5/31/2023 0 Comments Viscosity equation![]() Note that this study does not focus on comparing the physical significance of these models. Through this theory, denoting the temperature-dependent parameters in the model as specific expressions is a feasible way to study the viscosity-temperature relationship of the glass-forming liquids. However, the properties of glass in the forming process is hardly influenced by pressure, so the impact of pressure can be neglected. Among these studies, a model with connectivity of the activation volume to the activation energy was used for fitting the pressure-dependent viscosity of liquids at a constant temperature, and the calculated values were in good agreement with the measured results. Thus far, many modified models have been established by improving the calculation accuracy of activation energy in the Eyring equation. The Eyring viscosity equation as a conventional method was derived from Eyring’s absolute rate theory, which is used to define the viscous flow of a liquid as the activation process. However, the Arrhenius equation is habitually suitable for the low-viscosity range, which means non-Arrhenius behavior would occur when the temperature drops because the changes of network structures become the main factors that influence the viscosity. The Arrhenius equation was firstly used for the viscosity calculation of fluids many years ago, i.e., ln η = A + B/ T, where A and B are dependent of composition, with T being the temperature. Among them, glass-forming liquids belong to the Newtonian fluids, which are in category of many other similar organic or inorganic liquids and have been extensively studied. Liquid viscosity is also one of the most important properties of chemical transportation, thus many viscosity models of molecular and polymer liquids have been developed in this area. Therefore, it is highly desirable to predict the viscosity more accurately by constructing an improved model using different mathematical expressions. However, it remains a great challenge for the phenomenon of overfitting when it comes to the high-viscosity region. Generally speaking, if the viscosity of glass-forming liquids is low enough, it would result in a linear relationship between ln η and 1/ T so that the modeling is relatively simple. MYGEA was derived from the analysis of energy landscape and the temperature-dependent constraint theory for configuration entropy. The AM model was developed on the assumption of random probability distribution of activation energies for molecular transport due to structural disorder. Following the VFT equation, other three-parameter models were later developed, such as the Adam–Gibbs equation (AG), the Avramov–Milchev (AM) equation, and the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) equation. The VFT equation was proposed mathematically based on the analysis of viscosity and widely applied in the glass company. The classical Vogel-Fulcher-Tammann (VFT) equation, a three-parameter model that works well for glasses with variable compositions, is suitable to predict viscosity across more than 10 orders of magnitude. Over the past few years, the analysis of experimental data has contributed to the modeling of temperature-dependent viscosity. ![]() 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. In addition, we have demonstrated that the different regression methods exert a great effect on the final prediction results. By means of combining high-temperature viscosity data and the glass transition temperature ( T g), nonlinear regression analysis was employed to obtain the accurate parameters of the equation. 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. 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. In fact, the introduction of the reliable viscosity-temperature data to viscosity equations is an effective approach to obtain the accurate parameters. Usually, this issue will lead to unsatisfactory predicted results when fitted to a real viscosity profile. The complex compositions of commercial glasses raise challenges to settle these parameters. Most viscosity models were generated along with several impact factors. 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.
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