RelaxPy: Python code for modeling of glass relaxation behavior

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

“…Phenomenological models for the equilibrium (Mauro‐Yue‐Ellison‐Gupta‐Allan, MYEGA) and nonequilibrium (Mauro‐Allan‐Potuzak, MAP) viscosity of glass were used to calculate the viscosities for the experimental stress and structural relaxation experiments, respectively. Fragility ( m ) and glass transition temperature ( T g ), as defined by Angell, were directly measured by conducting equilibrium viscosity measurements in the vicinity of the glass transition by using three‐point beam bending method as previously shown in Gulbiten et al The temperature dependence of the nonequilibrium viscosity of the glass was calculated using RelaxPy, a Python script that returns viscosity and fictive temperature components for any thermal history input by implementing a Prony series fit to approximate the stretched exponential form . The experimentally measured calorimetric fictive temperature for Jade ® was found to be 1108.5 K and was used as the target fictive temperature to model the thermal history for the samples in RelaxPy.…”

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

“…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. Furthermore, in combination with the relaxation models described by Guo et al, 42 in which multiple fictive temperatures are described using a Prony series and a temperature‐dependent modulus, one can construct a relaxation curve accounting for the temperature dependence and thermal history dependence of all relevant parameters:…”

“…Relaxation is one of the most important properties for designing new glass products, as the thermal history of glass affects all of its properties 1–8 . The mathematical form for glass relaxation () was originally proposed by Kohlrausch in 1854 based on the decay of charge in a Leyden jar, 1,3,9–13 where t is time, τ is the relaxation time of the system, and β is the dimensionless stretching exponent. Equation () was originally proposed empirically and is known as the stretched exponential relaxation (SER) function 1,9 .…”

“…The mathematical form for glass relaxation () was originally proposed by Kohlrausch in 1854 based on the decay of charge in a Leyden jar, 1,3,9–13 where t is time, τ is the relaxation time of the system, and β is the dimensionless stretching exponent. 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 .…”

“…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).…”