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 equation image; 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.