Diffusion anomaly in a three-dimensional lattice gas

We investigate the relationship between thermodynamic and dynamic properties of an associating lattice-gas (ALG) model. The ALG combines a three-dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom. The competition between the directional attractive forces and the soft core potential results in two liquid phases, double criticality and density anomaly. We study the mobility of the molecules in this model by calculating the diffusion constant at a constant temperature, D. We show that D has a maximum at a density ρ_max and a minimum at a density ρ_min<ρ_max. Between these densities the diffusivity differs from the one expected for normal liquids. We also show that in the pressure-temperature phase-diagram the line of extrema in diffusivity is close to the liquid-liquid critical point and it is partially inside the temperature of maximum density (TMD) line.