Packings of spheres serve as useful models of the geometry of many physical systems; in particular, the description of the void region in such packings ͑the region not occupied by the spheres͒ is crucial in many studies. The void region is, in general, composed of disconnected cavities. We present an algorithm for decomposing void space into cavities and determining the exact volumes and surface areas of such cavities in three-dimensional packings of monodisperse and polydisperse spheres. ͓S1063-651X͑97͒10711-5͔

Void-size distributions have been calculated for the shifted-force Lennard-Jones fluid over substantial temperature and density ranges, both for the liquid-state configurations themselves, as well as for their inherent structures ͑local potential energy minima͒. The latter distribution is far more structured than the former, displaying fcc-like short-range order, and a large-void tail due to system-spanning cavities. Either void distribution can serve as the basis for constraints that retain the liquid in metastable states of superheating or stretching by eliminating configurations that contain voids beyond an adjustable cutoff size. While acceptable cutoff sizes differ substantially in the two versions, ranges of choices have been identified yielding metastable equations of state that agree between the two approaches. Our results suggest that the structure-magnifying character of configuration mapping to inherent structures may be a useful theoretical and computational tool to identify the low-temperature mechanisms through which liquids and glasses lose their mechanical strength.

We revisit the successful scaled particle theory (SPT) of hard particle fluids, originally developed by Reiss, Frisch, and Lebowitz (J. Chem. Phys. 1959, 31, 369). In the initial formulation of SPT, five exact conditions were derived that constrained the form of the central function G. Only three of these conditions, however, were employed to generate an equation of state. Later, the number of relations used to determine G was increased to five (Mandell, M. J.; Reiss, H., J. Stat. Phys. 1975, 13, 113). The resulting equation of state was an improvement over the original formulation, although its accuracy was still limited at high densities. In an effort to increase the accuracy of SPT predictions, we propose two new formally exact conditions on the form of G. These sixth and seventh conditions relate exactly known derivatives of G to the slope and curvature of the hard sphere radial distribution function at contact, g‘(σ+) and g‘ ‘(σ+), respectively. To apply the new conditions, we derive, again within the framework of SPT, physically and geometrically based approximations to g‘(σ+) and g‘ ‘(σ+). These additional restrictions on the function G yield markedly improved predictions of the pressure, excess chemical potential, and work of cavity formation for the hard sphere fluid, now making SPT competitive with other existing equations of state.

For the superheated Lennard-Jones liquid, the free energy of forming a bubble with a given particle number and volume is calculated using density-functional theory. As conjectured, a consequence of known properties of the critical cavity [S. N. Punnathanam and D. S. Corti, J. Chem. Phys. 119, 10 224 (2003), the free energy surface terminates at a locus of instability. These stability limits reside, however, unexpectedly close to the saddle point. A new picture of homogeneous bubble nucleation and growth emerges from our study, being more appropriately described as an "activated instability."

Continued stresses on fresh water supplies necessitate the utilization of non-traditional resources to meet the growing global water demand. Desalination and hybrid membrane processes are capable of treating non-traditional water sources to the levels demanded by users. Specifically, desalination can produce potable water from seawater, and hybrid processes have the potential to recover valuable resources from wastewater while producing water of a sufficient quality for target applications. Despite the demonstrated successes of these processes, state-of-the-art membranes suffer from limitations that hinder the widespread adoption of these water treatment technologies. In this review, we discuss nanoporous membranes derived from self-assembled block polymer precursors for the purposes of water treatment. Due to their well-defined nanostructures, myriad chemical functionalities, and the ability to molecularly-engineer these properties rationally, block polymer membranes have the potential to advance water treatment technologies. We focus on block polymer-based efforts to: (1) nanomanufacture large areas of highperformance membranes; (2) reduce the characteristic pore size and push membranes into the reverse osmosis regime; and (3) design and implement multifunctional pore wall chemistries that enable solute-specific separations based on steric, electrostatic, and chemical affinity interactions. The use of molecular dynamics simulations to guide block polymer membrane design is also discussed because its ability to systematically examine the available design space is critical for rapidly translating fundamental understanding to water treatment applications. Thus, we offer a full review regarding the computational and experimental approaches taken in this arena to date while also providing insights into the future outlook of this emerging technology.