Maxwell relaxation time for nonexponential α‐relaxation phenomena in glassy systems

Abstract

We examine the mean relaxation time predicted by the Maxwell relation for stress and structural α‐relaxation phenomena. We express this relation using the Markov network framework and present an expression for the average relaxation time under equilibrium and nonequilibrium conditions that is rooted in the energy landscape of a material. We show that structural relaxation times calculated using the Maxwell relation must systematically underpredict the relaxation time. Finally, we report experimental evidence suggesting that the relaxation time obtained from shear viscosity measurements must correspond to a stress relaxation time.

Physics and Mathematics of the Photoluminescence of Complex Systems

“…However, as hinted in the Introduction, there are two ranges of β, and therefore there are two KWW functions and two dynamics, so that it is also expected to find two different origins behind the damping. The aim of this Section is to understand how, and especially in which cases, these differences emerge using the series expansion of the KWW function, the so-called Prony series [41,42]. The Prony series reproduces quite faithfully the behavior of the KWW function using a finite sum of simple exponential functions:…”

Fragility and temperature dependence of stretched exponential relaxation in glass‐forming systems

“…A combination of the MAP model for non‐equilibrium shear viscosity, 39 the model presented here primarily in Equation (), and the model presented by Wilkinson et al 49 for the temperature dependence of elastic modulus, allows for fully quantitative modeling of stress relaxation behavior. The missing model required to understand structural relaxation is the bulk viscosity curve 15 . All previous relaxation (structural or stress) models 9,42 have relied on approximations that use a constant exponent β and on a constant (temperature‐independent) modulus value, whereas here, every parameter of Equation () may be modeled as a function of temperature.…”

“…This method is implemented in RelaxPy, 9 as discussed in the next section. This serves as an approximation for the evolution of the non‐equilibrium state; however the temperature dependence of the bulk viscosity and a replacement for fictive temperature need to be quantified to improve the understanding of the underlying physics 15,16,50 …”

“…Equation () was originally proposed empirically and is known as the stretched exponential relaxation (SER) function 1,9 . The relaxation time, τ , depends on the composition, temperature, thermal history, pressure, and pressure history of the glass, as well as the property being measured 14,15 . For example, the stress relaxation time of a glass can be written as follows 15 :where η is the shear viscosity and G is the shear modulus of the glass‐forming system 9 .…”

“…(Variables are defined in Table 1). In addition to using Equation () to describe stress relaxation time, structural relaxation time has recently been hypothesized to follow Equation () with bulk viscosity and the difference of bulk modulus between infinite and 0 frequency replacing shear viscosity and shear modulus 15 . Both η and G vary with the temperature ( T ) and thermal history of the glass (as quantified via the fictive temperature, T f ) as well as the pressure ( P ) and its corresponding history (fictive pressure, P f ) 16 .…”