Kinetic Analyses of Solid-State Reactions with a Particle-Size Distribution

Kinetic analyses for the solid-state reactions of reactant particles in an assemblage with a particle-size distribution (PSD) have been reexamined for the reactions that proceed by the advance of the reaction interfaces inward toward the center of the individual reactant particles. The experimental kinetic curves for a particle assemblage are influenced by the existing PSD. It has been demonstrated that, even if PSD exists, a reliable activation energy E can be obtained from such overall kinetic curves by the empirical isothermal analysis without accounting for the PSD. The isoconversion methods, which enable us to determine the E value from the data points at a given fractional reaction of a series of experimental kinetic curves, are methodologically independent of the PSD. It is neccessary to incorporate the PSD into the kinetic equation to select an appropriate kinetic model and to evaluate the preexponential factor A . The method of kinetic calculation accounting for the PSD can be generalized, for the kinetic data under any thermal profiles, by extrapolating all the analytical conditions to infinite temperature. For the reaction characterized by the well-defined PSD and kinetic model function, the meaningful A value is obtained by the kinetic analysis at infinite temperature. Although the ability to discriminate the contracting geometry of the reaction interface in a single particle from the overall kinetic curve decreases with increasing PSD, the rate-controlling steps for the advance of the reaction interface, i.e., chemical reaction controlled or diffusion controlled, can be distinguised from each other even for the reactions with a fairly large PSD.