13 research outputs found
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 ( 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 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
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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
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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