Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.

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.

Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm. We suggest that this impasse can be broken by introducing the new concept of a maximally random jammed state, which can be made precise. 5.20.-y, 61.20.-p

Cold, noncrystalline states play an important role in understanding the physics of liquid water. From recent experimental and theoretical investigations, a coherent interpretation of water's properties is beginning to emerge.

Most materials attain a glassy state at low temperatures under suitable methods of preparation. This state exhibits the mechanical properties of a solid, but shows microscopic structural disorder 1,2 . A comprehensive understanding of the glassy state is, however, still lacking 3 . A widespread assumption is that the nonexponential relaxation processes observed in the dynamics of glasses-and also in protein dynamics, protein folding and population dynamics-are (in common with other manifestations of complex dynamics) strongly influenced by the underlying energy landscape associated with the structural configurations that the system may adopt. But concrete evidence for this in studies of glass formation has been scarce. Here we present such evidence, obtained from computer simulations of a model glassforming liquid. We demonstrate that the onset of non-exponential relaxation corresponds to a well defined temperature below which the depth of the potential-energy minima explored by the liquid increases with decreasing temperature, and above which it does not. At lower temperatures, we observe a sharp transition when the liquid gets trapped in the deepest accessible energy basin. This transition temperature depends on the cooling rate, in a manner analogous to the experimental glass transition. We also present evidence that the barrier heights separating potential-energy minima sampled by the liquid increase abruptly at a temperature above the glass transition but well below the onset of non-exponential relaxation. This identification of a relationship between static, topographic features of the energy landscape and complex dynamics holds letters to nature 554 NATURE | VOL 393 | 11 JUNE 1998 0.0 0.5 1.0 1.5 2.0 Temperature -7.05 -7.00 -6.95 -6.90 Energy Cooling rate = 1.08 ×10 -3 Cooling rate = 2.70 ×10 -4 Cooling rate = 8.33 ×10 -5Cooling rate = 3.33 ×10 -6 a Figure 1 Molecular dynamics simulations of a binary Lennard-Jones mixture 21 . 80% of the particles are of type A, 20% are type B, and Lennard-Jones parameters are e AA ¼ 1:0, e AB ¼ 1:5, e BB ¼ 0:5, j AA ¼ 1:0, j AB ¼ 0:8 and j BB ¼ 0:88. All quantities are in reduced units: length in units of j AA , temperature in units of e AA /k B , and time in units of (j 2 AA m/e AA ) 1/2 , where m is the mass of the particles. The density r in all cases is 1.2. The calculated pressures for the system remain positive except for T Ͻ 0:06, much below temperatures where the system forms a glass in all cases studied. The Lennard-Jones potential, with a quadratic cut-off and shifting of the potential at r ab c ¼ 2:5j ab (ref. 29), a; b ʦ A; B is used. Our cut-off procedure results in a potential minimum value which is ϳ4% smaller than that in ref. 21. The time step is dt ¼ 0:003. Each run was initialized by equilibration at a high temperature, followed by equilibration and data collection runs at a series of temperatures. The run length at each temperature, together with the number of temperatures chosen, determines the cooling rate. Equilibration was done at constant temperat...