Family of tunable spherically symmetric potentials that span the range from hard spheres to waterlike behavior

Abstract

We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, $\lambda$. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for $0⩽\lambda <6∕7$. As in water, the regions where these anomalies occur are nested domes in the $(T,\rho )$ or $(T,P)$ planes, with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters ($t$ and $Q_6$), and project equilibrium state points onto the $(t,Q_6)$ plane, or order map. The order map evolves from waterlike behavior to hard-sphere-like behavior upon varying $\lambda$ between $4∕7$ and $6∕7$. Thus, we traverse the range of liquid behavior encompassed by hard spheres $(\lambda =1)$ and waterlike $(\lambda \sim 4∕7)$ with a family of tunable spherically symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range $0⩽\lambda ⩽1$, waterlike structural anomalies (i.e., decrease in both $t$ and $Q_6$ upon compression and strictly correlated $t$ and $Q_6$ in the anomalous region) occur only around $\lambda =4∕7$. Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio $\lambda$ being the single control parameter, orientation-dependent interactions being absent by design.