Investigation of a new mathematical model for compression of pharmaceutical powders

Abstract

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.