Mathematical-physical imperfections in frequently used models for analyzing glass crystallization and glass transition processes

Abstract

In this paper, the modified Kissinger equation and the Ozava type equation were obtained by using a process of homogenization from dimensional analysis, thus making them correct in relation to the application of a logarithmic function. An equation that holds at maximum reaction rate is applied for the chosen reference heating rate βr and also for a heating rate βi that was used. In that way the modified Kissinger equation lnTmr2Tmi2βiβr=−ER1Tmi+ER1Tmr was obtained. The modified Ozava type equation was obtained in the form.lnβiβr=−mEnR1Tmi+mEnR1Tmrwhere Tmr and Tmi are the temperatures of the maximum obtained with βr and βi respectively. In these equations, free terms are explicitly defined and from their values it is possible to calculate the value of activation energy E, as from the slope of straight lines. The main advantage of the modified equations compared to the original Kissinger equation and the Ozava type equation is not the more accurate value of the activation energy, but the more precise form of the equation.With the goal to overcome all imperfections of the Lasocka equation, we propose the modified relationship Tg = Ag + Bg log(β/βr + 1) between the glass transition temperature Tg and the heating rate β. In this equation, the logarithm is calculated from dimensionless values, where βr is the chosen reference heating rate. In contrast to the original Lasocka equation, the modified Lasocka equation parameters Ag and Bg have the same units. The temperature Tg0 = Ag can be obtained by extrapolation of experimental results to β = 0. This is impossible to get from the original Lasocka equation, but it can be obtained from the modified one.