Glasses can be formed by many routes. In some cases, distinct polyamorphic forms are found. The normal mode of glass formation is cooling of a viscous liquid. Liquid behavior during cooling is classified between "strong" and "fragile," and the three canonical characteristics of relaxing liquids are correlated through the fragility. Strong liquids become fragile liquids on compression. In some cases, such conversions occur during cooling by a weak first-order transition. This behavior can be related to the polymorphism in a glass state through a recent simple modification of the van der Waals model for tetrahedrally bonded liquids. The sudden loss of some liquid degrees of freedom through such first-order transitions is suggestive of the polyamorphic transition between native and denatured hydrated proteins, which can be interpreted as single-chain glass-forming polymers plasticized by water and cross-linked by hydrogen bonds. The onset of a sharp change in d dT( is the Debye-Waller factor and T is temperature) in proteins, which is controversially indentified with the glass transition in liquids, is shown to be general for glass formers and observable in computer simulations of strong and fragile ionic liquids, where it proves to be close to the experimental glass transition temperature. The latter may originate in strong anharmonicity in modes ("bosons"), which permits the system to access multiple minima of its configuration space. These modes, the Kauzmann temperature T(K), and the fragility of the liquid, may thus be connected.

https://science.sciencemag.org/content/sci/267/5206/1924.full.pdf

Formation of glasses from liquids and biopolymers.

Deviations from thermally activated and from exponential response are typical features of the vitrification phenomenon and previously have been studied using viscoelastic, dielectric, calorimetric, optical, and other techniques. Linear response data from literature on about 70 covalent glass formers, ionic melts, supercooled liquids, amorphous polymers, and glassy crystals are surveyed. Except for orientational glasses and monohydric aliphatic alcohols a distinct but broad correlation of non‐Debye behavior with non‐Arrhenius relaxations is found. Within the broad trend several groups of materials, distinguished by their respective molecular complexity, can be identified and are shown to exhibit narrow correlations. At a given degree of deviation from Arrhenius behavior externally imposed stresses are relaxed with a departure from exponential behavior which is stronger the more the molecular or atomic subunits of the glassforming material are interconnected with each other.

Nonexponential relaxations in strong and fragile glass formers

An overview of relaxational phenomenology is given in a manner intended to highlight a number of the important problems which, notwithstanding much recent sophisticated investigation, continue to confront the field. The rapidly lengthening timescale for diffusional and/or reorientational motion, which provokes the glass transition, is examined within the framework of the ‘strong’ and ‘fragile’ classification of both liquids and plastic crystals. The behavior patterns observed are related to the topological features of the potential energy hypersurfaces which may characterize each extreme. In view of the implication that the observed glass transition is the kinetically obscured reflection of an underlying higher order thermodynamic transition which could be associated with a diverging length scale (at least for fragile systems), the problem of the basic diffusional length scale at the glass transition, using a probe molecule approach, is considered. Then, details of the kinetics of relaxation under isothermal conditions are reviewed to decide on the range of deviations from Debye behavior which may be encountered. A correlation with fragility is strongly indicated. The phenomena of serial decoupling of relaxational modes from the main structural relaxation as T g is approached is outlined and, finally, the additional phenomena that may be encountered in experiments that explore the state-dependence (or non-linearity) of relaxation are briefly examined.

Relaxation in liquids, polymers and plastic crystals — strong/fragile patterns and problems☆

A theoretical perspective is provided on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations in studying and understanding the dynamics of systems close to the glass transition at the molecular level is given. The recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics is reviewed. The main theoretical approaches are presented describing the glass transition in supercooled liquids, focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheology of soft glassy materials are then discussed, and recent theoretical progress is described. For each section, an extensive overview is given of the most recent advances, but we also describe in some detail the important open problems that will occupy a central place in this field in the coming years.

Theoretical perspective on the glass transition and amorphous materials

The pronounced glass-forming tendencies of alloys of S and Se with Ge and/or As are discussed topologically. An atomic model is introduced which for predominantly covalent forces constitutes the first microscopic realization of Kauzmann's description of the glass transition as an entropy (not enthalpy or volume) crisis. The model contains no adjustable parameters and predicts the glass-forming tendency as a function of composition in excellent agreement with experiment. Several related properties, including phase diagrams, radial distribution functions and crystal structures are discussed in the context of chemical bonding and short-range order in the non-crystalline covalent networks of these materials.

Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys

An equation derived by Ritland relating the cooling rate and fictive temperature for glasses without memory is extended to those with memory, i.e. those which exhibit a spectrum of relaxation times. Provided that the spectrum of relaxation times is temperature-independent, the limiting fictive temperature, T′f, obtained when a glass is cooled through the transition region, is shown to be related to the cooling rate, q, by d In |q|/d(1/T'f)=-Δh★/R

where R is the ideal gas constant and Δh★ the activation enthalpy for the relaxation times controlling the structural relaxation. Values of T′f vs q obtained from enthalpy measurements by differential scanning calorimetry are presented for B2O3, 0.4Ca(NO3)2—0.6KNO3, and borosilicate crown glasses; Δh★ is equal, within experimental error, to the activation enthalpy for shear viscosity. Values of T′f from volume and enthalpy measurements obtained at the same cooling rate for the borosilicate crown glass are equal.

Dependence of the Fictive Temperature of Glass on Cooling Rate

When a liquid is subjected to a sudden change in temperature T or pressure P, its properties (volume V , enthalpy H , index of refraction n, shear viscosity v , etc.) exhibit an instantaneous, solidlike change. This is followed by a slower, liquidlike structural relaxation to new equilibrium values a t the new temperature or pressure. It is generally presumed that this structural relaxation involves some change of the average molecular configuration of the liquid. The time scale for the structural relaxation increases rapidly with decreasing temperature and increasing pressure and in the so-called glass transition region-which should be thought of as an area in the T-P plane-reaches magnitudes (seconds to days) readily perceptible to human investigators. Above the glass transition region, (i.e., a t temperatures above and pressures below) the structure rearranges promptly in response to changes in T o r P and measured properties ( H , V , n , etc.) are said to be those of the equilibrium liquid. Below the glass transition region (ix., a t temperatures below and pressures above), the structural rearrangement is kinetically arrested, measured changes in properties ( H , V , n, etc.) in response to changes in T and P d o not contain contributions from the structural rearrangement, and the material is referred to as a glass. As a consequence, there is in general a difference between the second derivatives of Gibbs free energy-namely, heat capacity Cp, the thermal expansion coefficient a, and isothermal compressibility, K-for equilibrium liquid and glass. In FIGURES 1 and 2 the time dependence of liquid properties due to the structural relaxation is shown schematically for the the isobaric response of enthalpy to temperature changes. In FIGURE 1 the system is initially a t equilibrium a t temperature To; the temperature is stepped at time t , by an amount A T . Immediately the system exhibits the solidlike enthalpy change AH, from the initial equilibrium value He, at To; this is followed by a further change with time by an amount A H , due to the structural relaxation to the equilibrium value H e , at the new temperature. The equilibrium liquid and glass heat capacities, C,, and Cpg, are then defined in terms of this experiment by

Structural relaxation in vitreous materials

A method was developed to determine the kinetic parameters controlling structural relaxation in the glass transition region from data acquired during continuous heating or cooling. The nonexponential character of the relaxation is accounted for by assuming an equilibrium isothermal relaxation function of the form exp [−(t/Toe)s], where Toe is a relaxation time and 0<β1. The data are linearized using the method of Narayanaswamy, and the continuous temperature variation during heating or cooling is dealt with by invoking the superposition principle. The analysis yields the kinetic parameters A, the relaxation-time preexponential term; Δh★, the relaxation-time activation enthalpy; x, a term describing the relative effects of temperature and structure on the rate of relaxation; and β. The method was applied to analysis of the variation of the enthalpy of vitreous B2O3 during rate heating through the transition region following rate cooling through the same region at a variety of rates.

Analysis of Structural Relaxation in Glass Using Rate Heating Data

Heat capacities of a series of mixed-alkali glasses of composition (in mol%) 24.4(Na2O + K2O)-75.6SiO2 were measured in the transition region by differential scanning calorimetry. The glass heat capacities at 700 K and the equilibrium liquid heat capacities are the same for all glasses on a per-g atom basis and equal, respectively, to 5.6 ± 0.1 and 6.8 ± 0.1 cal/g atom K. The glass transition temperatures exhibited negative deviations from additivity, but the heat capacity curves in the transition region of all the glasses for identical heating rates and thermal histories could be superimposed on the same reduced plot. This behavior indicates that the shapes of the structural relaxation functions are the same for all the glasses. These results support Shelby's conclusion that there is no unique “mixed-alkali effect” on thermodynamic or structural relaxation properties and that the term should be reserved for properties relating to ionic transport.

Heat Capacity and Structural Relaxation of Mixed‐Alkali Glasses

The evolution of enthalpy of As2Se3 glass during structural relaxation in the glass transition region was measured via differential scanning calorimetry for two types of time-temperature programs: rate-heating at 10 K/min following a cool at a constant rate (-20 to -0.31 K/min) and isothermal annealing following a temperature step from an equilibrium state. The rate-heating data yield kinetic parameters for the structural relaxation which predict accurately the evolution of the enthalpy during isothermal annealing. The glass heat capacities were independent of cooling rate within experimental precision (≤0.2%). In this respect, As2Se3 is unlike previously studied glasses whose heat capacities are more dependent on thermal history.

A. J. Easteal

Papers

Dependence of the Fictive Temperature of Glass on Cooling Rate

Structural relaxation in vitreous materials

Analysis of Structural Relaxation in Glass Using Rate Heating Data

Heat Capacity and Structural Relaxation of Mixed‐Alkali Glasses

Heat Capacity and Structural Relaxation of Enthalpy in As2Se3 Glass