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+\bibliographystyle{achemso}
+\begin{document}
+\begin{doublespace}
+\begin{abstract}
-<
+The abstract version 2
->
->
+With the Non-Isotropic Velocity Scaling algorithm (NIVS) we have
->
+developed, an unphysical thermal flux can be effectively set up even
->
+for non-homogeneous systems like interfaces in non-equilibrium
->
+molecular dynamics simulations. In this work, this algorithm is
->
+applied for simulating thermal conductance at metal / organic solvent
->
+interfaces with various coverages of butanethiol capping
->
+agents. Different solvents and force field models were tested. Our
->
+results suggest that the United-Atom models are able to provide an
->
+estimate of the interfacial thermal conductivity comparable to
->
+experiments in our simulations with satisfactory computational
->
+efficiency. From our results, the acoustic impedance mismatch between
->
+metal and liquid phase is effectively reduced by the capping
->
+agents, and thus leads to interfacial thermal conductance
->
+enhancement. Furthermore, this effect is closely related to the
->
+capping agent coverage on the metal surfaces and the type of solvent
->
+molecules, and is affected by the models used in the simulations.
->
+\end{abstract}
+\newpage
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Introduction}
-+
+Due to the importance of heat flow in nanotechnology, interfacial
-+
+thermal conductance has been studied extensively both experimentally
-+
+and computationally.\cite{cahill:793} Unlike bulk materials, nanoscale
-+
+materials have a significant fraction of their atoms at interfaces,
-+
+and the chemical details of these interfaces govern the heat transfer
-+
+behavior. Furthermore, the interfaces are
-+
+heterogeneous (e.g. solid - liquid), which provides a challenge to
-+
+traditional methods developed for homogeneous systems.
-<
+The intro.
->
+Experimentally, various interfaces have been investigated for their
->
+thermal conductance. Wang {\it et al.} studied heat transport through
->
+long-chain hydrocarbon monolayers on gold substrate at individual
->
+molecular level,\cite{Wang10082007} Schmidt {\it et al.} studied the
->
+role of CTAB on thermal transport between gold nanorods and
->
+solvent,\cite{doi:10.1021/jp8051888} and Juv\'e {\it et al.} studied
->
+the cooling dynamics, which is controlled by thermal interface
->
+resistence of glass-embedded metal
->
+nanoparticles.\cite{PhysRevB.80.195406} Although interfaces are
->
+normally considered barriers for heat transport, Alper {\it et al.}
->
+suggested that specific ligands (capping agents) could completely
->
+eliminate this barrier
->
+($G\rightarrow\infty$).\cite{doi:10.1021/la904855s}
-+
+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 have yet to be studied with their
-+
+approach. 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\cite{MullerPlathe:1997xw,kuang:164101} would have the
-+
+advantage of applying this difficult to measure flux (while measuring
-+
+the resulting gradient), given that the simulation methods being able
-+
+to effectively apply an unphysical flux in non-homogeneous systems.
-+
+Garde and coworkers\cite{garde:nl2005,garde:PhysRevLett2009} applied
-+
+this approach to various liquid interfaces and studied how thermal
-+
+conductance (or resistance) is dependent on chemistry details of
-+
+interfaces, e.g. hydrophobic and hydrophilic aqueous interfaces.
-+
-+
+Recently, we have developed a 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 effective thermal exchange
-+
+between particles of different identities, and thus makes the study of
-+
+interfacial conductance much simpler.
-+
-+
+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 the phenomena was investigated.
-+
-+
+\section{Methodology}
-+
+\subsection{Imposd-Flux Methods in MD Simulations}
-+
+Steady state MD simulations have an advantage in that not many
-+
+trajectories are needed to study the relationship between thermal flux
-+
+and thermal gradients. For systems with low interfacial conductance,
-+
+one must have a method capable of generating or measuring relatively
-+
+small fluxes, compared to those required for bulk conductivity. This
-+
+requirement makes the calculation even more difficult for
-+
+slowly-converging equilibrium methods.\cite{Viscardy:2007lq} Forward
-+
+NEMD methods impose a gradient (and measure a flux), but at interfaces
-+
+it is not clear what behavior should be imposed at the boundaries
-+
+between materials.  Imposed-flux reverse non-equilibrium
-+
+methods\cite{MullerPlathe:1997xw} set the flux {\it a priori} and
-+
+the thermal response becomes an easy-to-measure quantity.  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
-+
+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 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 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 an interface with relatively low interfacial conductance, and a
-+
+thermal flux between two distinct bulk regions, the regions on either
-+
+side of the interface rapidly come to a state in which the two phases
-+
+have relatively homogeneous (but distinct) temperatures. The
-+
+interfacial thermal conductivity $G$ can therefore be approximated as:
-+
+\begin{equation}
-+
+  G = \frac{E_{total}}{2 t L_x L_y \left( \langle T_\mathrm{hot}\rangle -
-+
+    \langle T_\mathrm{cold}\rangle \right)}
-+
+\label{lowG}
-+
+\end{equation}
-+
+where ${E_{total}}$ is the total imposed non-physical kinetic energy
-+
+transfer during the simulation and ${\langle T_\mathrm{hot}\rangle}$
-+
+and ${\langle T_\mathrm{cold}\rangle}$ are the average observed
-+
+temperature of the two separated phases.
-+
-+
+When the interfacial conductance is {\it not} small, there are two
-+
+ways to define $G$. 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 reaches its
-+
+maximum, given that $\lambda$ is well-defined throughout the space:
-+
+\begin{equation}
-+
+G^\prime = \Big|\frac{\partial\lambda}{\partial z}\Big|
-+
+         = \Big|\frac{\partial}{\partial z}\left(-J_z\Big/
-+
+           \left(\frac{\partial T}{\partial z}\right)\right)\Big|
-+
+         = |J_z|\Big|\frac{\partial^2 T}{\partial z^2}\Big|
-+
+         \Big/\left(\frac{\partial T}{\partial z}\right)^2
-+
+\label{derivativeG}
-+
+\end{equation}
-+
-+
+With temperature profiles obtained from simulation, one is able to
-+
+approximate the first and second derivatives of $T$ with finite
-+
+difference methods and calculate $G^\prime$. In what follows, both
-+
+definitions have been used, and are compared in the results.
-+
-+
+To investigate the interfacial conductivity at metal / solvent
-+
+interfaces, we have modeled a metal slab with its (111) surfaces
-+
+perpendicular to the $z$-axis of our simulation cells. The metal slab
-+
+has been prepared both with and without capping agents on the exposed
-+
+surface, and has been solvated with simple organic solvents, as
-+
+illustrated in Figure \ref{gradT}.
-+
-+
+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 obtained a temperature profile and its spatial
-+
+derivatives. Figure \ref{gradT} shows how an applied thermal flux can
-+
+be used to obtain the 1st and 2nd derivatives of the temperature
-+
+profile.
-+
-+
+\begin{figure}
-+
+\includegraphics[width=\linewidth]{gradT}
-+
+\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}
-+
-+
+\section{Computational Details}
-+
+\subsection{Simulation Protocol}
-+
+The NIVS algorithm has been implemented in our MD simulation code,
-+
+OpenMD\cite{Meineke:2005gd,openmd}, and was used for our simulations.
-+
+Metal slabs of 6 or 11 layers of Au atoms were first equilibrated
-+
+under atmospheric pressure (1 atm) and 200K. After equilibration,
-+
+butanethiol capping agents were placed at three-fold hollow sites on
-+
+the Au(111) surfaces. These sites are either {\it fcc} or {\it
-+
+  hcp} sites, although Hase {\it et al.} found that they are
-+
+equivalent in a heat transfer process,\cite{hase:2010} so we did not
-+
+distinguish between these sites in our study. The maximum butanethiol
-+
+capacity on Au surface is $1/3$ of the total number of surface Au
-+
+atoms, and the packing forms a $(\sqrt{3}\times\sqrt{3})R30^\circ$
-+
+structure\cite{doi:10.1021/ja00008a001,doi:10.1021/cr9801317}. A
-+
+series of lower coverages was also prepared by eliminating
-+
+butanethiols from the higher coverage surface in a regular manner. The
-+
+lower coverages were prepared in order to study the relation between
-+
+coverage and interfacial conductance.
-+
-+
+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 does 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.
-+
-+
+After the modified Au-butanethiol surface systems were equilibrated in
-+
+the canonical (NVT) 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 which has a planar shape (toluene), and one
-+
+which has similar vibrational frequencies to the capping agent and
-+
+chain-like shape ({\it n}-hexane).
-+
-+
+The simulation cells were not particularly extensive along the
-+
+$z$-axis, as a very long length scale for the thermal gradient may
-+
+cause excessively hot or cold temperatures in the middle of the
-+
+solvent region and lead to undesired phenomena such as solvent boiling
-+
+or freezing when a thermal flux is applied. Conversely, too few
-+
+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. The spacing
-+
+between periodic images of the gold interfaces is $35 \sim 75$\AA.
-+
-+
+The initial configurations generated are further equilibrated with the
-+
+$x$ and $y$ dimensions fixed, only allowing the $z$-length scale to
-+
+change. This is to ensure that the equilibration of liquid phase does
-+
+not affect the metal's crystalline structure. Comparisons were made
-+
+with simulations that allowed changes of $L_x$ and $L_y$ during NPT
-+
+equilibration. No substantial changes in the box geometry were noticed
-+
+in these simulations. After ensuring the liquid phase reaches
-+
+equilibrium at atmospheric pressure (1 atm), further equilibration was
-+
+carried out under canonical (NVT) and microcanonical (NVE) ensembles.
-+
-+
+After the systems reach equilibrium, NIVS was used to impose an
-+
+unphysical thermal flux between the metal and the liquid phases. Most
-+
+of our simulations were done under an average temperature of
-+
+$\sim$200K. Therefore, thermal flux usually came from the metal to the
-+
+liquid so that the liquid has a higher temperature and would not
-+
+freeze due to lowered temperatures. After this induced temperature
-+
+gradient had stablized, the temperature profile of the simulation cell
-+
+was recorded. To do this, the simulation cell is devided evenly into
-+
+$N$ slabs along the $z$-axis. The average temperatures of each slab
-+
+are recorded for 1$\sim$2 ns. When the slab width $d$ of each slab is
-+
+the same, the derivatives of $T$ with respect to slab number $n$ can
-+
+be directly used for $G^\prime$ calculations: \begin{equation}
-+
+  G^\prime = |J_z|\Big|\frac{\partial^2 T}{\partial z^2}\Big|
-+
+         \Big/\left(\frac{\partial T}{\partial z}\right)^2
-+
+         = |J_z|\Big|\frac{1}{d^2}\frac{\partial^2 T}{\partial n^2}\Big|
-+
+         \Big/\left(\frac{1}{d}\frac{\partial T}{\partial n}\right)^2
-+
+         = |J_z|\Big|\frac{\partial^2 T}{\partial n^2}\Big|
-+
+         \Big/\left(\frac{\partial T}{\partial n}\right)^2
-+
+\label{derivativeG2}
-+
+\end{equation}
-+
-+
+All of the above simulation procedures use a time step of 1 fs. Each
-+
+equilibration stage took a minimum of 100 ps, although in some cases,
-+
+longer equilibration stages were utilized.
-+
-+
+\subsection{Force Field Parameters}
-+
+Our simulations include a number of chemically distinct components.
-+
+Figure \ref{demoMol} demonstrates the sites defined for both
-+
+United-Atom and All-Atom models of the organic solvent and capping
-+
+agents in our simulations. Force field parameters 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
-+
+potentials include zero-point quantum corrections and are
-+
+reparametrized for accurate surface energies compared to the
-+
+Sutton-Chen potentials.\cite{Chen90}
-+
-+
+For the two solvent molecules, {\it n}-hexane and toluene, two
-+
+different atomistic models were utilized. Both solvents were modeled
-+
+using United-Atom (UA) and All-Atom (AA) models. The TraPPE-UA
-+
+parameters\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} are used
-+
+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 closer than 3 bonds. For non-bonded interactions, Lennard-Jones
-+
+potentials are used.
-+
-+
+By eliminating explicit hydrogen atoms, the TraPPE-UA models are
-+
+simple and computationally efficient, while maintaining good accuracy.
-+
+However, the TraPPE-UA model for alkanes is known to predict a slighly
-+
+lower boiling point than experimental values. This is one of the
-+
+reasons we used a lower average temperature (200K) for our
-+
+simulations. If heat is transferred to the liquid phase during the
-+
+NIVS simulation, the liquid in the hot slab can actually be
-+
+substantially warmer than the mean temperature in the simulation. The
-+
+lower mean temperatures therefore prevent solvent boiling.
-+
-+
+For UA-toluene, the non-bonded potentials between intermolecular sites
-+
+have a similar Lennard-Jones formulation. The toluene molecules were
-+
+treated as a single rigid body, so there was no need for
-+
+intramolecular interactions (including bonds, bends, or torsions) in
-+
+this solvent model.
-+
-+
+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, and 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} was adopted, and
-+
+a flexible model for the toluene molecule was utilized which included
-+
+bond, bend, torsion, and inversion potentials to enforce ring
-+
+planarity.
-+
-+
+The butanethiol capping agent in our simulations, were also modeled
-+
+with both UA and AA model. The TraPPE-UA force field includes
-+
+parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used for
-+
+UA butanethiol model in our simulations. The OPLS-AA also provides
-+
+parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111)
-+
+surfaces do not have the hydrogen atom bonded to sulfur. To derive
-+
+suitable parameters for butanethiol adsorbed on Au(111) surfaces, we
-+
+adopt the S parameters from Luedtke and Landman\cite{landman:1998} and
-+
+modify the parameters for the CTS atom to maintain charge neutrality
-+
+in the molecule.  Note that the model choice (UA or AA) for the 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 atoms,
-+
+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 for the Au(111)
-+
+surface.\cite{hautman:4994} As our simulations require the gold slab
-+
+to be flexible to accommodate thermal excitation, the pair-wise form
-+
+of potentials they developed was used for our study.
-+
-+
+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. However,
-+
+the Lennard-Jones parameters between Au and other types of particles,
-+
+(e.g. AA alkanes) have not yet been established. For these
-+
+interactions, the Lorentz-Berthelot mixing rule can be used to derive
-+
+effective single-atom LJ parameters for the metal using the fit values
-+
+for toluene. These are then used to construct reasonable mixing
-+
+parameters for the interactions between the gold and other atoms.
-+
+Table \ref{MnM} summarizes the ``metal/non-metal'' parameters used in
-+
+our simulations.
-+
-+
+\begin{table*}
-+
+  \begin{minipage}{\linewidth}
-+
+    \begin{center}
-+
+      \caption{Non-bonded interaction parameters (including cross
-+
+        interactions with Au atoms) for both force fields used in this
-+
+        work.}
-+
+      \begin{tabular}{lllllll}
-+
+        \hline\hline
-+
+        & Site  & $\sigma_{ii}$ & $\epsilon_{ii}$ & $q_i$ &
-+
+        $\sigma_{Au-i}$ & $\epsilon_{Au-i}$ \\
-+
+        & & (\AA) & (kcal/mol) & ($e$) & (\AA) & (kcal/mol) \\
-+
+        \hline
-+
+        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}
-+
+    \end{center}
-+
+  \end{minipage}
-+
+\end{table*}
-+
-+
+\subsection{Vibrational Power Spectrum}
-+
-+
+To investigate the mechanism of interfacial thermal conductance, the
-+
+vibrational power spectrum was computed. Power spectra were taken for
-+
+individual components in different simulations. To obtain these
-+
+spectra, simulations were run after equilibration, in the NVE
-+
+ensemble, and without a thermal gradient. Snapshots of configurations
-+
+were collected at a frequency that is higher than that of the fastest
-+
+vibrations occuring in the simulations. With these configurations, the
-+
+velocity auto-correlation functions can be computed:
-+
+\begin{equation}
-+
+C_A (t) = \langle\vec{v}_A (t)\cdot\vec{v}_A (0)\rangle
-+
+\label{vCorr}
-+
+\end{equation}
-+
+The power spectrum is constructed via a Fourier transform of the
-+
+symmetrized velocity autocorrelation function,
-+
+\begin{equation}
-+
+  \hat{f}(\omega) =
-+
+  \int_{-\infty}^{\infty} C_A (t) e^{-2\pi it\omega}\,dt
-+
+\label{fourier}
-+
+\end{equation}
-+
-+
+\section{Results and Discussions}
-+
+In what follows, how the parameters and protocol of simulations would
-+
+affect the measurement of $G$'s is first discussed. With a reliable
-+
+protocol and set of parameters, the influence of capping agent
-+
+coverage on thermal conductance is investigated. Besides, different
-+
+force field models for both solvents and selected deuterated models
-+
+were tested and compared. Finally, a summary of the role of capping
-+
+agent in the interfacial thermal transport process is given.
-+
-+
+\subsection{How Simulation Parameters Affects $G$}
-+
+We have varied our protocol or other parameters of the simulations in
-+
+order to investigate how these factors would affect the measurement of
-+
+$G$'s. It turned out that while some of these parameters would not
-+
+affect the results substantially, some other changes to the
-+
+simulations would have a significant impact on the measurement
-+
+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
-+
+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
-+
+change of solvent molecule numbers for the same Au-butanethiol
-+
+surfaces. We did this study on our Au-butanethiol/hexane
-+
+simulations. Nevertheless, the results obtained from systems of
-+
+different $N_{hexane}$ did not indicate that the measurement of $G$ is
-+
+susceptible to this parameter. For computational efficiency concern,
-+
+smaller system size would be preferable, given that the liquid phase
-+
+structure is not affected.
-+
-+
+Our NIVS algorithm allows change of unphysical thermal flux both in
-+
+direction and in quantity. This feature extends our investigation of
-+
+interfacial thermal conductance. However, the magnitude of this
-+
+thermal flux is not arbitary if one aims to obtain a stable and
-+
+reliable thermal gradient. A temperature profile would be
-+
+substantially affected by noise when $|J_z|$ has a much too low
-+
+magnitude; while an excessively large $|J_z|$ that overwhelms the
-+
+conductance capacity of the interface would prevent a thermal gradient
-+
+to reach a stablized steady state. NIVS has the advantage of allowing
-+
+$J$ to vary in a wide range such that the optimal flux range for $G$
-+
+measurement can generally be simulated by the algorithm. Within the
-+
+optimal range, we were able to study how $G$ would change according to
-+
+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{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.
-+
-+
+\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. Error estimates indicated in parenthesis.}
-+
-+
+      \begin{tabular}{ccccccc}
-+
+        \hline\hline
-+
+        $\langle T\rangle$ & $N_{hexane}$ & 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
-+
+& 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
-+
+& 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}
-+
+    \end{center}
-+
+  \end{minipage}
-+
+\end{table*}
-+
-+
+Furthermore, we also attempted to increase system average temperatures
-+
+to above 200K. These simulations are first equilibrated in the NPT
-+
+ensemble under normal pressure. As stated above, the TraPPE-UA model
-+
+for hexane tends to predict a lower boiling point. In our simulations,
-+
+hexane had diffculty to remain in liquid phase when NPT equilibration
-+
+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 SLAB DENSITY FIGURE]
-+
+And this reduced contact would
-+
+probably be accountable for a lower interfacial thermal conductance,
-+
+as shown in Table \ref{AuThiolHexaneUA}.
-+
-+
+A similar study for TraPPE-UA toluene agrees with the above result as
-+
+well. Having a higher boiling point, toluene tends to remain liquid in
-+
+our simulations even equilibrated under 300K in NPT
-+
+ensembles. Furthermore, the expansion of the toluene liquid phase is
-+
+not as significant as that of the hexane. This prevents severe
-+
+decrease of liquid-capping agent contact and the results (Table
-+
+\ref{AuThiolToluene}) show only a slightly decreased interface
-+
+conductance. Therefore, solvent-capping agent contact should play an
-+
+important role in the thermal transport process across the interface
-+
+in that higher degree of contact could yield increased conductance.
-+
-+
+\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. 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
-+
+& 0.933 &  2.15 & 204(12) & 113(12) \\
-+
+            &       & -1.86 & 180(3)  & 135(21) \\
-+
+            &       & -3.93 & 176(5)  & 113(12) \\
-+
+        \hline
-+
+& 0.855 & -1.91 & 143(5)  & 125(2)  \\
-+
+            &       & -4.19 & 135(9)  & 113(12) \\
-+
+        \hline\hline
-+
+      \end{tabular}
-+
+      \label{AuThiolToluene}
-+
+    \end{center}
-+
+  \end{minipage}
-+
+\end{table*}
-+
-+
+Besides lower interfacial thermal conductance, surfaces in relatively
-+
+high temperatures are susceptible to reconstructions, when
-+
+butanethiols have a full coverage on the Au(111) surface. These
-+
+reconstructions include surface Au atoms migrated outward to the S
-+
+atom layer, and butanethiol molecules embedded into the original
-+
+surface Au layer. The driving force for this behavior is the strong
-+
+Au-S interactions in our simulations. And these reconstructions lead
-+
+to higher ratio of Au-S attraction and thus is energetically
-+
+favorable. Furthermore, this phenomenon agrees with experimental
-+
+results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt
-+
+{\it et al.} had kept their Au(111) slab rigid so that their
-+
+simulations can reach 300K without surface reconstructions. Without
-+
+this practice, simulating 100\% thiol covered interfaces under higher
-+
+temperatures could hardly avoid surface reconstructions. However, our
-+
+measurement is based on assuming homogeneity on $x$ and $y$ dimensions
-+
+so that measurement of $T$ at particular $z$ would be an effective
-+
+average of the particles of the same type. Since surface
-+
+reconstructions could eliminate the original $x$ and $y$ dimensional
-+
+homogeneity, measurement of $G$ is more difficult to conduct under
-+
+higher temperatures. Therefore, most of our measurements are
-+
+undertaken at $\langle T\rangle\sim$200K.
-+
-+
+However, when the surface is not completely covered by butanethiols,
-+
+the simulated system is more resistent to the reconstruction
-+
+above. Our Au-butanethiol/toluene system had the Au(111) surfaces 90\%
-+
+covered by butanethiols, but did not see this above phenomena even at
-+
+$\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. 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.
-+
-+
+\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}
-+
-+
+It turned out that with partial covered butanethiol on the Au(111)
-+
+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 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.
-+
-+
+Interestingly, as one could observe from our results, the maximum
-+
+conductance enhancement (largest $G$) happens while the surfaces are
-+
+about 75\% covered with butanethiols. This again indicates that
-+
+solvent-capping agent contact has an important role of the thermal
-+
+transport process. Slightly lower butanethiol coverage allows small
-+
+gaps between butanethiols to form. And these gaps could be filled with
-+
+solvent molecules, which acts like ``heat conductors'' on the
-+
+surface. The higher degree of interaction between these solvent
-+
+molecules and capping agents increases the enhancement effect and thus
-+
+produces a higher $G$ than densely packed butanethiol arrays. However,
-+
+once this maximum conductance enhancement is reached, $G$ decreases
-+
+when butanethiol coverage continues to decrease. Each capping agent
-+
+molecule reaches its maximum capacity for thermal
-+
+conductance. Therefore, even higher solvent-capping agent contact
-+
+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. [NEED
-+
+SNAPSHOT SHOWING THE PHENOMENA / SLAB DENSITY ANALYSIS]
-+
-+
+A comparison of the results obtained from differenet organic solvents
-+
+can also provide useful information of the interfacial thermal
-+
+transport process. The deuterated hexane (UA) results do not appear to
-+
+be much different from those of normal hexane (UA), given that
-+
+butanethiol (UA) is non-deuterated for both solvents. These UA model
-+
+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 $G$ (Figure \ref{uahxnua}).
-+
-+
+\begin{figure}
-+
+\includegraphics[width=\linewidth]{uahxnua}
-+
+\caption{Vibrational spectra obtained for normal (upper) and
-+
+  deuterated (lower) hexane in Au-butanethiol/hexane
-+
+  systems. Butanethiol spectra are shown as reference. Both hexane and
-+
+  butanethiol were using United-Atom models.}
-+
+\label{uahxnua}
-+
+\end{figure}
-+
-+
+Furthermore, results for rigid body toluene solvent, as well as other
-+
+UA-hexane solvents, are reasonable within the general experimental
-+
+ranges\cite{Wilson:2002uq,cahill:793,PhysRevB.80.195406}. This
-+
+suggests that explicit hydrogen might not be a required factor for
-+
+modeling thermal transport phenomena of systems 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 $G$ remains at
-+
+approximately the same magnitue when butanethiol coverage differs from
-+
+\% to 75\%. This might be rooted in the molecule shape difference
-+
+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
-+
+increasing until the capping agent coverage reaches a relatively low
-+
+level. This becomes an offset for decreasing butanethiol molecules on
-+
+its effect to the process of interfacial thermal transport. Thus, one
-+
+can see a plateau of $G$ vs. butanethiol coverage in our results.
-+
-+
+\subsection{Influence of Chosen Molecule Model on $G$}
-+
+In addition to UA solvent/capping agent models, AA models are included
-+
+in our simulations as well. Besides simulations of the same (UA or AA)
-+
+model for solvent and capping agent, different models can be applied
-+
+to different components. Furthermore, regardless of models chosen,
-+
+either the solvent or the capping agent can be deuterated, similar to
-+
+the previous section. Table \ref{modelTest} summarizes the results of
-+
+these studies.
-+
-+
+\begin{table*}
-+
+  \begin{minipage}{\linewidth}
-+
+    \begin{center}
-+
-+
+      \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. (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}{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    & 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}
-+
+    \end{center}
-+
+  \end{minipage}
-+
+\end{table*}
-+
-+
+To facilitate direct comparison, the same system with differnt models
-+
+for different components uses the same length scale for their
-+
+simulation cells. Without the presence of capping agent, using
-+
+different models for hexane yields similar results for both $G$ and
-+
+$G^\prime$, and these two definitions agree with eath other very
-+
+well. This indicates very weak interaction between the metal and the
-+
+solvent, and is a typical case for acoustic impedance mismatch between
-+
+these two phases.
-+
-+
+As for Au(111) surfaces completely covered by butanethiols, the choice
-+
+of models for capping agent and solvent could impact the measurement
-+
+of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane
-+
+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 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 (Figure
-+
+\ref{aahxntln}). 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 efficiency.
-+
-+
+\begin{figure}
-+
+\includegraphics[width=\linewidth]{aahxntln}
-+
+\caption{Spectra obtained for All-Atom model Au-butanethil/solvent
-+
+  systems. When butanethiol is deuterated (lower left), its
-+
+  vibrational overlap with hexane would decrease significantly,
-+
+  compared with normal butanethiol (upper left). However, this
-+
+  dramatic change does not apply to toluene as much (right).}
-+
+\label{aahxntln}
-+
+\end{figure}
-+
-+
+However, for Au-butanethiol/toluene interfaces, having the AA
-+
+butanethiol deuterated did not yield a significant change in the
-+
+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 heat exchange
-+
+process. 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{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, 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{Role of Capping Agent in Interfacial Thermal Conductance}
-+
+The vibrational spectra for gold slabs in different environments are
-+
+shown as in Figure \ref{specAu}. Regardless of the presence of
-+
+solvent, 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. Therefore, in our
-+
+simulations, the Au/S interfaces do not appear major heat barriers
-+
+compared to the butanethiol / solvent interfaces.
-+
-+
+Simultaneously, the vibrational overlap between butanethiol and
-+
+organic solvents suggests higher thermal exchange efficiency between
-+
+these two components. Even exessively high heat transport was observed
-+
+when All-Atom models were used and C-H vibrations were treated
-+
+classically. Compared to metal and organic liquid phase, the heat
-+
+transfer efficiency between butanethiol and organic solvents is closer
-+
+to that within bulk liquid phase.
-+
-+
+Furthermore, our observation validated previous
-+
+results\cite{hase:2010} that the intramolecular heat transport of
-+
+alkylthiols is highly effecient. As a combinational effects of these
-+
+phenomena, butanethiol acts as a channel to expedite thermal transport
-+
+process. The acoustic impedance mismatch between the metal and the
-+
+liquid phase can be effectively reduced with the presence of suitable
-+
+capping agents.
-+
-+
+\begin{figure}
-+
+\includegraphics[width=\linewidth]{vibration}
-+
+\caption{Vibrational spectra obtained for gold in different
-+
+  environments.}
-+
+\label{specAu}
-+
+\end{figure}
-+
-+
+[MAY ADD COMPARISON OF AU SLAB WIDTHS]
-+
-+
+\section{Conclusions}
-+
+The NIVS algorithm we developed has been applied to simulations of
-+
+Au-butanethiol surfaces with organic solvents. This algorithm allows
-+
+effective unphysical thermal flux transferred between the metal and
-+
+the liquid phase. With the flux applied, we were able to measure the
-+
+corresponding thermal gradient and to obtain interfacial thermal
-+
+conductivities. Under steady states, single trajectory simulation
-+
+would be enough for accurate measurement. This would be advantageous
-+
+compared to transient state simulations, which need multiple
-+
+trajectories to produce reliable average results.
-+
-+
+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 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. Moderately lower coverages allow higher contact between
-+
+capping agent and solvent, and thus could further enhance the heat
-+
+transfer process.
-+
-+
+Our measurement results, particularly of the UA models, agree with
-+
+available experimental data. This indicates that our force field
-+
+parameters have a nice description of the interactions between the
-+
+particles at the interfaces. AA models tend to overestimate the
-+
+interfacial thermal conductance in that the classically treated C-H
-+
+vibration would be overly sampled. Compared to the AA models, the UA
-+
+models have higher computational efficiency with satisfactory
-+
+accuracy, and thus are preferable in interfacial thermal transport
-+
+modelings. Of the two definitions for $G$, the discrete form
-+
+(Eq. \ref{discreteG}) was easier to use and gives out relatively
-+
+consistent results, while the derivative form (Eq. \ref{derivativeG})
-+
+is not as versatile. Although $G^\prime$ gives out comparable results
-+
+and follows similar trend with $G$ when measuring close to fully
-+
+covered or bare surfaces, the spatial resolution of $T$ profile is
-+
+limited for accurate computation of derivatives data.
-+
-+
+Vlugt {\it et al.} has investigated the surface thiol structures for
-+
+nanocrystal gold and pointed out that they differs from those of the
-+
+Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to
-+
+change of interfacial thermal transport behavior as well. To
-+
+investigate this problem, an effective means to introduce thermal flux
-+
+and measure the corresponding thermal gradient is desirable for
-+
+simulating structures with spherical symmetry.
-+
+\section{Acknowledgments}
+Support for this project was provided by the National Science
+Foundation under grant CHE-0848243. Computational time was provided by
+the Center for Research Computing (CRC) at the University of Notre
-<
+Dame.  \newpage
->
+Dame. \newpage
+\bibliography{interfacial}

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Comparing interfacial/interfacial.tex (file contents): Revision 3718 by gezelter, Thu Jan 27 16:30:51 2011 UTC vs. Revision 3751 by gezelter, Tue Jul 26 19:43:10 2011 UTC

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Comparing interfacial/interfacial.tex (file contents):
Revision 3718 by gezelter, Thu Jan 27 16:30:51 2011 UTC vs.
Revision 3751 by gezelter, Tue Jul 26 19:43:10 2011 UTC