Relation between local density and density relaxation near glass transition in a glass forming binary mixture

We employ molecular dynamics simulation to elucidate the microscopic origin of slow relaxation in supercooled Lennard-Jones liquids.These studies show a direct correlation between the growth of the highest peak of the radial distribution function g(r), radial force from this peak, and density relaxation. From the available free-volume of a neighboring pairs for string-like motion, we derive a relation between surface density of the spherical shell rho_{loc} around a reference particle at the highest peak of g(r)and density relaxation tau_alpha, i.e., tau_alpha propto exp (rho_0/(rho_0-rho_{loc})), where dynamics diverge at rho_0 that is akin to Vogel-Fulcher-Tammann (VFT) relation connecting tau_alpha and temperature. This relation works well in the supercooled regime of the model systems simulated.