A method of finding invariant values of kinetic parameters

Abstract

A method of calculating the Arrhenius parameters has been proposed, based on an evaluation of the coordinates of intersection of greatly extended confidence regions determined in solving the inverse kinetic problem. The validity of this method is illustrated by comparison of the Arrhenius parameters found from non-isothermal and isothermal data reported by other investigators.The kinetic parameters characterizing the chemical stage of solid-phase reactions are determined by isothermal kinetic methods, provided certain approaches to the selection of a theoretical model are observed and rigid constraints are imposed on the experiment [1]. Such constraints may yield a positive result in non-isothermal kinetics [2] as well. However, finding t'he kinetic parameters from experimental data, i.e. solving an invers kinetic problem, may run into certain difficulties, for such problems are ill-posed mathematical problems characterized by a poor statement of the problem conditions (the determinant of the information matrix is close to zero). Therefore, such problems have no unique solution unless special methods are used [3]. This problem was analyzed in [4,5] for dynamic thermogravimetry conditions. The poor statement of the problem conditions determines its solution in the form of a greatly extended region, so that experimental data can be described with equal accuracy with the help of Arrhenius parameters A and E variable over a very wide range in this region, the compensative effect being an artefact of computation. Calculated by different methods, A and E characterize the mathematical method used rather than the reaction itself. This also follows from [6][7][8][9]. The artefact can be eliminated, The invariant characteristics of the process can also be calculated with a different, quite general means, by constructing a statistical model of the process as a polynomial [3]. In this paper a method is suggested for determining invariant values of the activation energy (E) and a pre-exponential factor (A), which corresponds to the above general approach. Isokinetic temperature and a polynomial as a polylinear expansion [12] are used in the method. This makes it very simple to use in computation and provides a very clear interpretation that reveals the physical meaning of the invariants

Some methodological problems concerning nonisothermal kinetic analysis of heterogeneous solid–gas reactions

“…Using the relation of the compensation effect for each heating rate, the compensation parameters α * v and β * v are determined. The straight lines In A v vs. E v for several heating rates intersect in a point that corresponds to the true values of A and E. These were called invariant activation parameters (A inv , E inv ) by Lesnikovich and Levchik [27,28]. Certain variations of the experimental conditions actually determine a region of intersection in the space ( A, E).…”

“…The invariant kinetic parameter (IKP) method suggested by Lesnikovich and Levchik [27,28] needs special mention. It is based on the observation that the activation parameters evaluated by using a single α = α(T )curve and some analytical form of f (α) are correlated through the relation of the compensation effect:…”

The Structural Influence in the Stability of Polymer‐Bound Diazonium Salts

“…[51] The method is based on the observation that by choosing a different analytical form of the kinetic function, f(1Àa), the values of the two parameters E and A, calculated from the data recorded at a single heating rate, are linearly related to each other through a so-called "apparent compensation effect" [Eq. (10)] in which c1 and c2 are two appropriate constants: [50] lnðAÞ ¼ c1E þ c2 ð10Þ…”

Comparative thermal degradation studies on glycolide/trimethylene carbonate and lactide/trimethylene carbonate copolymers

“…Another method used to evaluate the kinetic parameters is the IKP (invariant kinetic parameters) method. 27,28 According to this procedure, the values of the activation parameters, obtained from various forms of f(a), are correlated through an apparent compensation effect:…”