A combinatorial approach to surface contacts in solid phase reactions

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Macro-kinetic models for solid phase reactions require information about the contact area between reactants. A classical probability is presented to calculate the expectancy value for contact between two specified species when three different solid phases are present in the system. Consider the generic reaction aA(s)+ bB(s)→ cC(s,g) (if C is volatile the two-phase problem results). The expectancy value depends on the surface area densities σ i = N i v where N i denotes the particle density of species i and v i is the volume per particle—instead of using distributions, the analysis is based on average particle sizes. To include the important role of particle geometry, the reactants are modeled as rectangular rhombi. The differences in reaction rate are investigated for cubes (quasi-spheres), platelets and needles by adjusting the aspect ratios. As the reaction proceeds reactants are consumed and products form that change the probabilities for reactant contacts. The evolution of particle sizes must be tracked and mechanisms that affect particle sizes must be included in the model. The dimensions change with reaction, compression and fracture. Fracture is described by the Hiramatsu–Oko equation that relates bed pressure with an equilibrium dimension. The particle size of the (solid) product depends specifically on the reaction mechanism. To illustrate the combinatorial approach, it is applied to a mechanism where C desorbs from the A/B interface, but then it either nucleates to form C particles or adsorbs on existing C particles. Factors that influence the reaction rate are initial particle sizes, aspect ratios, fracture criteria and stoichiometry.