Modified Young's modulus of microcrystalline cellulose tablets and the directed continuum percolation model

The purpose of this investigation was to analyze the modified Young's modulus of microcrystalline cellulose tablets at comparatively low relative densities, based on concepts of percolation theory. Tablets were prepared and tested using a Zwick 1478 universal testing instrument. For statistical evaluation a new method is introduced for power laws, which exhibits highly correlated model parameters. According to our results the model Leuenberger, Leu is consistent with an Effective Medium Approximation which exhibits an exponent equal to one far away from the percolation threshold. In addition, the results show that it is essential to evaluate the elastic behavior of tablets close to the percolation threshold. For the different types of MCC a critical exponent q = 3.95 +/- 0.14 was obtained. This result is very essential, as it is in good agreement with the theoretically expected value of 3.9 from an elastic network (central force model). The proposed model describes the modified Young's modulus better than former model equations taking into account the relative density. Thus, the process during uniaxial compaction can be imagined as a directed continuum percolation and the relative density of compacts can be identified as a space-occupation probability density phi yielding reasonable percolation thresholds.