Investigation of a new mathematical model for compression of pharmaceutical powders

A new compaction equation, the log-exp model: V=V(l)-w log(P)+V(e) exp(P/P(m)) is presented. The model presumes that two compaction processes: a logarithmic and an exponential decline may be active simultaneously. Using non-linear regression techniques the model gives an excellent fit to a number of model substances with wide differences in compaction behaviour. Compared to the Kawakita equation the model covers a broader range of the compaction profile. The new model and the Cooper and Eaton equation fit the data on the same level, but the parameters derived from the log-exp model seems to have more discriminative power between substances and have a close relation to the apparent plastic or brittle densification mechanism. The log-exp model has potential as a tool in estimation of the strength of agglomerated materials. A proposal for a set-up to an iterative non-linear regression calculation in a spreadsheet program is attached.