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Merge /home/krebse/deft

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droundy committed Jun 7, 2012
2 parents 29f4195 + ef14b40 commit 51c4f65a2503c6117aab6392ea11103679f39a56
@@ -42,9 +42,12 @@ set key inside bottom
#set xlabel 'y (nm)'
#set ylabel 'z (nm)'
-set style line 1 lt 1 lc 1 lw 3
+set style line 1 lt 1 lc 7 lw 3
set style line 2 lt 1 lc 3 lw 3
-set style line 3 lt 1 lc 7 lw 3
+set style line 3 lt 1 lc 1 lw 3
+set style line 5 lt 1 lc 8 lw 3
+set style line 6 lt 1 lc 2 lw 3
+set style line 7 lt 1 lc 5 lw 3
set style line 4 lt 3 lc 3 lw 3
#splot [:] [:] [:] \
@@ -64,12 +67,12 @@ nl=0.004938863
nm = 18.8972613 # 1 nm equals this many bohrs
gpermL=4.9388942e-3/0.996782051315 # conversion from atomic units to mass density
-plot [:1.50] [:] \
+plot [:1.30] [:] \
'figs/single-rod-slice-02.0.dat' u ($2/nm):($4/gpermL) notitle with lines ls 1 , \
'figs/single-rod-slice-01.6.dat' u ($2/nm):($4/gpermL) notitle with lines ls 2 , \
'figs/single-rod-slice-01.0.dat' u ($2/nm):($4/gpermL) notitle with lines ls 3 , \
-'figs/single-rod-slice-00.6.dat' u ($2/nm):($4/gpermL) notitle with lines ls 1 , \
-'figs/single-rod-slice-00.3.dat' u ($2/nm):($4/gpermL) notitle with lines ls 2 , \
-'figs/single-rod-slice-00.1.dat' u ($2/nm):($4/gpermL) notitle with lines ls 3 , \
+'figs/single-rod-slice-00.6.dat' u ($2/nm):($4/gpermL) notitle with lines ls 5 , \
+'figs/single-rod-slice-00.3.dat' u ($2/nm):($4/gpermL) notitle with lines ls 6 , \
+'figs/single-rod-slice-00.1.dat' u ($2/nm):($4/gpermL) notitle with lines ls 7 , \
'figs/single-rod-slice-00.6.dat' u ($2/nm):(nl/gpermL) notitle with lines ls 4 , \
-'figs/single-rods-calculated-density.dat' u ($1/nm):($2/gpermL) notitle with points ls 1
+'figs/single-rods-calculated-density.dat' u ($1/nm):($2/gpermL) notitle with points ls 3
@@ -37,118 +37,118 @@
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0 18.9972 0 0.00492847 -1.38775e-07 0.0317431 0.130144
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0 19.9971 0 0.00502878 1.18814e-07 0.0330886 0.130117
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@@ -99,8 +99,8 @@ \subsection{Water---the universal solvent}
As common as water is, its large dielectric constant, small
molecular size, strong hydrogen-bonding network and anomolous
-thermodynamic properties make ``the universal solvent'' an interesting
-subject of study.
+thermodynamic properties make ``the universal solvent'' a unique
+and interesting material.
\subsection{Classical density-functional theory}
@@ -178,10 +178,7 @@ \subsection{Classical density-functional theory}
gloor2004accurate, gross2009density, kahl2008modified, felipe2001examination}.
These functionals are based on a perturbative thermodynamic
expansion, and give a reasonable prediction for the temperature
-dependence of the surface tension. However, they also overestimate
-the surface tension by a factor of about 1.5, and \fixme{most?} are unsuited
-for studying systems that have density variations on a molecular
-length scale due to the use of a local density approximation.
+dependence of the surface tension.
\subsection{Statistical associating fluid theory}
@@ -207,7 +204,11 @@ \subsection{Statistical associating fluid theory}
relevant for water. While a number of SAFT formulations have been
published, we will focus on SAFT-VR\cite{gil-villegas-1997-SAFT-VR},
which has been used by Clark \emph{et al} to construct an optimal SAFT
-model for water\cite{clark2006developing}.
+model for water\cite{clark2006developing}. A majority of the empirical
+parameters used in our functional are taken from the Clark\emph{et al}
+SAFT functional which contains five empirical parameters and give the
+correct pressure at liquid-vapor coexistince curve shown in Figure
+\ref{fig:pressure-with-isotherms}.
\begin{figure}
\begin{center}
@@ -216,24 +217,15 @@ \subsection{Statistical associating fluid theory}
\caption{The pressure versus density for various temperatures, including
experimental pressure data from NIST\cite{nistwater}. The dash-dotted lines
indicate the computationally calculated pressure and the open circles are
-NIST data points. The solid and dotted lines
-represent the theoretical and experimental coexistence curves.}
+NIST data points. The solid and dotted lines represent the theoretical
+and experimental coexistence curves.}
\label{fig:pressure-with-isotherms}
\end{figure}
SAFT has also been used to construct classical density functionals,
which have been applied to study the surface tension as a function of
temperature\cite{whotocite}. Such functionals have qualitatively
-predicted the dependence of surface tension on temperature, but have
-in general provided poor quantitative agreement with experiment.
-Moreover, the vast majority of SAFT-based classical density
-functionals have made local-density approximations that make them
-unsuitable for application to systems that obey the contact-value
-theorem. \cite{felipe2001examination, gloor2002saft,
- gloor2004accurate, clark2006developing, gloor2007prediction,
- kahl2008modified, gross2009density}.\
-
- However, they also overestimate
+predicted the dependence of surface tension on temperature, however, they also overestimate
the surface tension by a factor of about 1.5, and \fixme{most?} are unsuited
for studying systems that have density variations on a molecular
length scale due to the use of a local density approximation.
@@ -255,9 +247,8 @@ \subsection{Statistical associating fluid theory}
\begin{equation}\label{contactvaluethm}
F = n k_BT V
\end{equation}
-\fixme{add this here? :} The contact-value theorem is satisfied for
-functionals for with the only purely local term is the free energy of
-an ideal gas.
+The contact-value theorem is satisfied for functionals where the
+only purely local term is the free energy of an ideal gas.
\section{Theory and Methods}
We construct a new classical density functional for water. We treat
@@ -810,7 +801,7 @@ \subsection{Hydrophobic interaction of two rods}
~\ref{fig:rods-energy-vs-distance}, we see that for small $d$ all the rods
have the same behavior with a positive linear relationship
between free energy per length and separation during the initial state
-(where the rods have vapor between them). This indicates that the force
+with vapor between them. This indicates that the force
per length on the rods is constant, and surprisingly independent of separation.
To estimate how the transition from vapor to liquid between the rods depends on their

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