--- interfacial/interfacial.tex	2011/07/08 22:41:03	3733
+++ interfacial/interfacial.tex	2011/07/15 17:55:16	3742
@@ -23,8 +23,8 @@
 \setlength{\belowcaptionskip}{30 pt}
 
 %\renewcommand\citemid{\ } % no comma in optional reference note
-\bibpunct{[}{]}{,}{s}{}{;}
-\bibliographystyle{aip}
+\bibpunct{[}{]}{,}{n}{}{;}
+\bibliographystyle{achemso}
 
 \begin{document}
 
@@ -74,13 +74,15 @@ experimentally and computationally, due to its importa
 
 \section{Introduction}
 Interfacial thermal conductance is extensively studied both
-experimentally and computationally, due to its importance in nanoscale
-science and technology. Reliability of nanoscale devices depends on
-their thermal transport properties. Unlike bulk homogeneous materials,
-nanoscale materials features significant presence of interfaces, and
-these interfaces could dominate the heat transfer behavior of these
+experimentally and computationally\cite{cahill:793}, due to its
+importance in nanoscale science and technology. Reliability of
+nanoscale devices depends on their thermal transport
+properties. Unlike bulk homogeneous materials, nanoscale materials
+features significant presence of interfaces, and these interfaces
+could dominate the heat transfer behavior of these
 materials. Furthermore, these materials are generally heterogeneous,
-which challenges traditional research methods for homogeneous systems.
+which challenges traditional research methods for homogeneous
+systems.
 
 Heat conductance of molecular and nano-scale interfaces will be
 affected by the chemical details of the surface. Experimentally,
@@ -97,61 +99,77 @@ Theoretical and computational studies were also engage
 that specific ligands (capping agents) could completely eliminate this
 barrier ($G\rightarrow\infty$)\cite{doi:10.1021/la904855s}.
 
-Theoretical and computational studies were also engaged in the
-interfacial thermal transport research in order to gain an
-understanding of this phenomena at the molecular level. However, the
-relatively low thermal flux through interfaces is difficult to measure
-with EMD or forward NEMD simulation methods. Therefore, developing
-good simulation methods will be desirable in order to investigate
-thermal transport across interfaces. 
+Theoretical and computational models have also been used to study the
+interfacial thermal transport in order to gain an understanding of
+this phenomena at the molecular level. Recently, Hase and coworkers
+employed Non-Equilibrium Molecular Dynamics (NEMD) simulations to
+study thermal transport from hot Au(111) substrate to a self-assembled
+monolayer of alkylthiol with relatively long chain (8-20 carbon
+atoms)\cite{hase:2010,hase:2011}. However, ensemble averaged
+measurements for heat conductance of interfaces between the capping
+monolayer on Au and a solvent phase has yet to be studied. 
+The comparatively low thermal flux through interfaces is
+difficult to measure with Equilibrium MD or forward NEMD simulation
+methods. Therefore, the Reverse NEMD (RNEMD) methods would have the
+advantage of having this difficult to measure flux known when studying
+the thermal transport across interfaces, given that the simulation
+methods being able to effectively apply an unphysical flux in
+non-homogeneous systems.
+
 Recently, we have developed the Non-Isotropic Velocity Scaling (NIVS)
 algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm
 retains the desirable features of RNEMD (conservation of linear
 momentum and total energy, compatibility with periodic boundary
 conditions) while establishing true thermal distributions in each of
-the two slabs. Furthermore, it allows more effective thermal exchange
-between particles of different identities, and thus enables extensive
-study of interfacial conductance.
+the two slabs. Furthermore, it allows effective thermal exchange
+between particles of different identities, and thus makes the study of
+interfacial conductance much simpler.
 
-[BRIEF INTRO OF OUR PAPER]
-[WHY STUDY AU-THIOL SURFACE][CITE SHAOYI JIANG]
+The work presented here deals with the Au(111) surface covered to
+varying degrees by butanethiol, a capping agent with short carbon
+chain, and solvated with organic solvents of different molecular
+properties. Different models were used for both the capping agent and
+the solvent force field parameters. Using the NIVS algorithm, the
+thermal transport across these interfaces was studied and the
+underlying mechanism for this phenomena was investigated.
 
+[MAY ADD WHY STUDY AU-THIOL SURFACE; CITE SHAOYI JIANG]
+
 \section{Methodology}
-\subsection{Algorithm}
-[BACKGROUND FOR MD METHODS]
-There have been many algorithms for computing thermal conductivity
-using molecular dynamics simulations. However, interfacial conductance
-is at least an order of magnitude smaller. This would make the
-calculation even more difficult for those slowly-converging
-equilibrium methods. Imposed-flux non-equilibrium
+\subsection{Imposd-Flux Methods in MD Simulations}
+For systems with low interfacial conductivity one must have a method
+capable of generating relatively small fluxes, compared to those
+required for bulk conductivity. This requirement makes the calculation
+even more difficult for those slowly-converging equilibrium
+methods\cite{Viscardy:2007lq}.
+Forward methods impose gradient, but in interfacail conditions it is
+not clear what behavior to impose at the boundary...
+ Imposed-flux reverse non-equilibrium
 methods\cite{MullerPlathe:1997xw} have the flux set {\it a priori} and
-the response of temperature or momentum gradients are easier to
-measure than the flux, if unknown, and thus, is a preferable way to
-the forward NEMD methods. Although the momentum swapping approach for
-flux-imposing can be used for exchanging energy between particles of
-different identity, the kinetic energy transfer efficiency is affected
-by the mass difference between the particles, which limits its
-application on heterogeneous interfacial systems.
+the thermal response becomes easier to
+measure than the flux. Although M\"{u}ller-Plathe's original momentum
+swapping approach can be used for exchanging energy between particles
+of different identity, the kinetic energy transfer efficiency is
+affected by the mass difference between the particles, which limits
+its application on heterogeneous interfacial systems.
 
-The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach in
-non-equilibrium MD simulations is able to impose relatively large
-kinetic energy flux without obvious perturbation to the velocity
-distribution of the simulated systems. Furthermore, this approach has
+The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach to
+non-equilibrium MD simulations is able to impose a wide range of
+kinetic energy fluxes without obvious perturbation to the velocity
+distributions of the simulated systems. Furthermore, this approach has
 the advantage in heterogeneous interfaces in that kinetic energy flux
 can be applied between regions of particles of arbitary identity, and
-the flux quantity is not restricted by particle mass difference.
+the flux will not be restricted by difference in particle mass.
 
 The NIVS algorithm scales the velocity vectors in two separate regions
 of a simulation system with respective diagonal scaling matricies. To
 determine these scaling factors in the matricies, a set of equations
 including linear momentum conservation and kinetic energy conservation
-constraints and target momentum/energy flux satisfaction is
-solved. With the scaling operation applied to the system in a set
-frequency, corresponding momentum/temperature gradients can be built,
-which can be used for computing transportation properties and other
-applications related to momentum/temperature gradients. The NIVS
-algorithm conserves momenta and energy and does not depend on an
-external thermostat. 
+constraints and target energy flux satisfaction is solved. With the
+scaling operation applied to the system in a set frequency, bulk
+temperature gradients can be easily established, and these can be used
+for computing thermal conductivities. The NIVS algorithm conserves
+momenta and energy and does not depend on an external thermostat.
 
 \subsection{Defining Interfacial Thermal Conductivity $G$}
 For interfaces with a relatively low interfacial conductance, the bulk
@@ -169,13 +187,14 @@ When the interfacial conductance is {\it not} small, t
   T_\mathrm{cold}\rangle}$ are the average observed temperature of the
 two separated phases.
 
-When the interfacial conductance is {\it not} small, two ways can be
-used to define $G$.
+When the interfacial conductance is {\it not} small, there are two
+ways to define $G$.
 
-One way is to assume the temperature is discretely different on two
-sides of the interface, $G$ can be calculated with the thermal flux
-applied $J$ and the maximum temperature difference measured along the
-thermal gradient max($\Delta T$), which occurs at the interface, as:
+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:
 \begin{equation}
 G=\frac{J}{\Delta T}
 \label{discreteG}
@@ -196,34 +215,39 @@ difference method and thus calculate $G^\prime$.
 
 With the temperature profile obtained from simulations, one is able to
 approximate the first and second derivatives of $T$ with finite
-difference method and thus calculate $G^\prime$.
+difference methods and thus calculate $G^\prime$.
 
-In what follows, both definitions are used for calculation and comparison.
+In what follows, both definitions have been used for calculation and
+are compared in the results.
 
-[IMPOSE G DEFINITION INTO OUR SYSTEMS]
-To facilitate the use of the above definitions in calculating $G$ and
-$G^\prime$, we have a metal slab with its (111) surfaces perpendicular
-to the $z$-axis of our simulation cells. With or withour capping
-agents on the surfaces, the metal slab is solvated with organic
-solvents, as illustrated in Figure \ref{demoPic}.
+To compare the above definitions ($G$ and $G^\prime$), we have modeled
+a metal slab with its (111) surfaces perpendicular to the $z$-axis of
+our simulation cells. Both with and withour capping agents on the
+surfaces, the metal slab is solvated with simple organic solvents, as
+illustrated in Figure \ref{demoPic}.
 
 \begin{figure}
-\includegraphics[width=\linewidth]{demoPic}
-\caption{A sample showing how a metal slab has its (111) surface
-  covered by capping agent molecules and solvated by hexane.}
+\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 a simulation cell setup following the above manner, one is able
-to equilibrate the system and impose an unphysical thermal flux
-between the liquid and the metal phase with the NIVS algorithm. Under
-a stablized thermal gradient induced by periodically applying the
-unphysical flux, one is able to obtain a temperature profile and the
-physical thermal flux corresponding to it, which equals to the
-unphysical flux applied by NIVS. These data enables the evaluation of
-the interfacial thermal conductance of a surface. Figure \ref{gradT}
-is an example how those stablized thermal gradient can be used to
-obtain the 1st and 2nd derivatives of the temperature profile.
+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
+the unphysical flux, we are able to obtain a temperature profile and
+its spatial derivatives. These quantities enable the evaluation of the
+interfacial thermal conductance of a surface. Figure \ref{gradT} is an
+example how those applied thermal fluxes can be used to obtain the 1st
+and 2nd derivatives of the temperature profile.
 
 \begin{figure}
 \includegraphics[width=\linewidth]{gradT}
@@ -232,41 +256,36 @@ obtain the 1st and 2nd derivatives of the temperature 
 \label{gradT}
 \end{figure}
 
-[MAY INCLUDE POWER SPECTRUM PROTOCOL]
-
 \section{Computational Details}
 \subsection{Simulation Protocol}
-In our simulations, Au is used to construct a metal slab with bare
-(111) surface perpendicular to the $z$-axis. Different slab thickness
-(layer numbers of Au) are simulated. This metal slab is first
-equilibrated under normal pressure (1 atm) and a desired
-temperature. After equilibration, butanethiol is used as the capping
-agent molecule to cover the bare Au (111) surfaces evenly. The sulfur
-atoms in the butanethiol molecules would occupy the three-fold sites
-of the surfaces, and the maximal butanethiol capacity on Au surface is
-$1/3$ of the total number of surface Au atoms[CITATION]. A series of
-different coverage surfaces is investigated in order to study the
-relation between coverage and conductance.
+The NIVS algorithm has been implemented in our MD simulation code,
+OpenMD\cite{Meineke:2005gd,openmd}, and was used for our
+simulations. Different slab thickness (layer numbers of Au) were
+simulated. Metal slabs were first equilibrated under atmospheric
+pressure (1 atm) and a desired temperature (e.g. 200K). After
+equilibration, butanethiol capping agents were placed at three-fold
+sites on the Au(111) surfaces. The maximum butanethiol capacity on Au
+surface is $1/3$ of the total number of surface Au
+atoms\cite{vlugt:cpc2007154}. A series of different coverages was
+investigated in order to study the relation between coverage and
+interfacial conductance.
 
-[COVERAGE DISCRIPTION] However, since the interactions between surface
-Au and butanethiol is non-bonded, the capping agent molecules are
-allowed to migrate to an empty neighbor three-fold site during a
-simulation. Therefore, the initial configuration would not severely
-affect the sampling of a variety of configurations of the same
-coverage, and the final conductance measurement would be an average
-effect of these configurations explored in the simulations. [MAY NEED FIGURES]
+The capping agent molecules were allowed to migrate during the
+simulations. They distributed themselves uniformly and sampled a
+number of three-fold sites throughout out study. Therefore, the
+initial configuration would not noticeably affect the sampling of a
+variety of configurations of the same coverage, and the final
+conductance measurement would be an average effect of these
+configurations explored in the simulations. [MAY NEED FIGURES]
 
-After the modified Au-butanethiol surface systems are equilibrated
-under canonical ensemble, Packmol\cite{packmol} is used to pack
-organic solvent molecules in the previously vacuum part of the
-simulation cells, which guarantees that short range repulsive
-interactions do not disrupt the simulations. Two solvents are
-investigated, one which has little vibrational overlap with the
-alkanethiol and plane-like shape (toluene), and one which has similar
-vibrational frequencies and chain-like shape ({\it n}-hexane). [MAY
-EXPLAIN WHY WE CHOOSE THEM]
+After the modified Au-butanethiol surface systems were equilibrated
+under canonical ensemble, organic solvent molecules were packed in the
+previously empty part of the simulation cells\cite{packmol}. Two
+solvents were investigated, one which has little vibrational overlap
+with the alkanethiol and a planar shape (toluene), and one which has
+similar vibrational frequencies and chain-like shape ({\it n}-hexane).
 
-The spacing filled by solvent molecules, i.e. the gap between
+The space filled by solvent molecules, i.e. the gap between
 periodically repeated Au-butanethiol surfaces should be carefully
 chosen. A very long length scale for the thermal gradient axis ($z$)
 may cause excessively hot or cold temperatures in the middle of the
@@ -311,15 +330,26 @@ quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.5
 same type of particles and between particles of different species.
 
 The Au-Au interactions in metal lattice slab is described by the
-quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC
+quantum Sutton-Chen (QSC) formulation\cite{PhysRevB.59.3527}. The QSC
 potentials include zero-point quantum corrections and are
 reparametrized for accurate surface energies compared to the
 Sutton-Chen potentials\cite{Chen90}. 
 
-Figure [REF] demonstrates how we name our pseudo-atoms of the
-molecules in our simulations.
-[FIGURE FOR MOLECULE NOMENCLATURE] 
+Figure \ref{demoMol} demonstrates how we name our pseudo-atoms of the
+organic solvent molecules in our simulations.
 
+\begin{figure}
+\includegraphics[width=\linewidth]{structures}
+\caption{Structures of the capping agent and solvents utilized in
+  these simulations. The chemically-distinct sites (a-e) are expanded
+  in terms of constituent atoms for both United Atom (UA) and All Atom
+  (AA) force fields.  Most parameters are from
+  Refs. \protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} (UA) and
+  \protect\cite{OPLSAA} (AA).  Cross-interactions with the Au atoms are given
+  in Table \ref{MnM}.}
+\label{demoMol}
+\end{figure}
+
 For both solvent molecules, straight chain {\it n}-hexane and aromatic
 toluene, United-Atom (UA) and All-Atom (AA) models are used
 respectively. The TraPPE-UA
@@ -351,23 +381,27 @@ Au(111) surfaces, we adopt the S parameters from [CITA
 parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111)
 surfaces do not have the hydrogen atom bonded to sulfur. To adapt this
 change and derive suitable parameters for butanethiol adsorbed on
-Au(111) surfaces, we adopt the S parameters from [CITATION CF VLUGT]
-and modify parameters for its neighbor C atom for charge balance in
-the molecule. Note that the model choice (UA or AA) of capping agent
-can be different from the solvent. Regardless of model choice, the
-force field parameters for interactions between capping agent and
-solvent can be derived using Lorentz-Berthelot Mixing Rule: 
+Au(111) surfaces, we adopt the S parameters from Luedtke and
+Landman\cite{landman:1998} and modify parameters for its neighbor C
+atom for charge balance in the molecule. Note that the model choice
+(UA or AA) of capping agent can be different from the
+solvent. Regardless of model choice, the force field parameters for
+interactions between capping agent and solvent can be derived using
+Lorentz-Berthelot Mixing Rule:
+\begin{eqnarray}
+\sigma_{ij} & = & \frac{1}{2} \left(\sigma_{ii} + \sigma_{jj}\right) \\
+\epsilon_{ij} & = & \sqrt{\epsilon_{ii}\epsilon_{jj}}
+\end{eqnarray}
 
-
 To describe the interactions between metal Au and non-metal capping
 agent and solvent particles, we refer to an adsorption study of alkyl
 thiols on gold surfaces by Vlugt {\it et
   al.}\cite{vlugt:cpc2007154} They fitted an effective Lennard-Jones
 form of potential parameters for the interaction between Au and
 pseudo-atoms CH$_x$ and S based on a well-established and widely-used
-effective potential of Hautman and Klein[CITATION] for the Au(111)
-surface. As our simulations require the gold lattice slab to be
-non-rigid so that it could accommodate kinetic energy for thermal
+effective potential of Hautman and Klein\cite{hautman:4994} for the
+Au(111) surface. As our simulations require the gold lattice slab to
+be non-rigid so that it could accommodate kinetic energy for thermal
 transport study purpose, the pair-wise form of potentials is
 preferred.
 
@@ -386,25 +420,30 @@ parameters in our simulations.
 \begin{table*}
   \begin{minipage}{\linewidth}
     \begin{center}
-      \caption{Lennard-Jones parameters for Au-non-Metal
-        interactions in our simulations.}
-      
-      \begin{tabular}{ccc}
+      \caption{Non-bonded interaction parameters (including cross
+        interactions with Au atoms) for both force fields used in this
+        work.}      
+      \begin{tabular}{lllllll}
         \hline\hline
-        Non-metal atom   & $\sigma$ & $\epsilon$ \\
-        (or pseudo-atom) & \AA      & kcal/mol  \\
+        & Site  & $\sigma_{ii}$ & $\epsilon_{ii}$ & $q_i$ &
+        $\sigma_{Au-i}$ & $\epsilon_{Au-i}$ \\
+        & & (\AA) & (kcal/mol) & ($e$) & (\AA) & (kcal/mol) \\
         \hline
-        S    & 2.40   & 8.465   \\
-        CH3  & 3.54   & 0.2146  \\
-        CH2  & 3.54   & 0.1749  \\
-        CT3  & 3.365  & 0.1373  \\
-        CT2  & 3.365  & 0.1373  \\
-        CTT  & 3.365  & 0.1373  \\
-        HC   & 2.865  & 0.09256 \\
-        CHar & 3.4625 & 0.1680  \\
-        CRar & 3.555  & 0.1604  \\
-        CA   & 3.173  & 0.0640  \\
-        HA   & 2.746  & 0.0414  \\
+        United Atom (UA)
+        &CH3  & 3.75  & 0.1947  & -      & 3.54   & 0.2146  \\
+        &CH2  & 3.95  & 0.0914  & -      & 3.54   & 0.1749  \\
+        &CHar & 3.695 & 0.1003  & -      & 3.4625 & 0.1680  \\
+        &CRar & 3.88  & 0.04173 & -      & 3.555  & 0.1604  \\
+        \hline
+        All Atom (AA) 
+        &CT3  & 3.50  & 0.066   & -0.18  & 3.365  & 0.1373  \\
+        &CT2  & 3.50  & 0.066   & -0.12  & 3.365  & 0.1373  \\
+        &CTT  & 3.50  & 0.066   & -0.065 & 3.365  & 0.1373  \\
+        &HC   & 2.50  & 0.030   &  0.06  & 2.865  & 0.09256 \\
+        &CA   & 3.55  & 0.070   & -0.115 & 3.173  & 0.0640  \\
+        &HA   & 2.42  & 0.030   &  0.115 & 2.746  & 0.0414  \\
+        \hline
+        Both UA and AA & S    & 4.45  & 0.25    & -      & 2.40   & 8.465   \\
         \hline\hline
       \end{tabular}
       \label{MnM}
@@ -474,29 +513,31 @@ couple $J_z$'s and do not need to test a large series 
         interfaces with UA model and different hexane molecule numbers
         at different temperatures using a range of energy fluxes.}
       
-      \begin{tabular}{cccccccc}
+      \begin{tabular}{ccccccc}
         \hline\hline
-        $\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ &
-        $G$ & $G^\prime$ \\
-        (K) & $N_{hexane}$ & \multicolumn{3}{c}{(\AA)} & (GW/m$^2$) &
+        $\langle T\rangle$ & $N_{hexane}$ & Fixed & $\rho_{hexane}$ &
+        $J_z$ & $G$ & $G^\prime$ \\
+        (K) & & $L_x$ \& $L_y$? & (g/cm$^3$) & (GW/m$^2$) &
         \multicolumn{2}{c}{(MW/m$^2$/K)} \\
         \hline
-        200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 &
-        102()  & 80.0() \\
-            & 200 & 29.84 & 25.81 &  93.9 &  1.92 &
-        129()  & 87.3() \\
-            &     & 29.84 & 25.81 &  95.3 &  1.93 &
-        131()  & 77.5() \\
-            & 166 & 29.84 & 25.81 &  85.7 &  0.97 &
-        115()  & 69.3() \\
-            &     &       &       &       &  1.94 &
-        125()  & 87.1() \\
-        250 & 200 & 29.84 & 25.87 & 106.8 &  0.96 &
-        81.8() & 67.0() \\
-            & 166 & 29.87 & 25.84 &  94.8 &  0.98 &
-        79.0() & 62.9() \\
-            &     & 29.84 & 25.85 &  95.0 &  1.44 &
-        76.2() & 64.8() \\
+        200 & 266 & No  & 0.672 & -0.96 & 102()  & 80.0() \\
+            & 200 & Yes & 0.694 &  1.92 & 129()  & 87.3() \\
+            &     & Yes & 0.672 &  1.93 & 131()  & 77.5() \\
+            &     & No  & 0.688 &  0.96 & 125()  & 90.2() \\
+            &     &     &       &  1.91 & 139()  & 101()  \\
+            &     &     &       &  2.83 & 141()  & 89.9() \\
+            & 166 & Yes & 0.679 &  0.97 & 115()  & 69.3() \\
+            &     &     &       &  1.94 & 125()  & 87.1() \\
+            &     & No  & 0.681 &  0.97 & 141()  & 77.7() \\
+            &     &     &       &  1.92 & 138()  & 98.9() \\
+        \hline
+        250 & 200 & No  & 0.560 &  0.96 & 74.8() & 61.8() \\
+            &     &     &       & -0.95 & 49.4() & 45.7() \\
+            & 166 & Yes & 0.570 &  0.98 & 79.0() & 62.9() \\
+            &     & No  & 0.569 &  0.97 & 80.3() & 67.1() \\
+            &     &     &       &  1.44 & 76.2() & 64.8() \\
+            &     &     &       & -0.95 & 56.4() & 54.4() \\
+            &     &     &       & -1.85 & 47.8() & 53.5() \\
         \hline\hline
       \end{tabular}
       \label{AuThiolHexaneUA}
@@ -527,7 +568,7 @@ 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 Lxyz AND ERROR ESTIMATE TO TABLE]
+[ADD ERROR ESTIMATE TO TABLE]
 \begin{table*}
   \begin{minipage}{\linewidth}
     \begin{center}
@@ -536,16 +577,17 @@ in that higher degree of contact could yield increased
         interface at different temperatures using a range of energy
         fluxes.}
       
-      \begin{tabular}{cccc}
+      \begin{tabular}{ccccc}
         \hline\hline
-        $\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\
-        (K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
+        $\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\
+        (K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
         \hline
-        200 & -1.86 & 180() & 135() \\
-            &  2.15 & 204() & 113() \\
-            & -3.93 & 175() & 114() \\
-        300 & -1.91 & 143() & 125() \\
-            & -4.19 & 134() & 113() \\
+        200 & 0.933 & -1.86 & 180() & 135() \\
+            &       &  2.15 & 204() & 113() \\
+            &       & -3.93 & 175() & 114() \\
+        \hline
+        300 & 0.855 & -1.91 & 143() & 125() \\
+            &       & -4.19 & 134() & 113() \\
         \hline\hline
       \end{tabular}
       \label{AuThiolToluene}
@@ -578,13 +620,14 @@ even at $<T>\sim$300K. The Au(111) surfaces have a 90\
 However, when the surface is not completely covered by butanethiols,
 the simulated system is more resistent to the reconstruction
 above. Our Au-butanethiol/toluene system did not see this phenomena
-even at $<T>\sim$300K. The Au(111) surfaces have a 90\% coverage of
-butanethiols and have empty three-fold sites. These empty sites could
-help prevent surface reconstruction in that they provide other means
-of capping agent relaxation. It is observed that butanethiols can
-migrate to their neighbor empty sites during a simulation. Therefore,
-we were able to obtain $G$'s for these interfaces even at a relatively
-high temperature without being affected by surface reconstructions.
+even at $\langle T\rangle\sim$300K. The Au(111) surfaces have a 90\%
+coverage of butanethiols and have empty three-fold sites. These empty
+sites could help prevent surface reconstruction in that they provide
+other means of capping agent relaxation. It is observed that
+butanethiols can migrate to their neighbor empty sites during a
+simulation. Therefore, we were able to obtain $G$'s for these
+interfaces even at a relatively high temperature without being
+affected by surface reconstructions.
 
 \subsection{Influence of Capping Agent Coverage on $G$}
 To investigate the influence of butanethiol coverage on interfacial
@@ -660,32 +703,14 @@ can see a plateau of $G$ vs. butanethiol coverage in o
 its effect to the process of interfacial thermal transport. Thus, one
 can see a plateau of $G$ vs. butanethiol coverage in our results.
 
-[NEED ERROR ESTIMATE, MAY ALSO PUT J HERE]
-\begin{table*}
-  \begin{minipage}{\linewidth}
-    \begin{center}
-      \caption{Computed interfacial thermal conductivity ($G$) values
-        for the Au-butanethiol/solvent interface with various UA
-        models and different capping agent coverages at $\langle
-        T\rangle\sim$200K using certain energy flux respectively.}
-      
-      \begin{tabular}{cccc}
-        \hline\hline
-        Thiol & \multicolumn{3}{c}{$G$(MW/m$^2$/K)} \\
-        coverage (\%) & hexane & hexane(D) & toluene \\
-        \hline
-        0.0   & 46.5() & 43.9() & 70.1() \\
-        25.0  & 151()  & 153()  & 249()  \\
-        50.0  & 172()  & 182()  & 214()  \\
-        75.0  & 242()  & 229()  & 244()  \\
-        88.9  & 178()  & -      & -      \\
-        100.0 & 137()  & 153()  & 187()  \\
-        \hline\hline
-      \end{tabular}
-      \label{tlnUhxnUhxnD}
-    \end{center}
-  \end{minipage}
-\end{table*}
+\begin{figure}
+\includegraphics[width=\linewidth]{coverage}
+\caption{Comparison of interfacial thermal conductivity ($G$) values
+  for the Au-butanethiol/solvent interface with various UA models and
+  different capping agent coverages at $\langle T\rangle\sim$200K
+  using certain energy flux respectively.}
+\label{coverage}
+\end{figure}
 
 \subsection{Influence of Chosen Molecule Model on $G$}
 [MAY COMBINE W MECHANISM STUDY]
@@ -698,7 +723,6 @@ these studies.
 the previous section. Table \ref{modelTest} summarizes the results of
 these studies.
 
-[MORE DATA; ERROR ESTIMATE]
 \begin{table*}
   \begin{minipage}{\linewidth}
     \begin{center}
@@ -706,23 +730,37 @@ these studies.
       \caption{Computed interfacial thermal conductivity ($G$ and
         $G^\prime$) values for interfaces using various models for
         solvent and capping agent (or without capping agent) at
-        $\langle T\rangle\sim$200K.}
+        $\langle T\rangle\sim$200K. (D stands for deuterated solvent
+        or capping agent molecules; ``Avg.'' denotes results that are
+        averages of simulations under different $J_z$'s. Error
+        estimates indicated in parenthesis.)}
       
-      \begin{tabular}{ccccc}
+      \begin{tabular}{llccc}
         \hline\hline
         Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\
         (or bare surface) & model & (GW/m$^2$) &
         \multicolumn{2}{c}{(MW/m$^2$/K)} \\
         \hline
-        UA    & AA hexane  & 1.94 & 135()  & 129()  \\
-              &            & 2.86 & 126()  & 115()  \\
-              & AA toluene & 1.89 & 200()  & 149()  \\
-        AA    & UA hexane  & 1.94 & 116()  & 129()  \\
-              & AA hexane  & 3.76 & 451()  & 378()  \\
-              &            & 4.71 & 432()  & 334()  \\
-              & AA toluene & 3.79 & 487()  & 290()  \\
-        AA(D) & UA hexane  & 1.94 & 158()  & 172()  \\
-        bare  & AA hexane  & 0.96 & 31.0() & 29.4() \\
+        UA    & UA hexane    & Avg. & 131(9)    & 87(10)    \\
+              & UA hexane(D) & 1.95 & 153(5)    & 136(13)   \\
+              & AA hexane    & Avg. & 131(6)    & 122(10)   \\
+              & UA toluene   & 1.96 & 187(16)   & 151(11)   \\
+              & AA toluene   & 1.89 & 200(36)   & 149(53)   \\
+        \hline
+        AA    & UA hexane    & 1.94 & 116(9)    & 129(8)    \\
+              & AA hexane    & Avg. & 442(14)   & 356(31)   \\
+              & AA hexane(D) & 1.93 & 222(12)   & 234(54)   \\
+              & UA toluene   & 1.98 & 125(25)   & 97(60)    \\
+              & AA toluene   & 3.79 & 487(56)   & 290(42)   \\
+        \hline
+        AA(D) & UA hexane    & 1.94 & 158(25)   & 172(4)    \\
+              & AA hexane    & 1.92 & 243(29)   & 191(11)   \\
+              & AA toluene   & 1.93 & 364(36)   & 322(67)   \\
+        \hline
+        bare  & UA hexane    & Avg. & 46.5(3.2) & 49.4(4.5) \\
+              & UA hexane(D) & 0.98 & 43.9(4.6) & 43.0(2.0) \\
+              & AA hexane    & 0.96 & 31.0(1.4) & 29.4(1.3) \\
+              & UA toluene   & 1.99 & 70.1(1.3) & 65.8(0.5) \\
         \hline\hline
       \end{tabular}
       \label{modelTest}
@@ -759,18 +797,21 @@ measurement results.
 
 However, for Au-butanethiol/toluene interfaces, having the AA
 butanethiol deuterated did not yield a significant change in the
-measurement results.
-. , so extra degrees of freedom
-such as the C-H vibrations could enhance heat exchange between these
-two phases and result in a much higher conductivity.
+measurement results. Compared to the C-H vibrational overlap between
+hexane and butanethiol, both of which have alkyl chains, that overlap
+between toluene and butanethiol is not so significant and thus does
+not have as much contribution to the ``Intramolecular Vibration
+Redistribution''[CITE HASE]. Conversely, extra degrees of freedom such
+as the C-H vibrations could yield higher heat exchange rate between
+these two phases and result in a much higher conductivity.
 
-
 Although the QSC model for Au is known to predict an overly low value
-for bulk metal gold conductivity[CITE NIVSRNEMD], our computational
+for bulk metal gold conductivity\cite{kuang:164101}, our computational
 results for $G$ and $G^\prime$ do not seem to be affected by this
-drawback of the model for metal. Instead, the modeling of interfacial
-thermal transport behavior relies mainly on an accurate description of
-the interactions between components occupying the interfaces.
+drawback of the model for metal. Instead, our results suggest that the
+modeling of interfacial thermal transport behavior relies mainly on
+the accuracy of the interaction descriptions between components
+occupying the interfaces.
 
 \subsection{Mechanism of Interfacial Thermal Conductance Enhancement
   by Capping Agent}
@@ -786,6 +827,7 @@ power spectrum via a Fourier transform.
 the velocity auto-correlation functions, which is used to construct a
 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
@@ -798,7 +840,7 @@ thermal conductance enhancement in the all-atom model.
 combination of these two effects produces the drastic interfacial
 thermal conductance enhancement in the all-atom model.
 
-[MAY NEED TO CONVERT TO JPEG]
+[REDO. MAY NEED TO CONVERT TO JPEG]
 \begin{figure}
 \includegraphics[width=\linewidth]{vibration}
 \caption{Vibrational spectra obtained for gold in different
