--- trunk/langevinHull/langevinHull.tex	2010/11/17 20:59:25	3701
+++ trunk/langevinHull/langevinHull.tex	2011/01/12 22:03:36	3713
@@ -431,7 +431,7 @@ The region we used is a spherical volume of 10 \AA\ ra
 )_{T}.
 \label{eq:BMN}
 \end{equation}
-The region we used is a spherical volume of 10 \AA\ radius centered in
+The region we used is a spherical volume of 20 \AA\ radius centered in
 the middle of the cluster. $N$ is the average number of molecules
 found within this region throughout a given simulation. The geometry
 and size of the region is arbitrary, and any bulk-like portion of the
@@ -518,7 +518,7 @@ the total surface area of the cluter exposed to the ba
 temperature respond to the Langevin Hull for nanoparticles that were
 initialized far from the target pressure and temperature.  As
 expected, the rate at which thermal equilibrium is achieved depends on
-the total surface area of the cluter exposed to the bath as well as
+the total surface area of the cluster exposed to the bath as well as
 the bath viscosity.  Pressure that is applied suddenly to a cluster
 can excite breathing vibrations, but these rapidly damp out (on time
 scales of 30 -- 50 ps).
@@ -613,7 +613,7 @@ the water molecules on the surfaces of the clusterss w
 hydrophobic boundary, or orientational or radial constraints.
 Therefore, the orientational correlations of the molecules in water
 clusters are of particular interest in testing this method.  Ideally,
-the water molecules on the surfaces of the clusterss will have enough
+the water molecules on the surfaces of the clusters will have enough
 mobility into and out of the center of the cluster to maintain
 bulk-like orientational distribution in the absence of orientational
 and radial constraints.  However, since the number of hydrogen bonding
@@ -655,41 +655,70 @@ forming a dangling hydrogen bond acceptor site.
 orientations. Molecules included in the convex hull show a slight
 preference for values of $\cos{\theta} < 0.$ These values correspond
 to molecules with oxygen directed toward the exterior of the cluster,
-forming a dangling hydrogen bond acceptor site.
+forming dangling hydrogen bond acceptor sites.
 
-The orientational preference exhibited by liquid phase hull molecules in the Langevin Hull is significantly weaker than the preference caused by an explicit hydrophobic bounding potential.  Additionally, the Langevin Hull does not require that the orientation of any molecules be fixed in order to maintain bulk-like structure, even at the cluster surface.
+The orientational preference exhibited by water molecules on the hull
+is significantly weaker than the preference caused by an explicit
+hydrophobic bounding potential.  Additionally, the Langevin Hull does
+not require that the orientation of any molecules be fixed in order to
+maintain bulk-like structure, even near the cluster surface.
 
-Previous molecular dynamics simulations
-of SPC/E water using periodic boundary conditions have shown that molecules on the liquid side of the liquid/vapor interface favor a similar orientation where oxygen is directed away from the bulk.\cite{Taylor1996} These simulations had both a liquid phase and a well-defined vapor phase in equilibrium and showed that vapor molecules generally had one hydrogen protruding from the surface, forming a dangling hydrogen bond donor. Our water cluster simulations do not have a true lasting vapor phase, but rather a few transient molecules that leave the liquid droplet. Thus while we are unable to comment on the orientational preference of vapor phase molecules in a Langevin Hull simulation, we achieve good agreement for the orientation of liquid phase molecules at the interface.
+Previous molecular dynamics simulations of SPC/E liquid / vapor
+interfaces using periodic boundary conditions have shown that
+molecules on the liquid side of interface favor a similar orientation
+where oxygen is directed away from the bulk.\cite{Taylor1996} These
+simulations had well-defined liquid and vapor phase regions
+equilibrium and it was observed that {\it vapor} molecules generally
+had one hydrogen protruding from the surface, forming a dangling
+hydrogen bond donor. Our water clusters do not have a true vapor
+region, but rather a few transient molecules that leave the liquid
+droplet (and which return to the droplet relatively quickly).
+Although we cannot obtain an orientational preference of vapor phase
+molecules in a Langevin Hull simulation, but we do agree with previous
+estimates of the orientation of {\it liquid phase} molecules at the
+interface.
 
 \subsection{Heterogeneous nanoparticle / water mixtures}
 
 To further test the method, we simulated gold nanopartices ($r = 18$
-\AA) solvated by explicit SPC/E water clusters using the Langevin
-Hull.  This was done at pressures of 1, 2, 5, 10, 20, 50, 100 and 200 atm
-in order to observe the effects of pressure on the ordering of water
-ordering at the surface.  In Fig. \ref{fig:RhoR} we show the density
-of water adjacent to the surface and
-the density of gold at the surface as a function of pressure.
+\AA) solvated by explicit SPC/E water clusters using a model for the
+gold / water interactions that has been used by Dou {\it et. al.} for
+investigating the separation of water films near hot metal
+surfaces.\cite{ISI:000167766600035} The Langevin Hull was used to
+sample pressures of 1, 2, 5, 10, 20, 50, 100 and 200 atm, while all
+simulations were done at a temperature of 300 K.   At these
+temperatures and pressures, there is no observed separation of the
+water film from the surface.  
 
-Higher applied pressures de-structure the outermost layer of the gold nanoparticle and the water at the metal/water interface. Increased pressure shows more overlap of the gold and water densities, indicating a less well-defined interfacial surface.
+In Fig. \ref{fig:RhoR} we show the density of water and gold as a
+function of the distance from the center of the nanoparticle.  Higher
+applied pressures appear to destroy structural correlations in the
+outermost monolayer of the gold nanoparticle as well as in the water
+at the near the metal / water interface.  Simulations at increased
+pressures exhibit significant overlap of the gold and water densities,
+indicating a less well-defined interfacial surface.
 
 \begin{figure}
 \includegraphics[width=\linewidth]{RhoR}
-\caption{Densities of gold and water at the nanoparticle surface. Higher applied pressures de-structure both the gold nanoparticle surface and water at the metal/water interface.}
+\caption{Density profiles of gold and water at the nanoparticle
+  surface. Each curve has been normalized by the average density in
+  the bulk-like region available to the corresponding material.  Higher applied pressures
+  de-structure both the gold nanoparticle surface and water at the
+  metal/water interface.}
 \label{fig:RhoR}
 \end{figure}
 
-At higher pressures, problems with the gold - water interaction
-potential became apparent.  The model we are using (due to Spohr) was
-intended for relatively low pressures; it utilizes both shifted Morse
-and repulsive Morse potentials to model the Au/O and Au/H
-interactions, respectively.  The repulsive wall of the Morse potential
-does not diverge quickly enough at short distances to prevent water
-from diffusing into the center of the gold nanoparticles.  This
-behavior is likely not a realistic description of the real physics of
-the situation.  A better model of the gold-water adsorption behavior
-appears to require harder repulsive walls to prevent this behavior.
+At even higher pressures (500 atm and above), problems with the metal
+- water interaction potential became quite clear.  The model we are
+using appears to have been parameterized for relatively low pressures;
+it utilizes both shifted Morse and repulsive Morse potentials to model
+the Au/O and Au/H interactions, respectively.  The repulsive wall of
+the Morse potential does not diverge quickly enough at short distances
+to prevent water from diffusing into the center of the gold
+nanoparticles.  This behavior is likely not a realistic description of
+the real physics of the situation.  A better model of the gold-water
+adsorption behavior appears to require harder repulsive walls to
+prevent this behavior.
 
 \section{Discussion}
 \label{sec:discussion}