Model of a fluid at small and large length scales and the hydrophobic effect

We present a statistical field theory to describe large length scale effects induced by solutes in a cold and otherwise placid liquid. The theory divides space into a cubic grid of cells. The side length of each cell is of the order of the bulk correlation length of the bulk liquid. Large length scale states of the cells are specified with an Ising variable. Finer length scale effects are described with a Gaussian field, with mean and variance affected by both the large length scale field and by the constraints imposed by solutes. In the absence of solutes and corresponding constraints, integration over the Gaussian field yields an effective lattice gas Hamiltonian for the large length scale field. In the presence of solutes, the integration adds additional terms to this Hamiltonian. We identify these terms analytically. They can provoke large length scale effects, such as the formation of interfaces and depletion layers. We apply our theory to compute the reversible work to form a bubble in liquid water, as a function of the bubble radius. Comparison with molecular simulation results for the same function indicates that the theory is reasonably accurate. Importantly, simulating the large length scale field involves binary arithmetic only. It thus provides a computationally convenient scheme to incorporate explicit solvent dynamics and structure in simulation studies of large molecular assemblies

Optimized random phase approximations for arbitrary reference systems: extremum conditions and thermodynamic consistence

The optimized random phase approximation (ORPA) for classical liquids is re-examined in the framework of the generating functional approach to the integral equations. We show that the two main variants of the approximation correspond to the addition of the same correction to two different first order approximations of the homogeneous liquid free energy. Furthermore, we show that it is possible to consistently use the ORPA with arbitrary reference systems described by continuous potentials and that the same approximation is equivalent to a particular extremum condition for the corresponding generating functional. Finally, it is possible to enforce the thermodynamic consistence between the thermal and the virial route to the equation of state by requiring the global extremum condition on the generating functional.Comment: 8 pages, RevTe

Transitions between Inherent Structures in Water

The energy landscape approach has been useful to help understand the dynamic properties of supercooled liquids and the connection between these properties and thermodynamics. The analysis in numerical models of the inherent structure (IS) trajectories -- the set of local minima visited by the liquid -- offers the possibility of filtering out the vibrational component of the motion of the system on the potential energy surface and thereby resolving the slow structural component more efficiently. Here we report an analysis of an IS trajectory for a widely-studied water model, focusing on the changes in hydrogen bond connectivity that give rise to many IS separated by relatively small energy barriers. We find that while the system \emph{travels} through these IS, the structure of the bond network continuously modifies, exchanging linear bonds for bifurcated bonds and usually reversing the exchange to return to nearly the same initial configuration. For the 216 molecule system we investigate, the time scale of these transitions is as small as the simulation time scale ($\approx 1$ fs). Hence for water, the transitions between each of these IS is relatively small and eventual relaxation of the system occurs only by many of these transitions. We find that during IS changes, the molecules with the greatest displacements move in small ``clusters'' of 1-10 molecules with displacements of $\approx 0.02-0.2$ nm, not unlike simpler liquids. However, for water these clusters appear to be somewhat more branched than the linear ``string-like'' clusters formed in a supercooled Lennar d-Jones system found by Glotzer and her collaborators.Comment: accepted in PR

Diffraction studies of ion--water interactions

Ionic solutions were among the first liquids to which x-ray diffraction was applied, and a large number of studies have been reported over the years. However, the interpretation of a single diffraction pattern is always difficult, often ambiguous, and never unique. This ambiguity of interpretation is greatly reduced if a solution is studied with several types of radiation (x-ray, neutron, electron), and a few such studies have been reported. The only currently feasible way of uniquely determining the correlations between water molecules and monatomic ions in solution is to vary the scattering factor of the ion; a simple difference measurement then yields the ion-water correlations. This has been done using the isotopic substitution method in neutron diffraction. It can also be done using synchrotron x-radiation and anomalous dispersion techniques. Diffraction studies of ion-water interactions have yielded detailed and unambiguous information for only a few concentrated solutions. 5 figures

Neutron scattering from solutions: the hydration of lanthanide and actinide ions

The neutron scattering difference method is described and applied to investigations of the aqua rare-earth ions, Nd/sup 3 +/ and Dy/sup 3 +/. Metal-water distances and hydration numbers have been unambiguously determined for these ions' inner coordination spheres. The values of the hydration number, n, of 8.5 +- 0.2 for Nd/sup 3 +/ and 7.4 +- 0.5 for Dy/sup 3 +/, directly support the claim of Spedding et al. that n decreases by one unit across the lanthanide series. The possible application of this method to actinide ions in solution is also discussed. 7 refs., 4 figs