The influence of gas partial pressures and the elementary mechanisms in the study of solid-gas reactions

Michèle Pijolat (1, 2, 3) , Loïc Favergeon (1, 2, 3)

1 SPIN-ENSMSE - Centre Sciences des Processus Industriels et Naturels
2 PRESSIC-ENSMSE - Procédés et REactivité des Systèmes Solide-gaz, Instrumentation et Capteurs
3 LGF-ENSMSE - Laboratoire Georges Friedel

The usual methods of kinetic analysis require the kinetic rate dα/dt to follow both conditions: (i) to admit an apparent activation energy and (ii) to be a function of the conversion extent α. In general, reactions in solid-gas systems are not as simple as required by these conditions, since the rate may not follow an Arrhenius law nor varies as a f(α) function. The gases (reactants and products) present in the thermobalance may have a strong effect on the kinetics. It is then necessary to perform isothermal experiments, while maintaining as far as possible constant the partial pressures in all the gases supposed to have an effect on the kinetics. A more general equation of the kinetic rate may be advantageously used due to: (*) a function Φ(T, Pi) of the thermodynamic variables of the system under study (typically the temperature T and the partial pressures Pi) to account for the deviations from Arrhenius equation and for the influence of reactive gases, in mol m^-2s^-1, (*) a function of time Sm(t) to account for deviations from the f(α) dependency (such as in the case of surface nucleation and growth models), in m²mol^-1. Provided that the growth kinetics of the new phase is controlled by a rate-determining step, the rate follows Equation (1) : dα/dt = Φ(T, Pi) Sm(t)(1) the usual dα/dt =Aexp(-E/RT)f(α) equation being then considered as a particular case of Equation (1). Both functions Φ(T, Pi) and Sm(t) may be calculated from two distinct appropriate modeling’s. While the Sm(t) function has been shown to take various expressions according to the various geometrical aspects for nucleation, growth and competitive nucleation and growth processes, the Φ(T, Pi) function may appear to be much more difficult to relate to the elementary mechanisms. The presentation will thus be focused on the proposal of elementary mechanisms of growth with the determination of the related expressions of the areic reactivity. A typical mechanism consists in a set of elementary steps where the adsorbed species and the point defects are the actual intermediates of the transformation. Basic knowledge in point defects thermodynamics (Kröger’s notation, defect formation and consumption through interfacial equilibriums), solid state diffusion and adsorption/desorption phenomena is necessary to settle the equations of the system. It will be shown how the mechanisms may be decomposed into elementary steps as previously proposed to explain the oxidation of metals. Due to the rate-determining step assumption it is possible to find the analytical solution of a system of equations and to get the law of variation of the areic reactivity with the thermodynamic variables. The case of reactions near to equilibrium will be considered due to a term specific of the deviation from equilibrium of the operating conditions. This term can be deduced from the calculation of Φ(T, Pi) for a given mechanism and a given rate-determining step. Examples of expressions of the areic reactivity will be given for various solid-gas and decompositions reactions: oxidation, reduction, dehydration, etc…

Mots clés: point defects thermodynamics; modeling; adsorption; nucleation; partial pressures; growth kinetics; solid-gas systems

Domaines: Génie des procédés

Michèle Pijolat, Loïc Favergeon. The influence of gas partial pressures and the elementary mechanisms in the study of solid-gas reactions. ESTAC 2014 (11th European Symposium on Thermal Analysis and Calorimetry), Aug 2014, Espoo, Finland. ⟨hal-01103369⟩