Formation of a tablet: a site and bond percolation phenomenon

The concepts of percolation theory are used to elucidate the formation of a tablet by compression of particulate matter. The process of compaction can be considered as a combination of site and bond percolation phenomena. Because of effects of different particle size and shape of the particles in a powder bed and effects of brittle fracture and plastic flow, moisture content of the powder, and finite size of the tablet, no sharp percolation thresholds are expected. Thus, it is interesting to test the validity of the fundamental equation of percolation theory: the power law X = S(p - pc)q, where X is the system property, S is the scaling factor, p is the site occupation or bond formation probability, and q is the critical exponent. This model is, in certain cases, only rigorously valid close to the percolation threshold (range, [+/- 0.1 pc]). Combination of the Heckel equation with an equation derived earlier for the properties (X) of tensile strength (sigma t) and deformation hardness (P) yields a power law with q = 1, S'(sigma t) = sigma tmax/(1 - pc), and S(P) = Pmax/(1 - pc). With respect to the simplifying assumptions made, the power law agrees well with the experimental results obtained. Substantial improvements in the interpretation of the compression-compaction process are possible with these findings, and some interpretations differ from previous ones in earlier publications.