--- interfacial/interfacial.tex	2011/07/20 19:02:46	3744
+++ interfacial/interfacial.tex	2011/07/21 00:04:26	3745
@@ -193,13 +193,27 @@ gradient max($\Delta T$), which occurs at the Gibbs de
 One way is to assume the temperature is discrete on the two sides of
 the interface. $G$ can be calculated using the applied thermal flux
 $J$ and the maximum temperature difference measured along the thermal
-gradient max($\Delta T$), which occurs at the Gibbs deviding surface,
-as:
+gradient max($\Delta T$), which occurs at the Gibbs deviding surface
+(Figure \ref{demoPic}):
 \begin{equation}
 G=\frac{J}{\Delta T}
 \label{discreteG}
 \end{equation}
 
+\begin{figure}
+\includegraphics[width=\linewidth]{method}
+\caption{Interfacial conductance can be calculated by applying an
+  (unphysical) kinetic energy flux between two slabs, one located
+  within the metal and another on the edge of the periodic box.  The
+  system responds by forming a thermal response or a gradient.  In
+  bulk liquids, this gradient typically has a single slope, but in
+  interfacial systems, there are distinct thermal conductivity
+  domains.  The interfacial conductance, $G$ is found by measuring the
+  temperature gap at the Gibbs dividing surface, or by using second
+  derivatives of the thermal profile.}
+\label{demoPic}
+\end{figure}
+
 The other approach is to assume a continuous temperature profile along
 the thermal gradient axis (e.g. $z$) and define $G$ at the point where
 the magnitude of thermal conductivity $\lambda$ change reach its
@@ -226,20 +240,6 @@ illustrated in Figure \ref{demoPic}.
 surfaces, the metal slab is solvated with simple organic solvents, as
 illustrated in Figure \ref{demoPic}.
 
-\begin{figure}
-\includegraphics[width=\linewidth]{method}
-\caption{Interfacial conductance can be calculated by applying an
-  (unphysical) kinetic energy flux between two slabs, one located
-  within the metal and another on the edge of the periodic box.  The
-  system responds by forming a thermal response or a gradient.  In
-  bulk liquids, this gradient typically has a single slope, but in
-  interfacial systems, there are distinct thermal conductivity
-  domains.  The interfacial conductance, $G$ is found by measuring the
-  temperature gap at the Gibbs dividing surface, or by using second
-  derivatives of the thermal profile.}
-\label{demoPic}
-\end{figure}
-
 With the simulation cell described above, we are able to equilibrate
 the system and impose an unphysical thermal flux between the liquid
 and the metal phase using the NIVS algorithm. By periodically applying
@@ -251,8 +251,10 @@ and 2nd derivatives of the temperature profile.
 
 \begin{figure}
 \includegraphics[width=\linewidth]{gradT}
-\caption{The 1st and 2nd derivatives of temperature profile can be
-  obtained with finite difference approximation.}
+\caption{A sample of Au-butanethiol/hexane interfacial system and the
+  temperature profile after a kinetic energy flux is imposed to
+  it. The 1st and 2nd derivatives of the temperature profile can be
+  obtained with finite difference approximation (lower panel).}
 \label{gradT}
 \end{figure}
 
@@ -294,7 +296,7 @@ corresponding spacing is usually $35 \sim 60$\AA.
 solvent molecules would change the normal behavior of the liquid
 phase. Therefore, our $N_{solvent}$ values were chosen to ensure that
 these extreme cases did not happen to our simulations. And the
-corresponding spacing is usually $35 \sim 60$\AA.
+corresponding spacing is usually $35 \sim 75$\AA.
 
 The initial configurations generated by Packmol are further
 equilibrated with the $x$ and $y$ dimensions fixed, only allowing
@@ -386,7 +388,7 @@ added as an extra potential for maintaining the planar
 adopted. Without the rigid body constraints, bonding interactions were
 included. For the aromatic ring, improper torsions (inversions) were
 added as an extra potential for maintaining the planar shape.
-[MORE CITATIONS?]
+[MORE CITATION?]
 
 The capping agent in our simulations, the butanethiol molecules can
 either use UA or AA model. The TraPPE-UA force fields includes
@@ -531,7 +533,8 @@ a large series of fluxes.
       \caption{Computed interfacial thermal conductivity ($G$ and
         $G^\prime$) values for the 100\% covered Au-butanethiol/hexane
         interfaces with UA model and different hexane molecule numbers
-        at different temperatures using a range of energy fluxes.}
+        at different temperatures using a range of energy
+        fluxes. Error estimates indicated in parenthesis.}
       
       \begin{tabular}{ccccccc}
         \hline\hline
@@ -540,10 +543,10 @@ a large series of fluxes.
         (K) & & $L_x$ \& $L_y$? & (g/cm$^3$) & (GW/m$^2$) &
         \multicolumn{2}{c}{(MW/m$^2$/K)} \\
         \hline
-        200 & 266 & No  & 0.672 & -0.96 & 102()     & 80.0()    \\
+        200 & 266 & No  & 0.672 & -0.96 & 102(3)    & 80.0(0.8) \\
             & 200 & Yes & 0.694 &  1.92 & 129(11)   & 87.3(0.3) \\
             &     & Yes & 0.672 &  1.93 & 131(16)   & 78(13)    \\
-            &     & No  & 0.688 &  0.96 & 125()     & 90.2()    \\
+            &     & No  & 0.688 &  0.96 & 125(16)   & 90.2(15)  \\
             &     &     &       &  1.91 & 139(10)   & 101(10)   \\
             &     &     &       &  2.83 & 141(6)    & 89.9(9.8) \\
             & 166 & Yes & 0.679 &  0.97 & 115(19)   & 69(18)    \\
@@ -589,26 +592,25 @@ in that higher degree of contact could yield increased
 important role in the thermal transport process across the interface
 in that higher degree of contact could yield increased conductance.
 
-[ADD ERROR ESTIMATE TO TABLE]
 \begin{table*}
   \begin{minipage}{\linewidth}
     \begin{center}
       \caption{Computed interfacial thermal conductivity ($G$ and
         $G^\prime$) values for a 90\% coverage Au-butanethiol/toluene
         interface at different temperatures using a range of energy
-        fluxes.}
+        fluxes. Error estimates indicated in parenthesis.}
       
       \begin{tabular}{ccccc}
         \hline\hline
         $\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\
         (K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
         \hline
-        200 & 0.933 & -1.86 & 180() & 135() \\
-            &       &  2.15 & 204() & 113() \\
-            &       & -3.93 & 175() & 114() \\
+        200 & 0.933 &  2.15 & 204(12) & 113(12) \\
+            &       & -1.86 & 180(3)  & 135(21) \\
+            &       & -3.93 & 176(5)  & 113(12) \\
         \hline
-        300 & 0.855 & -1.91 & 143() & 125() \\
-            &       & -4.19 & 134() & 113() \\
+        300 & 0.855 & -1.91 & 143(5)  & 125(2)  \\
+            &       & -4.19 & 135(9)  & 113(12) \\
         \hline\hline
       \end{tabular}
       \label{AuThiolToluene}
@@ -851,24 +853,23 @@ power spectrum via a Fourier transform.
 power spectrum via a Fourier transform.
 
 [MAY RELATE TO HASE'S]
- The gold surfaces covered by
-butanethiol molecules, compared to bare gold surfaces, exhibit an
-additional peak observed at a frequency of $\sim$170cm$^{-1}$, which
-is attributed to the vibration of the S-Au bonding. This vibration
-enables efficient thermal transport from surface Au atoms to the
-capping agents. Simultaneously, as shown in the lower panel of
-Fig. \ref{vibration}, the large overlap of the vibration spectra of
-butanethiol and hexane in the all-atom model, including the C-H
-vibration, also suggests high thermal exchange efficiency. The
-combination of these two effects produces the drastic interfacial
-thermal conductance enhancement in the all-atom model.
+The gold surfaces covered by butanethiol molecules, compared to bare
+gold surfaces, exhibit an additional peak observed at the frequency of
+$\sim$170cm$^{-1}$, which is attributed to the S-Au bonding
+vibration. This vibration enables efficient thermal transport from
+surface Au layer to the capping agents.
+[MAY PUT IN OTHER SECTION] Simultaneously, as shown in
+the lower panel of Fig. \ref{vibration}, the large overlap of the
+vibration spectra of butanethiol and hexane in the All-Atom model,
+including the C-H vibration, also suggests high thermal exchange
+efficiency. The combination of these two effects produces the drastic
+interfacial thermal conductance enhancement in the All-Atom model.
 
-[REDO. MAY NEED TO CONVERT TO JPEG]
+[NEED SEPARATE FIGURE. MAY NEED TO CONVERT TO JPEG]
 \begin{figure}
 \includegraphics[width=\linewidth]{vibration}
 \caption{Vibrational spectra obtained for gold in different
-  environments (upper panel) and for Au/thiol/hexane simulation in
-  all-atom model (lower panel).}
+  environments.}
 \label{vibration}
 \end{figure}
 
