General and mechanistic optimal relationships for tensile strength of doubly convex tablets under diametrical compression

TL;DR

This paper introduces a comprehensive framework for deriving optimal tensile strength relationships for doubly convex tablets under diametrical compression, unifying existing models and proposing new predictive models based on experimental optimization.

Contribution

It develops a general and mechanistic approach to model tensile strength, integrating and extending existing empirical and analytical models for convex tablets.

Findings

Derived a unified framework encompassing Hertz and Pitt's equations.

Identified two new effective and predictive tensile strength models.

Provided guidelines for assessing and optimizing tensile strength relationships.

Abstract

We propose a general framework for determining optimal relationships for tensile strength of doubly convex tablets under diametrical compression. This approach is based on the observation that tensile strength is directly proportional to the breaking force and inversely proportional to a non-linear function of geometric parameters and materials properties. This generalization reduces to the analytical expression commonly used for flat faced tablets, i.e., Hertz solution, and to the empirical relationship currently used in the pharmaceutical industry for convex-faced tablets, i.e., Pitt's equation. Under proper parametrization, optimal tensile strength relationship can be determined from experimental results by minimizing a figure of merit of choice. This optimization is performed under the first-order approximation that a flat faced tablet and a doubly curved tablet have the same tensile strength if they have the same relative density and are made of the same powder, under equivalent manufacturing conditions. Furthermore, we provide a set of recommendations and best practices for assessing the performance of optimal tensile strength relationships in general. Based on these guidelines, we identify two new models, namely the general and mechanistic models, which are effective and predictive alternatives to the tensile strength relationship currently used in the pharmaceutical industry.