--- trunk/langevinHull/langevinHull.tex	2011/02/16 22:13:56	3722
+++ trunk/langevinHull/langevinHull.tex	2011/02/18 14:08:15	3723
@@ -496,7 +496,8 @@ different radii under the Langevin Hull at a variety o
 periodic-boundary simulations of the bulk crystal have yielded values
 of 175.53 GPa.\cite{QSC2} Using the same force field, we have
 performed a series of 1 ns simulations on gold nanoparticles of three
-different radii under the Langevin Hull at a variety of applied
+different radii: 20 \AA~ (1985 atoms), 30 \AA~ (6699 atoms), and 40
+\AA~ (15707 atoms) utilizing the Langevin Hull at a variety of applied
 pressures ranging from 0 -- 10 GPa.  For the 40 \AA~ radius
 nanoparticle we obtain a value of 177.55 GPa for the bulk modulus of
 gold, in close agreement with both previous simulations and the
@@ -614,21 +615,23 @@ compressibilities. We achieved the best results using 
 effects of the empty space due to the vapor phase; for this reason, we
 recommend using the number density (Eq. \ref{eq:BMN}) or number
 density fluctuations (Eq. \ref{eq:BMNfluct}) for computing
-compressibilities. We achieved the best results using a sampling
-radius approximately 80\% of the cluster radius. This ratio of
-sampling radius to cluster radius excludes the problematic vapor phase
-on the outside of the cluster while including enough of the liquid
-phase to avoid poor statistics due to fluctuating local densities.
+compressibilities.  We obtained the results in
+Fig. \ref{fig:compWater} using a sampling radius that was
+approximately 80\% of the mean distance between the center of mass of
+the cluster and the hull atoms.  This ratio of sampling radius to
+average hull radius excludes the problematic vapor phase on the
+outside of the cluster while including enough of the liquid phase to
+avoid poor statistics due to fluctuating local densities.
 
 A comparison of the oxygen-oxygen radial distribution functions for
-SPC/E water simulated using the Langevin Hull and bulk SPC/E using
-periodic boundary conditions -- both at 1 atm and 300K -- reveals an
-understructuring of water in the Langevin Hull that manifests as a
-slight broadening of the solvation shells. This effect may be related
-to the introduction of surface tension around the entire cluster, an
-effect absent in bulk systems. As a result, molecules on the hull may
-experience an increased inward force, slightly compressing the
-solvation shell for these molecules.
+SPC/E water simulated using both the Langevin Hull and more
+traditional periodic boundary methods -- both at 1 atm and 300K --
+reveals an understructuring of water in the Langevin Hull that
+manifests as a slight broadening of the solvation shells.  This effect
+may be due to the introduction of a liquid-vapor interface in the
+Langevin Hull simulations (an interface which is missing in most
+periodic simulations of bulk water).  Vapor-phase molecules contribute
+a small but nearly flat portion of the radial distribution function.
 
 \subsection{Molecular orientation distribution at cluster boundary}
 
@@ -715,14 +718,14 @@ To further test the method, we simulated gold nanopart
 \subsection{Heterogeneous nanoparticle / water mixtures}
 
 To further test the method, we simulated gold nanoparticles ($r = 18$
-\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.  
+\AA~, 1433 atoms) solvated by explicit SPC/E water clusters (5000
+molecules) 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.
 
 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