A Modern Approach to the Heckel Equation: The Effect of CompactionPressure on the Yield Pressure of Ibuprofen and its Sodium Salt

Despite being heavily criticised in the literature the most widely used and accepted compaction equation is the Heckel equation proposed by Heckel in 1961. Its presence in literature for 55 years is due to the ease in which it can distinguish between plastic and brittle materials. Achieving the correct balance of plastic and brittle materials in a formulation is critical to ensure adequate tablet strength is achieved therefore classifying materials using the Heckel equation is attractive. Despite the importance of this understanding, especially in the design and manufacture of direct compression formulations, there are no set analytical testing standards or materials classification guidelines. Instead many workers have attempted to develop techniques for the measurement and classification of a materials deformation but there is still confusion and contradiction present in this field. In this study we report the effect of compaction pressure on the yield pressure of ibuprofen and its sodium salt. Ibuprofen and its sodium salt were selected as models for study due to the availability of comparative literature yield pressure values. The reported variation in yield pressure can be significant e.g, ibuprofen which has literature values of 21-1139 MPa. This study proposes an approach to determine yield pressure from the Heckel equation using a linear regression method. The full linear regression methodology utilised is described and is used to report the yield pressure of ibuprofen and its sodium salt dihydrate. This technique reveals the most representative compaction pressure in order to derive yield pressure to be 121 MPa. The yield pressure of ibuprofen and its sodium salt have been shown to increase with increasing compaction pressure. The reported values lie between 52-78 MPa for ibuprofen and 48-75 MPa for ibuprofen sodium dihydrate. The slightly lower reported yield pressure values for ibuprofen sodium suggest increased plasticity which could be attributed to the water contained within the structure acting as a plasticiser.