Quantifying errors in tableting data analysis using the Ryshkewitch equation due to inaccurate true density

Although inaccurate true density affects analysis of powder compaction data, such effects have not been systematically evaluated in the literature. This work is aimed at quantitatively evaluating effects of inaccurate true density on tableting data analysis using the Ryshkewitch equation, σ = σ₀ e^-bε, where ε is tablet porosity, σ is tensile strength, σ₀ and b are constants that are used to characterize tableting properties of a powder. Mathematical expressions are derived to enable reliable prediction of the influence of inaccurate true density on σ₀ and b. The validity of the expressions is suggested by modeling the effects of inaccurate true density based on a set of accurate literature tableting data and confirmed using multiple sets of tableting data of water-containing powders that exhibit inaccurate helium pycnometry densities. Percentage errors in fitted σ⁰ and b as functions of errors in true density follow the derived mathematical expressions. With increasing percentage error in true density, percentage errors increase exponentially in fitted σ₀ and increase linearly in fitted b, while R² is not affected. According to the mathematical expressions, true density with <0.28% error is required to achieve 4% accuracy in fitted σ₀ for typical pharmaceutical powders.