Role of particle geometry and surface contacts in solid-phase reactions

Given the surface areas of three different species A, B, and C, what is the most likely contact area between A and B? This problem finds many applications, but it is of specific importance in solid‐phase reactions. Reactions in powder mixtures depend strongly on contact area between reactants, even when one species may melt. The surface of particles is meshed with small “tiles,” and a combinatorial problem is formulated to map all tiles onto each other. The number of different contacts of n constituents is \documentclass{article}\pagestyle{empty}\begin{document}$\sum\limits_{i = 1}^n i$\end{document}; if pores are present, they are considered a constituent. The combinatorial problem for n > 3 is computationally overwhelming, but for two or three species, the desirable contacts can be calculated. The model was developed for contact between three different species (two species are included as a special case). This could constitute three different powders at 100% MTD, or a mixture of two powders that includes pores where the latter phase acts as a third species. The combinatorial approach is used to find the discrete probability‐distribution function (PDF), viz., p(z, A, B, C), where z is the number of desirable contacts (for example, A∖︁B), given the surface areas (A, B, C). The first moment of the PDF gives the expectancy value Ψ (A∖︁B, A, B, C) for contact between species A and B. The theory was demonstrated by two examples. A simple contact problem is solved for two powders that also contain pores. The second example compares kinetic rates for different shapes and sizes of particles.