A Novel Viscosity-Temperature Model of Glass-Forming Liquids by Modifying the Eyring Viscosity Equation

Abstract

Many models have been created and attempted to describe the temperature-dependent viscosity of glass-forming liquids, which is the foundational feature to lay out the mechanism of obtaining desired glass properties. Most viscosity models were generated along with several impact factors. The complex compositions of commercial glasses raise challenges to settle these parameters. Usually, this issue will lead to unsatisfactory predicted results when fitted to a real viscosity profile. In fact, the introduction of the reliable viscosity-temperature data to viscosity equations is an effective approach to obtain the accurate parameters. In this paper, the Eyring viscosity equation, which is widely adopted for molecular and polymer liquids, was applied in this case to calculate the viscosity of glass materials. On the basis of the linear variation of molar volume with temperature during glass cooling, a modified temperature-dependent Eyring viscosity equation was derived with a distinguished mathematical expression. By means of combining high-temperature viscosity data and the glass transition temperature (Tg), nonlinear regression analysis was employed to obtain the accurate parameters of the equation. In addition, we have demonstrated that the different regression methods exert a great effect on the final prediction results. The viscosity of a series of glasses across a wide temperature range was accurately predicted via the optimal regression method, which was further used to verify the reliability of the modified Eyring equation.

On Viscous Flow in Glass-Forming Organic Liquids

“…The Sheffield equation of viscosity provides data on chemical bond parameters, including both enthalpies and entropies. Recently developed artificial intelligence and machine learning techniques (see [16,19,57]) can effectively give detailed information on the bonding system of materials, thereby contributing to efforts to improve the properties and functionalities of novel glasses.…”

“…Comprehensive comparisons of viscosity models available for a number of oxide glasses were provided by Starodub et al [16], Sturm [17], and Chen et al [19]. Starodub et al [16] demonstrated that the outcomes of modeling can be effectively improved by using machine learning techniques applied to multiparameter tasks.…”

“…Starodub et al [16] demonstrated that the outcomes of modeling can be effectively improved by using machine learning techniques applied to multiparameter tasks. Chen et al [19] found that the viscosity values simulated by using both high-temperature and low-temperature viscosity data show higher accuracy than those using only high-temperature viscosity data. Although the Sheffield model in Sturm's analysis [17] did not rank the best among known viscosity models, it provides a direct link between the bond's strength and the activation energy of viscosity, which reveals the processes behind the variation of activation energy.…”

“…The salient feature characterizing a supercooled liquid is the dramatic increase of viscosity η(T) with decreasing temperature T, which may encompass some 15 orders of magnitude over a temperature range of almost several hundred K [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ]. The interest in analyzing the viscous flow in glass-forming materials is not diminishing, with many novel findings having occurred over the last decade [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. There are many theoretical models that can describe the viscous flow of glass-forming materials, which provide reasonably exact descriptions of viscosity–temperature relationships [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ].…”

“…It was found that the overall best fits over the entire temperature range above the glass transition temperature are given by the expression T·ln[η(T)/η ∞ ] = E ∞ + BT*[(T* − T)/T*] 8/3 Θ(T* − T), where Θ(T* − T) is the Heaviside step function and T* is usually greater than the melting point temperature. More recently, the Eyring viscosity equation typically used for glass-forming liquids [ 12 , 15 ] was applied to calculate the viscosity, resulting in a modified temperature-dependent Eyring viscosity equation [ 19 ]. It was shown that that different regression methods exert a great effect on the final prediction results, although the viscosity of a series of glasses across a wide temperature range was accurately predicted via the optimal regression method [ 19 ].…”