Fracture in disordered media and tensile strength of microcrystalline cellulose tablets at low relative densities.

The purpose of this study is to establish a theoretical basis for the tensile strength of low density tablets. In a first step, a lattice model based on percolation theory is presented. As a theoretical result, a power law is obtained for the lattice strength. The exponent in this law is expected to be universal and as a numerical value Tf congruent with 2.7 is proposed. The result is identical with an earlier theoretical finding from an alternative approach proposed by. In a second step, the new model equation is applied to the tensile strength of low density tablets. The compacts were manufactured and tested with an universal testing instrument Zwick UPM 1478 (Zwick-Roell). Different types of microcrystalline cellulose Emcocel 50M, Emcocel 90M, Avicel PH101 and Avicel PH102 were assayed as model excipients because of their ability to form tablets at comparatively low relative densities (rhor). For determination of the tensile strength, two different strain rates 0.5 and 25 mm min-1 were examined. All experimentally determined exponents were in the same range with an average of Tf=3.2+/-0.1 and the critical solid fractions (rhorc), yielded values close the relative bulk densities. In a third step, the new model is compared to the Ryshkewitch-Duckworth equation. This exponential relationship of the tensile strength and porosity was found to have an inferior fitting adequacy than the new power law. As a conclusion, the lattice model presented is able to explain the power law behaviour of the tensile strength as a function of the relative density with an exponent close to three. The expected universal character of this exponent was supported by the results of the assayed substances at two different strain rates. Plus, in the case of the tested substances, the new relationship between the tensile strength and the relative density should be preferred to the often used exponential function. However, further studies have to be conducted to know more about the validity of the new model.