Pressure susceptibility of polymer tablets as a critical property: A modified heckel equation

Abstract

The pressure susceptibility (χp), which is defined as the decrease of porosity (ε) under pressure was investigated. Of special interest are compacts obtained at very low pressures, because of the transition between the state of a powder and the state of a tablet. This range was found to be critical in respect to a diverging pressure susceptibility. Above a critical porosity (εc) or below the corresponding relative density (ρc), no pressure susceptibility can be defined, because of no rigid structure exists. To take this into account, a simple function was proposed for the pressure susceptibility: χp ∝ 1/(εc − ε). This proposal leads to a new porosity vs pressure relationship. The new model was compared to the Heckel equation that involves a constant pressure susceptibility. Various polymers were tested from “out of die” measurements, and the new relationship was found superior to the Heckel equation. As a conclusion, the pressure susceptibility exhibits a curvature that can be called critical at low relative densities. Consequently, a better understanding evolves as to why the Heckel equation is not valid at low pressures. The new model has proven to be adequate for polymer tablets but, so far it is not clear whether other substances exhibit the same performance. Especially tableting materials exhibiting brittle fracture will be of interest considering their importance in compaction technology.