All You Need to Know about the Kinetics of Thermally Stimulated Reactions Occurring on Cooling

Abstract

In this tutorial overview article the authors share their original experience in studying the kinetics of thermally stimulated reactions under the conditions of continuous cooling. It is stressed that the kinetics measured on heating is similar to that measured on cooling only for single-step reactions. For multi-step reactions the respective kinetics can differ dramatically. The application of an isoconversional method to thermogravimetry (TGA) or differential scanning calorimetry (DSC) data allows one to recognize multi-step kinetics in the form of the activation energy that varies with conversion. Authors’ argument is supported by theoretical considerations as well as by experimental examples that include the reactions of thermal decomposition and crosslinking polymerization (curing). The observed differences in the kinetics measured on heating and cooling ultimately manifest themselves in the Arrhenius plots of the opposite curvatures, which means that the heating kinetics cannot be used to predict the kinetics on cooling. The article provides important background knowledge necessary for conducting successful kinetic studies on cooling. It includes a practical advice on optimizing the parameters of cooling experiments as well as on proper usage of kinetic methods for analysis of obtained data.

Advanced Fitting Method for the Kinetic Analysis of Thermogravimetric Data

“…In particular, = 0.5 was predicted by collision theory in the homogeneous gas phase and = 1 was predicted by transition state theory. Other modifications of the Arrhenius equation, including the stretched exponential, super- and sub-Arrhenius models [ 21 , 30 , 31 ], can also be easily used within the proposed approach.…”

“…The classical Arrhenius equation is widely used for calculations in both methods, which may be considered as a disadvantage, since a number of studies have shown that its various modifications significantly improve the accuracy of determining the kinetic parameters [ 20 , 21 ]. In particular, Criado et al [ 20 ] examined the dependence of the preexponential factor on temperature and estimated the errors involved in the activation energy calculated from isothermal and non-isothermal methods.…”

“…The general differential equation of the model, which is widely used for thermal experiments, does not have any limitations regarding the temperature effect (heating or cooling the sample) [ 12 ]. Upon cooling, single-step thermally stimulated reactions are usually studied using the data obtained under continuous heating run [ 21 ], as it is assumed that the kinetics measured on cooling is similar to that measured on heating. When studying such processes, a number of authors concluded that the modified Arrhenius equation provides higher accuracy of the results.…”

Impact of Donor, Recipient, and Graft Characteristics on Corneal Transplantation Outcomes

“…The postulated decrease in the rate constant of cellular reactions that is theorized to occur with reduction of temperature may lead to better corneal donor preservation. 8 Even a one-hour delay in cooling results in lower glucose levels in the stroma and aqueous, harming endothelial integrity. 14 , 15 For corneal transplant surgery, the viability of the endothelium is largely predictive of successful transplants and some studies have assessed whether hypothermia can act to preserve the endothelium, with many either finding no correlation or a correlation only with a longer DTP time (>12hr).…”

“…4 The premise behind hypothermic storage of tissue stems from the concept that the rate constant of cellular reactions is exponentially proportional to temperature. 8 Therefore, at a reduced temperature, cells decrease their metabolism and oxygen consumption, preventing mitochondrial stress and hypoxia-induced apoptosis. Most corneal transplants depend largely on preservation of a viable endothelium.…”