Isokinetics

Abstract

The study of the rates of chemical reactions and their relationship to temperature began in the 19th century with empirical measurements of the time required to reach a particular reaction end point at a constant temperature. By the mid-20th century, the theory of reaction rates had advanced and instruments had been developed in which the temperature of the sample could be increased at a constant rate. These nonisothermal methods are now widely used to determine the kinetic parameters of reactions because of their convenience. In this paper, the mathematical relationship between measurements at constant temperature (isothermal) and constant heating rate (nonisothermal) is developed and it is shown that there is a point in the temperature history of a single-step reaction at which the isothermal and nonisothermal reaction rates are equal. This equal (iso) kinetic point occurs at a temperature early in the heating history of nonisothermal analyses at which the reaction rate begins to accelerate. The isokinetic temperature is the basis for a new method of nonisothermal kinetic analysis that provides a direct measurement of the Arrhenius frequency factor A and activation energy E a for the elementary step of a solid-state reaction without any assumptions about the relationship between these parameters (i.e., kinetic compensation) or the reaction mechanism.

Kinetic compensation effect of isoconversional methods

“…For reactions under dynamic conditions, time in Eq. 7 can be expressed as = [53]), and it is the reaction time of an actually observed reaction in the range of > 0.05 . Therefore, under dynamic conditions we omit the time in which the sample warms up, and the mass changes are not very significant.…”

“…Therefore, under dynamic conditions we omit the time in which the sample warms up, and the mass changes are not very significant. According to the theoretical considerations presented in [53], this stage of the process to the isokinetic temperature called "elbow" or "kness" has a great cognitive significance but mainly due to the technical and measuring reasons generally omitted. Formally, the integration range from T i = 0 is usually adopted.…”

“…According to [53] the reaction rates of solids dissociation measured at constant temperature (isothermal) and constant heating rate (nonisothermal) are equal at the isokinetic temperature T iso . This definition makes it possible to assign isokinetic temperatures to many kinetic models for the iso < 0.05 coordinate.…”

“…Thus, the definition of isokinetic temperature according to [53] under dynamic conditions truly corresponds to the temperature of the step growth of the reaction/ process rate. As a consequence, we observe for T ≤ T iso , 0 The isokinetic temperature can be determined using the kinetic equation for dynamic conditions and the Eq.…”

“…Certainly, a novelty is the determination of the isokinetic temperature according to [53], which is described by Eqs. [17][18][19], which suggests the experimentally determined start of the reaction/process.…”