A Model of Structural Relaxation in Glass

Abstract

Study of the time dependence of physical properties in the transformation range of glass is complicated by the "memory effect" and the inherent nonlinearity which are characteristic of structural relaxation. A multiparameter model of structural relaxation is presented that differs from earlier models in that it takes account of both these effects. This model fits available experimental data well; these data were obtained for the most part by observing the evolution of properties (such as density or refractive index) following a step change in temperature. The present model also permits prediction of the physical properties of glass subjected to arbitrary and more complex temperature-time histories. It should, therefore, also be useful in the rational design of heat treating processes such as annealing. InkoductionHE approach of glass structure toward its equilibrium T state has been studied extensively both for practical reasons and for a better understanding of the glass transition itself. Some practical applications are the annealing of flat glass, in which control of residual stresses is sought, and the annealing of optical glass to obtain a homogeneous structure and a high degree of uniformity of refractive index. Studies of relaxation processes are of fundamental importance in describing the structural state of a nonequilihrium glass. Experiments on the response of the structure of glass to heat treatment are intrinsically difficult, since the structure is both temperature-and time-dependent. In such experiments, structural evolution is studied by observing the temperature-and time-dependent changes in a physical property such as density. Although data on the relaxation of physical properties of glass are available, their interpretation is made difficult by the nonlinear character of the relaxation process.A plausible explanation of the nonlinearity of structural relaxation is that the changing structure alters viscosity and hence the rate of relaxation. Tool' proposed a model that sought to explain this aspect of structural relaxation; he introduced the concept of fictive temperature, T,, as a measure of the structural state of glass and expressed viscosity as a function of the actual and fictive temperatures. Tool's equation is Thus, the rate of change of the fictive temperature is proportional to its deviation from the actual temperature, and the proportionality factor depends on both T and TI. The bracketed factor is inversely proportional to viscosity and expresses the exponential dependence of viscosity* on the actual and fictive temperatures. Thus, viscosity and relaxation rate are as sensitive to changes in structure as they are to changes in temperature. This relation explains the marked nonlinearity served as the influence of past heat treatments on the future behavior of glass. Goldstein: who discussed this point in detail, has shown that "nonexponential relaxation," "spectrum effect," and "memory effect" refer to the same type of relaxation behavior; these terms may be used interchangeably.Ritlan...

Communication: Resolving the vibrational and configurational contributions to thermal expansion in isobaric glass-forming systems

“…rheology, 11,12 and the many phenomenological models for glass relaxation behavior. 13,14 Our result confirms that this underlying assumption of these models is indeed well founded. However, additional investigation is necessary for systems bound by anisotropic forces.…”

“…Many phenomenological models of rheology [11][12][13] and glass relaxation behavior [14][15][16][17] implicitly assume that configurational and vibrational components of isobaric thermal expansion can be expressed as separate terms. From a statistical mechanics point of view, the separability of vibrational and configurational thermal expansions implies a factoring of the partition function into independent configurational and vibrational contributions.…”

Revealing the fast atomic motion of network glasses

“…While the model is known to describe successfully the evolution of many macroscopic quantities in the glass transition region [49][50][51][52][53] , it fails to reproduce the XPCS data, predicting relaxation times several orders of magnitude longer than the measured ones. The model assumes indeed that the aging takes place on a time scale comparable to the structural relaxation time, and this is usually the case for macroscopic observables.…”

“…Following the Tool-Narayanaswamy-Moynihan model (TNM) 38,[49][50][51] , we can use the thermal protocol followed during the experiments to estimate the evolution of the fictive temperature 45 and of the relaxation time that one would expect from macroscopic measurements, through the relations:…”

Toward broadband mechanical spectroscopy

“…TTS states that the alpha relaxation spectrum retains the same width and shape when the temperature is changed. A wide range of practices in polymer processing, rheology, aging, and other areas are based on TTS (17)(18)(19)(20)(21), but it has never been tested directly for mechanical properties across most of the time scales spanned. TTS forms the basis of many early heuristic descriptions of supercooled liquids extending from high temperature all of the way to the glass transition temperature; TTS is also predicted at T > Tc by schematic MCT for the alpha process whenever it is well separated from the fast beta process (15,16).…”