In contrast to crystalline solids--for which a precise framework exists for describing structure--quantifying structural order in liquids and glasses has proved more difficult because even though such systems possess short-range order, they lack long-range crystalline order. Some progress has been made using model systems of hard spheres, but it remains difficult to describe accurately liquids such as water, where directional attractions (hydrogen bonds) combine with short-range repulsions to determine the relative orientation of neighbouring molecules as well as their instantaneous separation. This difficulty is particularly relevant when discussing the anomalous kinetic and thermodynamic properties of water, which have long been interpreted qualitatively in terms of underlying structural causes. Here we attempt to gain a quantitative understanding of these structure-property relationships through the study of translational and orientational order in a models of water. Using molecular dynamics simulations, we identify a structurally anomalous region--bounded by loci of maximum orientational order (at low densities) and minimum translational order (at high densities)--in which order decreases on compression, and where orientational and translational order are strongly coupled. This region encloses the entire range of temperatures and densities for which the anomalous diffusivity and thermal expansion coefficient of water are observed, and enables us to quantify the degree of structural order needed for these anomalies to occur. We also find that these structural, kinetic and thermodynamic anomalies constitute a cascade: they occur consecutively as the degree of order is increased.

Relationship between structural order and the anomalies of liquid water

Introduction to Geometry. By H. S. M. Coxeter. Pp. xiv, 443. 1961. (John Wiley)

A new order parameter, S, is introduced to test for tetrahedral configurations. It is applied to analyse the results of three simulations: (1) molecular dynamics simulation of ice Ih (hexagonal ice) at 200 K, using the SPC/E water potential; (2) Monte Carlo simulation of aqueous solution of methane, using the OPLS methane potential and the TIP4P water potential; and (3) Monte Carlo simulation of Lennard-Jones spheres. The quasi-tetrahedral configurations of water molecules in different states can be adequately described using S.

A new order parameter for tetrahedral configurations

Introduction 1. Packaging and covering densities 2. The existence of reasonably dense packings 3. The existence of reasonably economical coverings 4. The existence of reasonably dense lattice packings 5. The existence of reasonably economical lattice coverings 6. Packings of simplices cannot be very dense 8. Coverings with spheres cannot be very economical Bibliography Index.

Packing and Covering. By C. A. Rogers. Pp. viii, 111. 30s. 1964. (Cambridge)

Glasses are generally prepared by cooling from the liquid phase, and their properties depend on their thermal history. Recent experiments indicate that glasses prepared by vapour deposition onto a substrate can exhibit remarkable stability, and might correspond to equilibrium states that could hitherto be reached only by glasses aged for thousands of years. Here we create ultrastable glasses by means of a computer-simulation process that mimics physical vapour deposition. These stable glasses have, far below the conventional glass-transition temperature, the properties expected for the equilibrium supercooled liquid state, and optimal stability is attained when deposition occurs at the Kauzmann temperature. We also show that the glasses' extraordinary stability is associated with distinct structural motifs, in particular the abundance of regular Voronoi polyhedra and the relative lack of irregular polyhedra.

Ultrastable glasses from in silico vapour deposition

The problem of searching for quantitative laws governing the structure of simple liquids is formulated as a site percolation problem on the Voronoi network. The sites of this four-coordinated network correspond to the figures formed by the four neighbouring atoms (Delaunay simplices). Three quantitative characteristics of the form of the Delaunay simplices are introduced to enable one to colour the sites of the Voronoi network corresponding to the simplices of a specific form and to study the percolation of colouring through the network sites. The clusters of contiguous Delaunay simplices of the specific form have been studied and the percolation thresholds for various colouring types have been obtained for instantaneous configurations of the Lennard-Jones liquid (obtained by the Monte Carlo procedure) as well as for the configurations with removed thermal excitations (F structure). Percolation of all the types of colouring introduced turns out to be correlated, i.e., the Delaunay simplices of a given for...

Geometrical analysis of the structure of simple liquids : percolation approach

Various hydrogen bond lifetime distribution functions, used to describe the breaking and formation dynamics of these bonds in a computer experiment, are examined and relationships between them are found. The procedures for calculating these functions by the molecular dynamics method are described and the results for water models of 3456 molecules at 310 K are reported. The peak of short-lived spurious H-bonds, which results from short-time violations of hydrogen bonding criteria induced by dynamic intermolecular vibrations of molecules, prevails in the types of distributions most often referred to in the literature. A special distribution that appears to have not been used before is proposed. Along with short-lived bonds, it manifests long-lived ones whose lifetime is determined by the genuine, or random, hydrogen bond breaking rather than by dynamic. A technique to exclude dynamic effects and reveal the genuine H-bond breaking is proposed. This allows the evaluation of the average lifetime of “true” H-bonds that turns out to exceed 3 ps.

Hydrogen bond lifetime distributions in computer-simulated water

One-dimensional and two-dimensional distributions of the characteristics introduced previously for the forms of Delaunay simplices - tetrahedricity and octahedricity - have been investigated in computer models of a crystal, a liquid and an amorphous solid. It has been established that in the absence of thermal perturbations (in the proper structure of the liquid and in an amorphous substance) there exists a distinguishable class of simplices with five almost equal edges and the sixth being longer. This class of simplices named isopentacmons, in turn includes the types of good tetrahedra and good quartoctahedra (a quarter of octahedron). In disordered systems the fraction of tetrahedra relative to quartoctahedra exceeds substantially that in the FCC crystal.

Can Various Classes of Atomic Configurations (Delaunay Simplices) be Distinguished in Random Dense Packings of Spherical Particles

It is suggested to define the cavities that make up the empty interatomic space of any atomic model as associated overlapping interstitial spheres. The latter are determined unambiguously by the atomic arrangement with the help of the Voronoi-Delaunay methods for the division of space into polyhedra. Thus any complex cavity may be represented as a cluster of contiguous Delaunay simplices. These clusters are revealed by percolation analysis with the application of a special ' delta colouring' of the Voronoi network bonds. This paper presents a classification of all complex cavities discovered in computer models of crystals, liquids and amorphous solids. The number of cavity types is rather large and does not reduce to, say, the five canonical holes of Bernal. The latter occupy less than half of the volume. The greater part of the cavities represent branched chains with built-in rings of simplicial holes, octahedra and so on. Large clusters of more than 10 simplices are characteristic of liquids but they do not occur in amorphous solids.

http://iopscience.iop.org/article/10.1088/0953-8984/5/32/001/pdf

Empty interatomic space in computer models of simple liquids and amorphous solids

This paper is a review of our recent computational studies of volumetric characteristics using computer models of dilute solutions. Partial molar volume (PMV) and its components are calculated for simple and complex molecules in water (methane, noble gases, surfactants, polypeptides). Advantages and disadvantages of various computational methods are discussed. It is proposed to use the Voronoi-Delaunay technique to determine the reasonable boundary between a solute molecule and solvent molecules and to identify the PMV components related to the molecule, the boundary layer, and the solvent. It is noted that the observed increase in PMV with temperature for large molecules is due to an increase in the volume of voids in the boundary layer, i.e., due to the “thermal volume.” In this case, the solvent gives a negative contribution to the PMV. In contrast, for simple molecules (methane), the contribution from the solvent is positive and is the main factor in the increase in the PMV, which is associated with a specific change in water structure around a spherical hydrophobic particle outside the boundary layer. For surfactant molecules, the contribution from the solvent changes sign (from negative to positive) with increasing temperature.

V. P. Voloshin

Papers

Geometrical analysis of the structure of simple liquids : percolation approach

Hydrogen bond lifetime distributions in computer-simulated water

Can Various Classes of Atomic Configurations (Delaunay Simplices) be Distinguished in Random Dense Packings of Spherical Particles

Empty interatomic space in computer models of simple liquids and amorphous solids

Culation of partial molar volume and its components for molecular dynamics models of dilute solutions