The difficulty in the assessment of the compression behaviour of powder mixtures: Double layer tablets versus arithmetic additivity rule

The weighted arithmetic mean from values of a feature derived from the individual components is often used to calculate the theoretically expected compression behaviour of powder mixtures if no interparticulate interactions between the components occur. Alternatively, simulated and experimental double layer tablets are presented. The suitability of the various methods to serve as a reference for the assessment of the compression behaviour of powder mixtures shall be compared. Narrow and similar sieve fractions of maltitol and metamizol were mixed in various ratios of true volumes. Constant total true volumes of the single substances, powder mixtures, and layered powders of the same composition were compressed on an eccentric tabletting machine to a constant maximum geometric mean punch force. In addition, the compression of double layer tablets was mathematically simulated from the dynamic relative density-force data of the pure materials. At a given momentary force, the relative density of a simulated double layered powder bed is given by the harmonic mean of the relative density values of the pure materials weighted by their true volume fractions. The results show that the total, the net, and the expansion work change indeed almost linearly with the true volume fraction of the components in the double layer tablets, with the consequence that the plasticity index (=net work/total work×100) proceeds non-linearly. The slope of the Heckel plot 'at pressure' and the apparent mean yield pressure obtained from these Heckel data are non-linearly related to the true volume fraction. If the weighted arithmetic mean is used to analyse the compression behaviour of the powder mixtures, results are obtained which are incompatible or even contradictory between interrelated features. On the other hand, the double layer model provides a consistent evaluation. A good agreement between the results of the experimental and the simulated double layer tablets is found.