Metastable states of microgel fluids with Hertzian interaction potentials

We consider here a coarse-grained model for a soft matter system in which the particles interact with the Hertzian potential uH(r)=ϵ01−r/σμ, characterized by parameters {ϵ0,σ,μ}. Using the coarse-grained one-particle density ρ(x) as an order parameter, the free energy functional typical of the classical density functional theory (DFT) is studied. The static correlations of the uniform density state, required as an input in the DFT model, is calculated using the Bridge function method for the Hertzian fluid. The free energy functional analysis obtains new minima signifying metastable states between uniform liquid and the crystal. In particular, using classical DFT methods, a metastable amorphous state characterized by a low degree of mass localization is predicted. We obtain the transformation line on the density-temperature plot showing the possible liquid–liquid transition between the uniform liquid state and the inhomogeneous liquid state. With the increase of ϵ0 for the Hertzian interaction, the model reproduces the hard-sphere results.