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 tensi le 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 T(f)congruent to 2.7 is proposed. Th e result is identical with an earlier theoretical finding from an alternati ve approach proposed by Guyon et al. (1987). In a second step, the new mode l equation is applied to the tensile strength of low density tablets. The c ompacts were manufactured and tested with an universal testing instrument Z wick(R) UPM 1478 (Zwick-Roell). Different types of microcrystalline cellulo se Emcocel(R) 50M, Emcocel(R) 90M, Avicel(R) PH101 and Avicel(R) PH102 were assayed as model excipients because of their ability to form tablets at co mparatively low relative densities (rho(r)). For determination of the tensi le 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 av erage of (T) over bar(f) = 3.2 +/- 0.1 and the critical solid fractions (rh o(rc)), yielded values close the relative bulk densities. In a third step, the new model is compared to the Ryshkewitch-Duckworth equation. This expon ential relationship of the tensile strength and porosity was found to have an inferior fitting adequacy than the new power law. As a conclusion, the l attice model presented is able to explain the power law behaviour of the te nsile 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. Plu s, in the case of the tested substances, the new relationship between the t ensile strength and the relative density should be preferred to the often u sed exponential function. However, further studies have to be conducted to know more about the validity of the new model. (C) 1999 Elsevier Science B. V. All rights reserved.