Correlation between kinetic fragility and Poisson's ratio from analysis of data for soft colloids

Abstract

We consider the link between fragility and elasticity that follows from the analysis of the data for a set of soft colloid materials consisting of deformable spheres reported by [Mattsson et al., Nature, 2009, 462, 83]. The present work makes a quantitative analysis through an explicit definition for fragility index m in terms of density dependence, extending the corresponding formula of m for molecular systems in terms of temperature dependence. In addition, we fit the data for the high-frequency shear modulus for the respective soft-colloid to a corresponding theoretical expression for the same modulus. This expression for the elastic constant is in terms of the corresponding pair correlation function for the liquid treated as of uniform density. The pair correlation function is adjusted through a proper choice of the parameters for the two body interaction potential for the respective soft-colloid material. The nature of correlation between the fragility and Poisson ratio observed for the soft colloids is qualitatively different, as compared to the same for molecular glasses. The observed link between fragility of a metastable liquid and its elastic coefficients is a manifestation of the effects of structure of the fluid on its dynamics. The present work thus analyses the data on soft colloids and by introducing definitions from statistical mechanics obtains a correlation between kinetic fragility and Poissons's ratio for the soft material.