Equivalence of the Arrhenius and non-Arrhenian temperature functions in the temperature range of measurement

Šesták–Berggren equation: now questioned but formerly celebrated—what is right

“…(1) can be likewise exploited in two different manners: as a resource of individual mechanisms (cf. Table 1) or as a bridging equation toward the novel method model-free kinetics [48][49][50]. Anyhow we have to take care about some unsettling regards which are unfortunately mixing in the customary methods of traditional kinetic evaluations, which are so far not solved seriously enough, among others indicating:…”

“…: 1/P = ln(1 -a) -ln(1 -a) n -{(1 -a)/a} ln(1 -a)m which yields on simplification: 1/P = n -(3/4)m. However, these attempts to associate the SB alternatives with a particular model of JMAYK seems be somehow irrelevant because it is linking two incommensurable kinetics exhibiting divergent philosophical strategies [37,46]: the geometrical JMAYK versus the logistic SB. Certainly, the values of n and m can be categorized and cataloged, but they better should serve as the characteristic values for the novel method of the so-called nonparametric kinetics [48] based on the so-called modelfree kinetics [49,50]. Its acuteness can be substantiated by analyzing the most common kinetic models associated with the shrinking core of a globular particle, which requires a sharp reaction boundary [37,46].…”

The quandary aspects of non-isothermal kinetics beyond the ICTAC kinetic committee recommendations

“…It approved doubts [32] revealing that the ln g(a) vs. 1/T plot is twice better as that of the former two parameters (T and 1/T) yielding E's with an error up to of 15% which is further reduced within the logarithm form applied [34]. Such an intrinsic ambiguity is caused by the approximation of an integral form of Arrhenius function f exp (x) ) p (x) [8,33] applied with the differing multiplication parameters, which itself introduces some inexactness into this kind of kinetic appraisal.…”

“…A better insight for this investigation was provided by the use of an asymptotic expansion in [34] by means of a series with a dimensionless parameter replacing E app . It approved doubts [32] revealing that the ln g(a) vs. 1/T plot is twice better as that of the former two parameters (T and 1/T) yielding E's with an error up to of 15% which is further reduced within the logarithm form applied [34].…”

“…Such an intrinsic ambiguity is caused by the approximation of an integral form of Arrhenius function f exp (x) ) p (x) [8,33] applied with the differing multiplication parameters, which itself introduces some inexactness into this kind of kinetic appraisal. The reason resides in the fact that, in a narrow temperature range, the functions 1/T, ln T and T are linearly related to each other [34]. This verdict can be generalized for all model-fitting methods accentuating that the equivalence of the temperature functions must hold within the temperature range of measurement [34], see next paragraph dealing with model-free methods…”