A new model for the hardness of a compacted particle system, applied to tablets of pharmaceutical polymers

This paper presents a new theoretical model for the hardness of tablets. Based on the Leuenberger theory of powder compression, a new equation is obtained, describing the indentation hardness as a function of the relative density that includes two parameters having a defined physical meaning. These parameters are the maximal hardness at zero porosity, P-max, and the starting value of the relative density, rho(c), needed for minimal shear strength of the powder bulk. The model was evaluated for 12 different pharmaceutical polymers. The choice of these pharmaceutically used model excipients was done according to their ability to form tablets in a broad density range. The tablets were compressed and the indentation hardness tested with a universal testing instrument. The obtained experimental results, support the validity of the proposed hardness model. Despite the simplicity of the theoretical approach, some interesting new insights were attained with respect to the evolution of mechanical strength in tablets. Thus, the importance of the critical porosity, epsilon(c), or the corresponding relative density, rho(c), as reference values is especially emphasized. Accordingly, a normalization of the porosity or the relative density by their critical values is proposed. The application of these parameters is beneficial for formulating the new hardness model, as well as for other equations dealing with the physics of compression. (C) 2000 Elsevier Science S.A. All rights reserved.