Structure of the first- and second-neighbor shells of simulated water: Quantitative relation to translational and orientational order

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

Phys. Rev. E 76, 051201 – Published 9 November 2007

Abstract

We perform molecular dynamics simulations of water using the five-site transferable interaction potential (TIP5P) model to quantify structural order in both the first shell (defined by four nearest neighbors) and second shell (defined by twelve next-nearest neighbors) of a central water molecule. We find that the anomalous decrease of orientational order upon compression occurs in both shells, but the anomalous decrease of translational order upon compression occurs mainly in the second shell. The decreases of translational order and orientational order upon compression (called the “structural anomaly”) are thus correlated only in the second shell. Our findings quantitatively confirm the qualitative idea that the thermodynamic, structural, and hence dynamic anomalies of water are related to changes upon compression in the second shell.

Received 19 April 2007

DOI:https://doi.org/10.1103/PhysRevE.76.051201

Authors & Affiliations

Zhenyu Yan¹, Sergey V. Buldyrev^2,1, Pradeep Kumar¹, 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. 76, Iss. 5 — November 2007

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(Color online) Anomalous regions in the $T − ρ$ plane. (i) The density anomaly region is defined by the locus of density maxima (TMD), inside of which the density increases when the system is heated at constant pressure. (ii) The diffusion anomaly region is defined by the loci of diffusion maxima or minima (DM), inside which the diffusivity increases with density. (iii) The structural anomaly region is defined by the loci of translational order minima $(t_{\min})$ and maxima $(t_{\max})$ , or orientational order maxima $(q_{\max})$ , inside which both translational and orientational orders decrease with density (see Fig. 3).Reuse & Permissions
Figure 2
(a) The number of neighbors $N (r)$ around a central water molecule. $r_{1}$ and $r_{2}$ correspond to the first and the second shell distances, defined such that $N (r_{1}) = 4$ and $N (r_{2}) = 16$ . (b) Oxygen-oxygen pair correlation function $g (r)$ . (c) Difference $Δ g (r)$ between $g (r)$ at a given density and $g (r)$ at $ρ_{0}$ and (d) difference $Δ N (r)$ between $N (r)$ at a given density and $N (r)$ at $ρ_{0}$ for TIP5P water. $ψ$ characterizes the local slope. The bold portions of the curves correspond to water’s second shell, $r_{1} < r \leq r_{2}$ , showing that the largest changes upon compression occur in the second shell.Reuse & Permissions
Figure 3
Translational order parameters $t$ $(= t_{1} + t_{2} + t_{3})$ , $t_{1}$ (first shell), $t_{2}$ (second shell), $t_{3}$ and orientational order parameters $q$ (first shell), $Q_{6}$ (second shell) of TIP5P water as function of density at different $T$ . The anomalous decrease of orientational order upon compression occurs in both shells $(q, Q_{6})$ , but the anomalous decrease of translational order upon compression mainly occurs in the second shell $(t_{2})$ .Reuse & Permissions
Figure 4
Histograms of (a) the local orientational order $q_{i}$ in the first shell, (b) $Q_{6 i}$ in the second shell, and (c) distance $r_{5 i}$ between a central water molecule $i$ and its fifth neighbor of TIP5P water. (a), (b), and (c) show the changes for three different $ρ$ at fixed $T = 280 K$ . (d), (e), and (f) show the changes for three different $T$ at fixed $ρ = 1.00 g ∕ {cm}^{3}$ . Upon compression or heating over the anomalous regions of the phase diagram, the fifth neighbor (and other interstitial water molecules in the second neighbor shell) shift towards first shell (see also Fig. 2 and [7]), corresponding to anomalous changes of structural order in the first and second shells, as quantified by Figs. 3, 5.Reuse & Permissions
Figure 5
(Color online) Order maps for TIP5P water. The arrows indicate the direction of increasing density from $0.84 g ∕ {cm}^{3}$ to $1.32 g ∕ {cm}^{3}$ . Only for the second shell order map, $t_{2} − Q_{6}$ in (f), the isotherms collapse on a line and the decrease of translational and orientational orders is correlated.Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics