Isoconversional Methods in Thermodynamic Principles

Abstract

The thermodynamic aspects of the methods commonly used in thermogravimetric analysis, that is, isothermal and dynamic, are presented. Models for isoconversional variants of dynamic methods are accepted. For the thermal dissociation of the solid phase, the free enthalpy of the system, called the Gibbs free energy state, and the stoichiometric principles according to de Donder's extent of reaction, were proposed as the starting point, binding the dissociative pressure in the gas phase with the rate of solid phase conversion. It was found that the isothermal methods and, surprisingly, the dynamic methods, occur in one system group, although with different energetic activity, whereas isoconversional variants of dynamic methods represent opposite effects in this range. Off-distance, which is formally defined as D = ΔΔ G, was proposed for the quantification of each analyzed case. According to the presented considerations, the isothermal and dynamic methods are dominated by enthalpy, whereas isoconversional methods are dominated by entropy.

Kinetic compensation effect of isoconversional methods

“…Distinguishing between pressure change directions with the same direction as the Arrhenius law is consistent with the assumptions presented in [55].…”

“…The slope in Eq. 20 is the compensation temperature T c = 1164.6K , which (for the analyzed data [22,54]) is very close to the theoretical equilibrium temperature of the chemical reaction T eq = ΔH • ∕ΔS • = 1172.4K [55]. If the compensation effect is the result of measurements carried out for a series of chemical reactions or many physicochemical processes (case a)), then the slope of Eq.…”

“…This temperature is defined by Krug [63] as "the temperature at which enthalpy variations precisely cancel entropy variations such that rate or equilibrium constants are completely invariant". Considering the conclusions presented in [55], we can assume that thermodynamic principles in the form of EEC related to temperature compensation are the source of KCE. In the case of isoconversional methods, ln A vs.E reveals weaker variability than we observe for isothermal and dynamic methods.…”

“…20. For = 1, H → 0 , ΔH • = 170 ⋅ 10 3 J mol −1 [55], so the system is heading towards the equilibrium temperature. This temperature is closer to the end of the reaction/process, and above it, the reaction is irreversible.…”

Isokinetic and Compensation Temperature in the Analysis of Thermal Dissociation of the Solid Phase under Dynamic Conditions

“…Equations ( 2) and ( 4) contain thermodynamic activation functions derived from Eyring's theory from 1935 [12]. The theory has been adapted for modeling complex reaction/process pathways, as well as for the practical use of selected relationships captured by Equations ( 2)- (5) [1,3,5,8,9,[13][14][15][16][17][18][19][20]. Some of the mentioned works combine Eyring's theory with the Arrhenius equation [13,14,18].…”