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

Zhenyu Yan, Sergey V. Buldyrev, Nicolas Giovambattista, Pablo G. Debenedetti, and H. Eugene Stanley

Phys. Rev. E 73, 051204 – Published 17 May 2006

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, $λ$ . We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for $0 ⩽ λ < 6 ∕ 7$ . As in water, the regions where these anomalies occur are nested domes in the $(T, ρ)$ 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 $λ$ between $4 ∕ 7$ and $6 ∕ 7$ . Thus, we traverse the range of liquid behavior encompassed by hard spheres $(λ = 1)$ and waterlike $(λ \sim 4 ∕ 7)$ 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 $0 ⩽ λ ⩽ 1$ , 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 $λ = 4 ∕ 7$ . Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio $λ$ being the single control parameter, orientation-dependent interactions being absent by design.

Received 24 January 2006

DOI:https://doi.org/10.1103/PhysRevE.73.051204

Authors & Affiliations

Zhenyu Yan¹, Sergey V. Buldyrev^2,1, Nicolas Giovambattista³, Pablo G. Debenedetti³, and H. Eugene Stanley¹

¹Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA
²Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA
³Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 73, Iss. 5 — May 2006

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The middle figure shows the ramp potential with two characteristic length scales; $σ_{0}$ corresponds to the hard core, $σ_{1}$ characterizes the onset of soft repulsion. When $λ = 0$ (left figure) we have a pure ramp potential (no hard core). When $λ = 1$ (right figure) we have a hard sphere potential. $λ_{c} \sim 0.6$ is the ratio near which the system exhibits waterlike structural, dynamic and thermodynamic behavior.Reuse & Permissions
Figure 2
Radial distribution function $g (r)$ at $T = 0.04$ for different $λ \equiv σ_{0} ∕ σ_{1}$ values. The arrows indicate the direction of increasing density. The density values are 1.0, 1.21, 1.66, 2.19 for $λ = 2 ∕ 7, 4 ∕ 7, 5 ∕ 7$ and 1.0, 1.21, 1.66, 1.86 for $λ = 0, 6 ∕ 7$ . The distance $r$ is normalized by $σ_{1}$ , the soft core length. The curves for different $λ$ are shifted vertically by integer numbers for clarity.Reuse & Permissions
Figure 3
The upper and lower panels (a1)-(e1) and (a2)-(e2) show the density dependence of the translational order parameter $t$ and orientational order parameter $Q_{6}$ for $λ = 0$ (a1, a2), $2 ∕ 7$ (b1, b2), $4 ∕ 7$ (c1, c2), $5 ∕ 7$ (d1, d2), and $6 ∕ 7$ (e1, e2). The solid lines are polynomial fits to the data. In each panel, the different curves correspond to isotherms (top to bottom) $T = 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10$ .Reuse & Permissions
Figure 4
Order map of the ramp fluid for different $λ$ . For each $λ$ , the eight isotherms (right to left) correspond to $T = 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10$ , and the arrow indicates the direction of increasing density.Reuse & Permissions
Figure 5
Loci of thermodynamic and dynamic anomalies for ramp fluids with different $λ$ values. The region of diffusion anomalies is defined by the loci of diffusion minima and maxima (DM) inside which the diffusivity increases upon isothermal compression. The thermodynamically anomalous region is defined by the locus of temperatures of maximum density (TMD), inside of which the density increases when the system is heated at constant pressure.Reuse & Permissions
Figure 6
Relationship between structural order and the density and diffusion anomalies in the $ρ - T$ plane. For $λ = 0$ and $2 ∕ 7$ , the domes of dynamic and thermodynamic anomalies are bounded by loci of $t$ maxima (C) and minima (A), between which isothermal compression causes a decrease in translational order. For $λ = 4 ∕ 7$ and $5 ∕ 7$ , the domes of dynamic and thermodynamic anomalies are bounded by loci of $Q_{6}$ maxima (B) and $t$ minima (A), between which isothermal compression causes a decrease in both translational and orientational order (structural anomaly). This cascade of anomalies is characteristic of water.Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics