Application of percolation model to the tensile strength and the reduced modulus of elasticity of three compacted pharmaceutical excipients

Percolation theory has been applied to several mechanical properties of pharmaceutical tablets. This power law describes the change of tablet’s properties with the relative density. It defines critical tablet densities from which the mechanical properties start to change. The exponent in the law is expected to be universal for a mechanical property and numerical values are proposed in the literature. In this work, the percolation model was applied to the tensile strength and the reduced modulus of elasticity (obtained from surface indentation test) of three compacted pharmaceutical excipients (a microcrystalline cellulose, a lactose and an anhydrous calcium phosphate). Two approaches were proposed. First, the exponent was kept constant and equal to the values used in the literature (2.7 for the tensile strength and 3.9 for the reduced modulus of elasticity). Secondly, the critical tablet density (i.e. the percolation threshold) and the exponent were determined from the model. In the first approach, the percolation thresholds were higher than the relative tapped density. Using the second approach, the experimentally determined exponents were not close to the values of the literature and the critical relative densities were higher than the relative tapped density or equal to zero. Then, this study showed that the exponent seems not universal and that the model must be used carefully.