Diffusion Anomaly in a three dimensional lattice gas

We investigate the relation 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. From the competition between the directional attractive forces and the soft core potential results 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 $\rho_{max}$ and a minimum at a density $\rho_{min}<\rho_{max}$. 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.