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

Small and large hydrophobic solutes exhibit remarkably different hydration thermodynamics. Small solutes are accommodated in water with minor perturbations to water structure, and their hydration is captured accurately by theories that describe density fluctuations in pure water. In contrast, hydration of large solutes is accompanied by dewetting of their surfaces and requires a macroscopic thermodynamic description. A unified theoretical description of these lengthscale dependencies was presented by Lum, Chandler, and Weeks [(1999) J. Phys. Chem. B 103, 4570 -4577]. Here, we use molecular simulations to study lengthscale-dependent hydrophobic hydration under various thermodynamic conditions. We show that the hydration of small and large solutes displays disparate dependencies on thermodynamic variables, including pressure, temperature, and additive concentration. Understanding these dependencies allows manipulation of the small-tolarge crossover lengthscale, which is nanoscopic under ambient conditions. Specifically, applying hydrostatic tension or adding ethanol decreases the crossover length to molecular sizes, making it accessible to atomistic simulations. With detailed temperaturedependent studies, we further demonstrate that hydration thermodynamics changes gradually from entropic to enthalpic near the crossover. The nanoscopic lengthscale of the crossover and its sensitivity to thermodynamic variables imply that quantitative modeling of biomolecular self-assembly in aqueous solutions requires elements of both molecular and macroscopic hydration physics. We also show that the small-to-large crossover is directly related to the Egelstaff-Widom lengthscale, the product of surface tension and isothermal compressibility, which is another fundamental lengthscale in liquids. molecular dynamics ͉ salt and additive effects ͉ density fluctuations ͉ nonpolar solvation B iological self-assembly processes in aqueous solutions are driven by water-mediated interactions between constituents taking part in the assembly. Of these, hydrophobic interactions have received particular attention because of their relevance to protein folding and interactions, micelle and membrane formation, and molecular recognition (1-5). Theoretical work in this direction has been focused on the modeling of primitive hydrophobic phenomena, such as hydration and association of small hydrophobic particles in water (6-13). However, biological assembly occurs over a spectrum of lengthscales from that of an amino acid to proteins and larger. Naturally, fundamental understanding of the lengthscale dependence of hydration and association of hydrophobic solutes in water will be relevant to the quantitative modeling of realistic macromolecular processes (14,15).Small hydrophobic solutes can be accommodated into the open hydrogen-bonded network of liquid water without significant perturbations. Indeed, theories that model density fluctuations over small lengthscales in pure water provide a quantitative description of the hydration thermodynamics of small...

This paper examines the prospects for quantifying disorder in simple molecular or colloidal systems. As a central element in this task, scalar measures for describing both translational and bond-orientational order are introduced. These measures are subsequently used to characterize the structures that result from a series of molecular-dynamics simulations of the hard-sphere system. The simulation results can be illustrated by a two-parameter ordering phase diagram, which indicates the relative placement of the equilibrium phases in order-parameter space. Moreover, the diagram serves as a useful tool for understanding the effect of history on disorder in nonequilibrium structures. Our investigation provides fresh insights into the types of ordering that can occur in equilibrium and glassy systems, including quantitative evidence that, at least in the case of hard spheres, contradicts the notion that glasses are simply solids with the "frozen in" structure of an equilibrium liquid. Furthermore, examination of the order exhibited by the glassy structures suggests, to our knowledge, a new perspective on the old problem of random close packing.

We study the diffusive dynamics of a hard-sphere fluid confined between parallel smooth hard walls. The position-dependent diffusion coefficient normal to the walls is larger in regions of high local packing density. High density regions also have the largest available volume, consistent with the fast local diffusivity. Indeed, local and global diffusivities as a function of the Widom insertion probability approximately collapse onto a master curve. Parallel and average normal diffusivities are strongly coupled at high densities and deviate from bulk fluid behavior.

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