Equilibrium Glassy Phase in a Polydisperse Hard-Sphere System (original) (raw)

2005, Physical Review Letters

The phase diagram of a polydisperse hard sphere system is examined by numerical minimization of a discretized form of the Ramakrishnan-Yussouff free energy functional. Crystalline and glassy local minima of the free energy are located and the phase diagram in the density-polydispersity plane is mapped out by comparing the free energies of different local minima. The crystalline phase disappears and the glass becomes the equilibrium phase beyond a "terminal" value of the polydispersity. A crystal to glass transition is also observed as the density is increased at high polydispersity. The phase diagram obtained in our study is qualitatively similar to that of hard spheres in a quenched random potential. PACS numbers: 82.70.Dd, 64.70.Pf, 64.60.Cn Colloidal suspensions of polystyrene spheres coated with thin polymeric layers effectively behave as hard sphere systems[1], exhibiting fluid and crystalline phases in equilibrium. For such systems, glass (amorphous solid) is believed to be a metastable phase[2], resulting from structural arrest. However, in recent theoretical studies of hard spheres in the presence of a quenched random potential, an equilibrium glassy phase was observed at high disorder strengths. While this phenomenon has not yet been confirmed experimentally, it brings forth the question of whether even the presence of annealed disorder in a system of hard spheres can result in an equilibrium glassy phase. The annealed disorder can be realized if the hard spheres have different sizes, which is the case for most colloidal suspensions. The size dispersity can be modeled by assuming that the diameters (σ) are sampled from a continuous distribution p(σ), characterized by a parameter δ, known as the polydispersity, and defined as the ratio of the standard deviation and the mean of the diameter distribution. In this paper we present calculations that show that for a system of polydisperse hard spheres, one does obtain an equilibrium glassy phase. In fact, our results suggest that for hard spheres, quenched and annealed disorder lead to qualitatively similar phase behavior.