Many solid-state kinetic models have been developed in the past century. Some models were based on mechanistic grounds while others lacked theoretical justification and some were theoretically incorrect. Models currently used in solid-state kinetic studies are classified according to their mechanistic basis as nucleation, geometrical contraction, diffusion, and reaction order. This work summarizes commonly employed models and presents their mathematical development.

Solid-State Kinetic Models: Basics and Mathematical Fundamentals

Thermal decomposition of ammonium perchlorate

Professor Vladimir V. Boldyrev has made numerous important contributions to a wide range of chemical topics, not only limited to studies of the decompositions of solids. Of particular value has been his emphasis on exploring, in detail, the chemical steps participating in the thermal reactions of solids by carefully designed experiments that rely on more observational evidence than the run-of-the-mill collection of overall kinetic data. Some of these major contributions to both the theory and the uses of solid-state reactions are identified here and discussed in relation to his illuminating and fundamental mechanistic studies of the thermal decompositions of silver oxalate, ammonium perchlorate, potassium permanganate and the dehydration of copper sulfate pentahydrate.

An appreciation of the chemical approach of V. V. Boldyrev to the study of the decomposition of solids

Aspects of the theories that are conventionally and widely used for the kinetic analyses of thermal decompositions of solids, crystolysis reactions, are discussed critically. Particular emphasis is placed on shortcomings which arise because reaction models, originally developed for simple homogeneous reactions, have been extended, without adequate justification, to represent heterogeneous breakdowns of crystalline reactants. A further difficulty in the mechanistic interpretation of kinetic data obtained for solid-state reactions is that these rate measurements are often influenced by secondary controls. These include: (i) variations of reactant properties (particle sizes, reactant imperfections, nucleation and growth steps, etc.), (ii) the effects of reaction reversibility, of self-cooling, etc. and (iii) complex reaction mechanisms (concurrent and/or consecutive reactions, melting, etc.). A consequence of the contributions from these secondary rate controls is that the magnitudes of many reported kinetic parameters are empirical and results of chemical significance are not necessarily obtained by the most frequently used methods of rate data interpretation. Insights into the chemistry, controls and mechanisms of solid-state decompositions, in general, require more detailed and more extensive kinetic observations than are usually made. The value of complementary investigations, including microscopy, diffraction, etc., in interpreting measured rate data is also emphasized. Three different approaches to the formulation of theory generally applicable to crystolysis reactions are distinguished in the literature. These are: (i) acceptance that the concepts of homogeneous reaction kinetics are (approximately) applicable (assumed by many researchers), (ii) detailed examination of all experimentally accessible aspects of reaction chemistry, but with reduced emphasis on reaction kinetics (Boldyrev) and (iii) identification of rate control with a reactant vaporization step (L’vov). From the literature it appears that, while the foundations of the widely used model (i) remain unsatisfactory, the alternatives, (ii) and (iii), have not yet found favour. Currently, there appears to be no interest in, or discernible effort being directed towards, resolving this unsustainable situation in which three alternative theories remain available to account for the same phenomena. Surely, this is an unacceptable and unsustainable situation in a scientific discipline and requires urgent resolution?

What can we learn about the mechanisms of thermal decompositions of solids from kinetic measurements

Combustion of six lignocellulosic wastes was studied using thermogravimetric analysis. Experimental data were analyzed using different kinetic methods Kissinger, FWO, DAEM linear multiple regression methods and Coast Redfern method. Also, their thermodynamic parameters (ΔG, ΔH, ΔS) were obtained. The activation energy (E) and the pre-exponential factor (A) values calculated by the DAEM, FWO and Kissinger methods were higher than those obtained by the linear multiple regression and Coast Redfern methods. The E values obtained from the Kissinger method are consistent with the range of values obtained by the FWO and DAEM methods and are very near to their average values (between 52.75 and 116.92 kJ/mol for all studied agro-industrial wastes). DAEM and FWO methods provides E and A distributions, detecting multi-step kinetics. However, Kissinger method provides only one E and A values for all heating rates, similar to obtained values applying DAEM and FWO methods. The linear multiple regression method provides the knowledge of kinetic triplets for each studied heating rate, presenting a slower fit than the other methods. On the other hand, Coast Redfern method supplies these triplets and the reaction mechanisms. However, using this method, the obtained E values are very different to the calculated values applying isoconversional methods. Using the last mentioned methods, the models of volume contraction and first order describe the devolatilization and char combustion stages, respectively. The obtained thermodynamic parameters values show that the lignocellulosic wastes combustion has a low reaction favorability.

V.V. Boldyrev

Papers

Topochemistry of thermal decompositions of solids