Fragility of a Generalized Hertz Potential System from Thermodynamic Perspective

We investigate the thermodynamic fragility of a system of soft spheres interacting through a purely repulsive and bounded generalized Hertz potential, where the interaction exponent controls the functional form of the repulsive interaction. The fragility is evaluated using its thermodynamic indicator, the configurational entropy, obtained within the framework of classical density functional theory (DFT). In DFT, the inhomogeneous density distribution of the amorphous solid is represented by localized density profiles around a set of lattice sites, with the underlying structure characterized through the pair correlation function. We determine the configurational entropy for different values of the interaction exponent of the generalized Hertz potential from the free energy obtained using DFT and extrapolate these results to estimate the Kauzmann temperature. We find that the Kauzmann temperature decreases with increasing interaction exponent. The variation of thermodynamic fragility with the interaction exponent is analyzed at different densities. In addition, the influence of the amorphous structure-dependent parameter used in the density functional calculation on the thermodynamic fragility is investigated.