Abstract
The basic theorem of isokinetic relationships is formulated as “if there exists a linear correlation “structure∼properties” at two temperatures, the point of their intersection will be a common point for the same correlation at other temperatures, until the Arrhenius law is violated”. The theorem is valid in various regions of thermally activated processes, in which only one parameter changes. A detailed examination of the consequences of this theorem showed that it is easy to formulate a number of empirical regularities known as the “kinetic compensation effect”, the well-known formula of the Meyer–Neldel rule, or the so-called concept of “multi-excitation entropy”. In a series of similar processes, we examined the effect of different variable parameters of the process on the free energy of activation, and we discuss possible applications.
Highlights
Exponential models of the temperature dependence of the properties of certain processes appeared in the scientific literature as early as the end of the 19th century
Chemists talk about the isokinetic relation in terms of the importance of the isokinetic temperature, condensed matter physicists and material scientists use the Meyer–Neldel rule, and biochemists use the compensation effect or rule
The above discussion shows that all linear correlations of the same type of processes obtained at different temperatures will intersect at one point until the Arrhenius law is violated. The establishment of this fact can be regarded as a proof of the above theorem as a “basic theorem of isokinetic relationships”
Summary
Exponential models of the temperature dependence of the properties of certain processes appeared in the scientific literature as early as the end of the 19th century. Similar correlations are widely used to describe the influence of certain parameters, generalized (e.g., the nature of the substrate or properties of the medium) in a series of thermally activated processes when this parameter is changed In this case, the variable (T) in Equation (1) is a function of two parameters, the temperature and the variable parameter (Equation (2)): φ( T ) ≡ φ( T, σ ). The correlation analysis of the temperature dependencies of different processes using the two-parameter Equations (1) and (2) made it possible to reveal another regularity for which statistical physics cannot answer the question of the reasons for its existence. One of the steps in this direction is the proof of the existence of a basic theorem of the isokinetic relationship (vide infra)
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