of which (a) has a stretched exponential form exp[-(t/\ensuremath{\tau}${)}^{\mathrm{\ensuremath{\beta}}}$], (b) shows a slowing down as T approaches ${\mathrm{T}}_{0}$ which scales with the Stokes-Einstein diffusion constant, and (c) tends to become the nonergodic fraction of the structure factor at ${\mathrm{T}}_{0}$. .AE

Neutron spin echo study of dynamic correlations near the liquid-glass transition

A time-of-flight inelastic neutron scattering study of Ca0.4K0.6(NO3)1.4 of the temperature dependence of the dynamic structure factor revealed a clear frequency-independent signature of the glass transition at the conventional transition temperature Tg. Above Tg the data combined with our previous neutron spin echo results display two relaxation processes at well-separated frequencies. The faster process was now found to be consistent with a scaling behaviour corresponding to a critical-type slowing-down when approaching a certain temperature T0, as predicted by recent mode coupling theories. The variation of various properties consistently points to a critical temperature T0 of about 30 K above Tg = 333 K.

Observation of Scaling Behaviour of Dynamic Correlations near Liquid-Glass Transition

Neutron spin echo measurements have been performed on the mixed ionic system Ca0.4K0.6(NO3)1.4 around the glass transition temperature Tg in order to determine the time dependence of the density-density correlation function q(t). This quantity plays a central role in recent mode-coupling theories of the glass transition in schematic models. On the liquid side of the transition our results reveal that there are two distinct slow relaxation processes. The faster one is situated in the 10-13-10-12s time domain. The second one (a) shows a rapid slowing down on T approaching the transition, which scales with the Stokes-Einstein diffusion constant (b) has a stretched exponential form exp (-(t/τ)β] with β 0.6 and (c) tends to become the non-ergodic fraction of the structure factor at the transition. The amplitude ratio of the second and the first relaxation steps varies between 3 and 6 in a smooth oscillatory fashion over the studied wave-number range of q = 0.1-2.1 A-1. These findings are in qualitative agreement with theoretical predictions, but only if the theoretically relevant glass transition temperature T0 is assumed to lie considerably above the phenomenological glass temperature Tg. This implies that the theory breaks down at relaxation times longer than some 10-5s. In contrast, the q dependence of the characteristic time τ of the slower relaxation step revealed a fully unexpected feature, a strong maximum at q0/2, where q0 is the position of the first peak in the structure factor. We propose that this slowing down of the mass density fluctuations reflects the maximum of the charge density structure factor. This new phenomenon is expected to allow the study of the static charge density correlations directly in the q space via the induced dynamic effects.

https://iopscience.iop.org/article/10.1088/0031-8949/1987/T19B/007/pdf

Neutron Spin Echo Study of Dynamic Correlations Near Liquid-Glass Transition

Incoherent neutron scattering has been found to give evidence for glassy freezing of the proton motion in the ionic glass former Ca(NO3)2 · 4H2O. Surprisingly, we have found little difference in the proton dynamics between the liquid and the crystalline phases. We conjecture that a proton glass state might occur in the crystalline matrix.

W. Knaak

Papers

Neutron spin echo study of dynamic correlations near the liquid-glass transition

Observation of Scaling Behaviour of Dynamic Correlations near Liquid-Glass Transition

Neutron Spin Echo Study of Dynamic Correlations Near Liquid-Glass Transition

Glass transition and proton dynamics in Ca(NO3)2·4H2O: A neutron spin echo study