--- interfacial/interfacial.tex	2011/07/08 22:41:03	3733
+++ interfacial/interfacial.tex	2011/07/21 00:04:26	3745
@@ -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
@@ -169,18 +187,33 @@ 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
+(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
@@ -196,77 +229,65 @@ 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 without 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.}
-\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
+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.
 
-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.
-
 \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}
 
-[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
@@ -275,7 +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
@@ -306,43 +327,68 @@ Our simulations include various components. Therefore,
 \end{equation}
 
 \subsection{Force Field Parameters}
-Our simulations include various components. Therefore, force field
-parameter descriptions are needed for interactions both between the
-same type of particles and between particles of different species.
+Our simulations include various components. Figure \ref{demoMol}
+demonstrates the sites defined for both United-Atom and All-Atom
+models of the organic solvent and capping agent molecules in our
+simulations. Force field parameter descriptions are needed for
+interactions both between the same type of particles and between
+particles of different species.
 
+\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}
+
 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] 
-
 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
 parameters\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} are used
-for our UA solvent molecules. In these models, pseudo-atoms are
-located at the carbon centers for alkyl groups. By eliminating
-explicit hydrogen atoms, these models are simple and computationally
-efficient, while maintains good accuracy. However, the TraPPE-UA for
-alkanes is known to predict a lower boiling point than experimental
-values. Considering that after an unphysical thermal flux is applied
-to a system, the temperature of ``hot'' area in the liquid phase would be
-significantly higher than the average, to prevent over heating and
-boiling of the liquid phase, the average temperature in our
-simulations should be much lower than the liquid boiling point. [MORE DISCUSSION]
-For UA-toluene model, rigid body constraints are applied, so that the
-benzene ring and the methyl-CRar bond are kept rigid. This would save
-computational time.[MORE DETAILS]
+for our UA solvent molecules. In these models, sites are located at
+the carbon centers for alkyl groups. Bonding interactions, including
+bond stretches and bends and torsions, were used for intra-molecular
+sites not separated by more than 3 bonds. Otherwise, for non-bonded
+interactions, Lennard-Jones potentials are used. [MORE CITATION?]
 
+By eliminating explicit hydrogen atoms, these models are simple and
+computationally efficient, while maintains good accuracy. However, the
+TraPPE-UA for alkanes is known to predict a lower boiling point than
+experimental values. Considering that after an unphysical thermal flux
+is applied to a system, the temperature of ``hot'' area in the liquid
+phase would be significantly higher than the average, to prevent over
+heating and boiling of the liquid phase, the average temperature in
+our simulations should be much lower than the liquid boiling point.
+
+For UA-toluene model, the non-bonded potentials between
+inter-molecular sites have a similar Lennard-Jones formulation. For
+intra-molecular interactions, considering the stiffness of the benzene
+ring, rigid body constraints are applied for further computational
+efficiency. All bonds in the benzene ring and between the ring and the
+methyl group remain rigid during the progress of simulations.
+
 Besides the TraPPE-UA models, AA models for both organic solvents are
 included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA}
-force field is used. [MORE DETAILS]
-For toluene, the United Force Field developed by Rapp\'{e} {\it et
-  al.}\cite{doi:10.1021/ja00051a040} is adopted.[MORE DETAILS]
+force field is used. Additional explicit hydrogen sites were
+included. Besides bonding and non-bonded site-site interactions,
+partial charges and the electrostatic interactions were added to each
+CT and HC site. For toluene, the United Force Field developed by
+Rapp\'{e} {\it et al.}\cite{doi:10.1021/ja00051a040} is
+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 CITATION?]
 
 The capping agent in our simulations, the butanethiol molecules can
 either use UA or AA model. The TraPPE-UA force fields includes
@@ -351,60 +397,74 @@ 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.
 
 Besides, the potentials developed from {\it ab initio} calculations by
 Leng {\it et al.}\cite{doi:10.1021/jp034405s} are adopted for the
-interactions between Au and aromatic C/H atoms in toluene.[MORE DETAILS]
+interactions between Au and aromatic C/H atoms in toluene. A set of
+pseudo Lennard-Jones parameters were provided for Au in their force
+fields. By using the Mixing Rule, this can be used to derive pair-wise
+potentials for non-bonded interactions between Au and non-metal sites.
 
 However, the Lennard-Jones parameters between Au and other types of
-particles in our simulations are not yet well-established. For these
-interactions, we attempt to derive their parameters using the Mixing
-Rule. To do this, the ``Metal-non-Metal'' (MnM) interaction parameters
-for Au is first extracted from the Au-CH$_x$ parameters by applying
-the Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM''
+particles, such as All-Atom normal alkanes in our simulations are not
+yet well-established. For these interactions, we attempt to derive
+their parameters using the Mixing Rule. To do this, Au pseudo
+Lennard-Jones parameters for ``Metal-non-Metal'' (MnM) interactions
+were first extracted from the Au-CH$_x$ parameters by applying the
+Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM''
 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}
@@ -425,14 +485,15 @@ during equilibrating the liquid phase. Due to the stif
 results.
 
 In some of our simulations, we allowed $L_x$ and $L_y$ to change
-during equilibrating the liquid phase. Due to the stiffness of the Au
-slab, $L_x$ and $L_y$ would not change noticeably after
-equilibration. Although $L_z$ could fluctuate $\sim$1\% after a system
-is fully equilibrated in the NPT ensemble, this fluctuation, as well
-as those comparably smaller to $L_x$ and $L_y$, would not be magnified
-on the calculated $G$'s, as shown in Table \ref{AuThiolHexaneUA}. This
-insensivity to $L_i$ fluctuations allows reliable measurement of $G$'s
-without the necessity of extremely cautious equilibration process. 
+during equilibrating the liquid phase. Due to the stiffness of the
+crystalline Au structure, $L_x$ and $L_y$ would not change noticeably
+after equilibration. Although $L_z$ could fluctuate $\sim$1\% after a
+system is fully equilibrated in the NPT ensemble, this fluctuation, as
+well as those of $L_x$ and $L_y$ (which is significantly smaller),
+would not be magnified on the calculated $G$'s, as shown in Table
+\ref{AuThiolHexaneUA}. This insensivity to $L_i$ fluctuations allows
+reliable measurement of $G$'s without the necessity of extremely
+cautious equilibration process.
 
 As stated in our computational details, the spacing filled with
 solvent molecules can be chosen within a range. This allows some
@@ -459,44 +520,47 @@ $J_z$ is listed in Table \ref{AuThiolHexaneUA} and [RE
 the thermal flux across the interface. For our simulations, we denote
 $J_z$ to be positive when the physical thermal flux is from the liquid
 to metal, and negative vice versa. The $G$'s measured under different
-$J_z$ is listed in Table \ref{AuThiolHexaneUA} and [REF]. These
-results do not suggest that $G$ is dependent on $J_z$ within this flux
-range. The linear response of flux to thermal gradient simplifies our
-investigations in that we can rely on $G$ measurement with only a
-couple $J_z$'s and do not need to test a large series of fluxes.
+$J_z$ is listed in Table \ref{AuThiolHexaneUA} and
+\ref{AuThiolToluene}. These results do not suggest that $G$ is
+dependent on $J_z$ within this flux range. The linear response of flux
+to thermal gradient simplifies our investigations in that we can rely
+on $G$ measurement with only a couple $J_z$'s and do not need to test
+a large series of fluxes.
 
-%ADD MORE TO TABLE
 \begin{table*}
   \begin{minipage}{\linewidth}
     \begin{center}
       \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}{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(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(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)    \\
+            &     &     &       &  1.94 & 125(9)    & 87.1(0.2) \\
+            &     & No  & 0.681 &  0.97 & 141(30)   & 78(22)    \\
+            &     &     &       &  1.92 & 138(4)    & 98.9(9.5) \\
+        \hline
+        250 & 200 & No  & 0.560 &  0.96 & 75(10)    & 61.8(7.3) \\
+            &     &     &       & -0.95 & 49.4(0.3) & 45.7(2.1) \\
+            & 166 & Yes & 0.570 &  0.98 & 79.0(3.5) & 62.9(3.0) \\
+            &     & No  & 0.569 &  0.97 & 80.3(0.6) & 67(11)    \\
+            &     &     &       &  1.44 & 76.2(5.0) & 64.8(3.8) \\
+            &     &     &       & -0.95 & 56.4(2.5) & 54.4(1.1) \\
+            &     &     &       & -1.85 & 47.8(1.1) & 53.5(1.5) \\
         \hline\hline
       \end{tabular}
       \label{AuThiolHexaneUA}
@@ -512,7 +576,8 @@ butanethiol as well.[MAY NEED FIGURE] And this reduced
 temperature is higher than 250K. Additionally, the equilibrated liquid
 hexane density under 250K becomes lower than experimental value. This
 expanded liquid phase leads to lower contact between hexane and
-butanethiol as well.[MAY NEED FIGURE] And this reduced contact would
+butanethiol as well.[MAY NEED SLAB DENSITY FIGURE] 
+And this reduced contact would
 probably be accountable for a lower interfacial thermal conductance,
 as shown in Table \ref{AuThiolHexaneUA}. 
 
@@ -527,25 +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 Lxyz AND 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}{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 &  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(5)  & 125(2)  \\
+            &       & -4.19 & 135(9)  & 113(12) \\
         \hline\hline
       \end{tabular}
       \label{AuThiolToluene}
@@ -577,40 +642,41 @@ above. Our Au-butanethiol/toluene system did not see t
 
 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.
+above. Our Au-butanethiol/toluene system had the Au(111) surfaces 90\%
+covered by butanethiols, but did not see this above phenomena even at
+$\langle T\rangle\sim$300K. The empty three-fold sites not occupied by
+capping agents 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
 thermal conductance, a series of different coverage Au-butanethiol
 surfaces is prepared and solvated with various organic
 molecules. These systems are then equilibrated and their interfacial
-thermal conductivity are measured with our NIVS algorithm. Table
-\ref{tlnUhxnUhxnD} lists these results for direct comparison between
-different coverages of butanethiol. To study the isotope effect in
-interfacial thermal conductance, deuterated UA-hexane is included as
-well.
+thermal conductivity are measured with our NIVS algorithm. Figure
+\ref{coverage} demonstrates the trend of conductance change with
+respect to different coverages of butanethiol. To study the isotope
+effect in interfacial thermal conductance, deuterated UA-hexane is
+included as well.
 
 It turned out that with partial covered butanethiol on the Au(111)
-surface, the derivative definition for $G$ (Eq. \ref{derivativeG}) has
-difficulty to apply, due to the difficulty in locating the maximum of
-change of $\lambda$. Instead, the discrete definition
-(Eq. \ref{discreteG}) is easier to apply, as max($\Delta T$) can still
-be well-defined. Therefore, $G$'s (not $G^\prime$) are used for this
-section. 
+surface, the derivative definition for $G^\prime$
+(Eq. \ref{derivativeG}) was difficult to apply, due to the difficulty
+in locating the maximum of change of $\lambda$. Instead, the discrete
+definition (Eq. \ref{discreteG}) is easier to apply, as the Gibbs
+deviding surface can still be well-defined. Therefore, $G$ (not
+$G^\prime$) was used for this section.
 
-From Table \ref{tlnUhxnUhxnD}, one can see the significance of the
+From Figure \ref{coverage}, one can see the significance of the
 presence of capping agents. Even when a fraction of the Au(111)
 surface sites are covered with butanethiols, the conductivity would
 see an enhancement by at least a factor of 3. This indicates the
 important role cappping agent is playing for thermal transport
-phenomena on metal/organic solvent surfaces.
+phenomena on metal / organic solvent surfaces.
 
 Interestingly, as one could observe from our results, the maximum
 conductance enhancement (largest $G$) happens while the surfaces are
@@ -629,7 +695,8 @@ case, $G$ decrease could not be offset but instead acc
 would not offset this effect. Eventually, when butanethiol coverage
 continues to decrease, solvent-capping agent contact actually
 decreases with the disappearing of butanethiol molecules. In this
-case, $G$ decrease could not be offset but instead accelerated.
+case, $G$ decrease could not be offset but instead accelerated. [NEED
+SNAPSHOT SHOWING THE PHENOMENA]
 
 A comparison of the results obtained from differenet organic solvents
 can also provide useful information of the interfacial thermal
@@ -639,7 +706,7 @@ difference for the results of $G$. [MAY NEED FIGURE]
 studies, even though eliminating C-H vibration samplings, still have
 C-C vibrational frequencies different from each other. However, these
 differences in the infrared range do not seem to produce an observable
-difference for the results of $G$. [MAY NEED FIGURE]
+difference for the results of $G$. [MAY NEED SPECTRA FIGURE]
 
 Furthermore, results for rigid body toluene solvent, as well as other
 UA-hexane solvents, are reasonable within the general experimental
@@ -648,10 +715,10 @@ trend with those for Au-butanethiol/hexane in that $G$
 such as Au-thiol/organic solvent.
 
 However, results for Au-butanethiol/toluene do not show an identical
-trend with those for Au-butanethiol/hexane in that $G$'s remain at
+trend with those for Au-butanethiol/hexane in that $G$ remains at
 approximately the same magnitue when butanethiol coverage differs from
 25\% to 75\%. This might be rooted in the molecule shape difference
-for plane-like toluene and chain-like {\it n}-hexane. Due to this
+for planar toluene and chain-like {\it n}-hexane. Due to this
 difference, toluene molecules have more difficulty in occupying
 relatively small gaps among capping agents when their coverage is not
 too low. Therefore, the solvent-capping agent contact may keep
@@ -660,32 +727,14 @@ 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 +747,6 @@ 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 +754,37 @@ 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}
@@ -745,13 +807,14 @@ the upper bond of experimental value range. This is pr
 interfaces, using AA model for both butanethiol and hexane yields
 substantially higher conductivity values than using UA model for at
 least one component of the solvent and capping agent, which exceeds
-the upper bond of experimental value range. This is probably due to
-the classically treated C-H vibrations in the AA model, which should
-not be appreciably populated at normal temperatures. In comparison,
-once either the hexanes or the butanethiols are deuterated, one can
-see a significantly lower $G$ and $G^\prime$. In either of these
-cases, the C-H(D) vibrational overlap between the solvent and the
-capping agent is removed. [MAY NEED FIGURE] Conclusively, the
+the general range of experimental measurement results. This is
+probably due to the classically treated C-H vibrations in the AA
+model, which should not be appreciably populated at normal
+temperatures. In comparison, once either the hexanes or the
+butanethiols are deuterated, one can see a significantly lower $G$ and
+$G^\prime$. In either of these cases, the C-H(D) vibrational overlap
+between the solvent and the capping agent is removed.
+ [MAY NEED SPECTRA FIGURE] Conclusively, the
 improperly treated C-H vibration in the AA model produced
 over-predicted results accordingly. Compared to the AA model, the UA
 model yields more reasonable results with higher computational
@@ -759,22 +822,25 @@ 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}
-%OR\subsection{Vibrational spectrum study on conductance mechanism}
+[OR: Vibrational Spectrum Study on Conductance Mechanism]
 
 [MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S]
 
@@ -786,28 +852,28 @@ power spectrum via a Fourier transform.
 the velocity auto-correlation functions, which is used to construct a
 power spectrum via a Fourier transform.
 
- The gold surfaces covered by
-butanethiol molecules, compared to bare gold surfaces, exhibit an
-additional peak observed at a frequency of $\sim$170cm$^{-1}$, which
-is attributed to the vibration of the S-Au bond. This vibration
-enables efficient thermal transport from surface Au atoms to the
-capping agents. Simultaneously, as shown in the lower panel of
-Fig. \ref{vibration}, the large overlap of the vibration spectra of
-butanethiol and hexane in the all-atom model, including the C-H
-vibration, also suggests high thermal exchange efficiency. The
-combination of these two effects produces the drastic interfacial
-thermal conductance enhancement in the all-atom model.
+[MAY RELATE TO HASE'S]
+The gold surfaces covered by butanethiol molecules, compared to bare
+gold surfaces, exhibit an additional peak observed at the frequency of
+$\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.
 
-[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}
 
-[COMPARISON OF TWO G'S; AU SLAB WIDTHS; ETC]
+[MAY ADD COMPARISON OF G AND G', AU SLAB WIDTHS, ETC]
 % The results show that the two definitions used for $G$ yield
 % comparable values, though $G^\prime$ tends to be smaller.
 
@@ -819,7 +885,7 @@ gold/liquid interfaces. The acoustic impedance mismatc
 corresponding thermal gradient and to obtain interfacial thermal
 conductivities. Our simulations have seen significant conductance
 enhancement with the presence of capping agent, compared to the bare
-gold/liquid interfaces. The acoustic impedance mismatch between the
+gold / liquid interfaces. The acoustic impedance mismatch between the
 metal and the liquid phase is effectively eliminated by proper capping
 agent. Furthermore, the coverage precentage of the capping agent plays
 an important role in the interfacial thermal transport process.
