A Family of Tunable Spherically-Symmetric Potentials that Span the Range from Hard Spheres to Water-like Behavior

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 $0\leq\lambda<6/7$. 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 water-like 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 water-like ($\lambda\sim4/7$) 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 $0\leq\lambda\leq1$, water-like 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 $\lambda=4/7$. Water-like anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, orientation-dependent interactions being absent by design.