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Revision 3745 by skuang, Thu Jul 21 00:04:26 2011 UTC

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23   \setlength{\belowcaptionskip}{30 pt}
24  
25   %\renewcommand\citemid{\ } % no comma in optional reference note
26 < \bibpunct{[}{]}{,}{s}{}{;}
27 < \bibliographystyle{aip}
26 > \bibpunct{[}{]}{,}{n}{}{;}
27 > \bibliographystyle{achemso}
28  
29   \begin{document}
30  
# Line 45 | Line 45 | We have developed a Non-Isotropic Velocity Scaling alg
45  
46   \begin{abstract}
47  
48 < We have developed a Non-Isotropic Velocity Scaling algorithm for
49 < setting up and maintaining stable thermal gradients in non-equilibrium
50 < molecular dynamics simulations. This approach effectively imposes
51 < unphysical thermal flux even between particles of different
52 < identities, conserves linear momentum and kinetic energy, and
53 < minimally perturbs the velocity profile of a system when compared with
54 < previous RNEMD methods. We have used this method to simulate thermal
55 < conductance at metal / organic solvent interfaces both with and
56 < without the presence of thiol-based capping agents.  We obtained
57 < values comparable with experimental values, and observed significant
58 < conductance enhancement with the presence of capping agents. Computed
59 < power spectra indicate the acoustic impedance mismatch between metal
60 < and liquid phase is greatly reduced by the capping agents and thus
61 < leads to higher interfacial thermal transfer efficiency.
48 > With the Non-Isotropic Velocity Scaling algorithm (NIVS) we have
49 > developed, an unphysical thermal flux can be effectively set up even
50 > for non-homogeneous systems like interfaces in non-equilibrium
51 > molecular dynamics simulations. In this work, this algorithm is
52 > applied for simulating thermal conductance at metal / organic solvent
53 > interfaces with various coverages of butanethiol capping
54 > agents. Different solvents and force field models were tested. Our
55 > results suggest that the United-Atom models are able to provide an
56 > estimate of the interfacial thermal conductivity comparable to
57 > experiments in our simulations with satisfactory computational
58 > efficiency. From our results, the acoustic impedance mismatch between
59 > metal and liquid phase is effectively reduced by the capping
60 > agents, and thus leads to interfacial thermal conductance
61 > enhancement. Furthermore, this effect is closely related to the
62 > capping agent coverage on the metal surfaces and the type of solvent
63 > molecules, and is affected by the models used in the simulations.
64  
65   \end{abstract}
66  
# Line 71 | Line 73 | leads to higher interfacial thermal transfer efficienc
73   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
74  
75   \section{Introduction}
74 – [BACKGROUND FOR INTERFACIAL THERMAL CONDUCTANCE PROBLEM]
76   Interfacial thermal conductance is extensively studied both
77 < experimentally and computationally, and systems with interfaces
78 < present are generally heterogeneous. Although interfaces are commonly
79 < barriers to heat transfer, it has been
80 < reported\cite{doi:10.1021/la904855s} that under specific circustances,
81 < e.g. with certain capping agents present on the surface, interfacial
82 < conductance can be significantly enhanced. However, heat conductance
83 < of molecular and nano-scale interfaces will be affected by the
84 < chemical details of the surface and is challenging to
85 < experimentalist. The lower thermal flux through interfaces is even
85 < more difficult to measure with EMD and forward NEMD simulation
86 < methods. Therefore, developing good simulation methods will be
87 < desirable in order to investigate thermal transport across interfaces.
77 > experimentally and computationally\cite{cahill:793}, due to its
78 > importance in nanoscale science and technology. Reliability of
79 > nanoscale devices depends on their thermal transport
80 > properties. Unlike bulk homogeneous materials, nanoscale materials
81 > features significant presence of interfaces, and these interfaces
82 > could dominate the heat transfer behavior of these
83 > materials. Furthermore, these materials are generally heterogeneous,
84 > which challenges traditional research methods for homogeneous
85 > systems.
86  
87 + Heat conductance of molecular and nano-scale interfaces will be
88 + affected by the chemical details of the surface. Experimentally,
89 + various interfaces have been investigated for their thermal
90 + conductance properties. Wang {\it et al.} studied heat transport
91 + through long-chain hydrocarbon monolayers on gold substrate at
92 + individual molecular level\cite{Wang10082007}; Schmidt {\it et al.}
93 + studied the role of CTAB on thermal transport between gold nanorods
94 + and solvent\cite{doi:10.1021/jp8051888}; Juv\'e {\it et al.} studied
95 + the cooling dynamics, which is controlled by thermal interface
96 + resistence of glass-embedded metal
97 + nanoparticles\cite{PhysRevB.80.195406}. Although interfaces are
98 + commonly barriers for heat transport, Alper {\it et al.} suggested
99 + that specific ligands (capping agents) could completely eliminate this
100 + barrier ($G\rightarrow\infty$)\cite{doi:10.1021/la904855s}.
101 +
102 + Theoretical and computational models have also been used to study the
103 + interfacial thermal transport in order to gain an understanding of
104 + this phenomena at the molecular level. Recently, Hase and coworkers
105 + employed Non-Equilibrium Molecular Dynamics (NEMD) simulations to
106 + study thermal transport from hot Au(111) substrate to a self-assembled
107 + monolayer of alkylthiol with relatively long chain (8-20 carbon
108 + atoms)\cite{hase:2010,hase:2011}. However, ensemble averaged
109 + measurements for heat conductance of interfaces between the capping
110 + monolayer on Au and a solvent phase has yet to be studied.
111 + The comparatively low thermal flux through interfaces is
112 + difficult to measure with Equilibrium MD or forward NEMD simulation
113 + methods. Therefore, the Reverse NEMD (RNEMD) methods would have the
114 + advantage of having this difficult to measure flux known when studying
115 + the thermal transport across interfaces, given that the simulation
116 + methods being able to effectively apply an unphysical flux in
117 + non-homogeneous systems.
118 +
119   Recently, we have developed the Non-Isotropic Velocity Scaling (NIVS)
120   algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm
121   retains the desirable features of RNEMD (conservation of linear
122   momentum and total energy, compatibility with periodic boundary
123   conditions) while establishing true thermal distributions in each of
124 < the two slabs. Furthermore, it allows more effective thermal exchange
125 < between particles of different identities, and thus enables extensive
126 < study of interfacial conductance.
124 > the two slabs. Furthermore, it allows effective thermal exchange
125 > between particles of different identities, and thus makes the study of
126 > interfacial conductance much simpler.
127  
128 + The work presented here deals with the Au(111) surface covered to
129 + varying degrees by butanethiol, a capping agent with short carbon
130 + chain, and solvated with organic solvents of different molecular
131 + properties. Different models were used for both the capping agent and
132 + the solvent force field parameters. Using the NIVS algorithm, the
133 + thermal transport across these interfaces was studied and the
134 + underlying mechanism for this phenomena was investigated.
135 +
136 + [MAY ADD WHY STUDY AU-THIOL SURFACE; CITE SHAOYI JIANG]
137 +
138   \section{Methodology}
139 < \subsection{Algorithm}
140 < [BACKGROUND FOR MD METHODS]
141 < There have been many algorithms for computing thermal conductivity
142 < using molecular dynamics simulations. However, interfacial conductance
143 < is at least an order of magnitude smaller. This would make the
144 < calculation even more difficult for those slowly-converging
145 < equilibrium methods. Imposed-flux non-equilibrium
139 > \subsection{Imposd-Flux Methods in MD Simulations}
140 > For systems with low interfacial conductivity one must have a method
141 > capable of generating relatively small fluxes, compared to those
142 > required for bulk conductivity. This requirement makes the calculation
143 > even more difficult for those slowly-converging equilibrium
144 > methods\cite{Viscardy:2007lq}.
145 > Forward methods impose gradient, but in interfacail conditions it is
146 > not clear what behavior to impose at the boundary...
147 > Imposed-flux reverse non-equilibrium
148   methods\cite{MullerPlathe:1997xw} have the flux set {\it a priori} and
149 < the response of temperature or momentum gradients are easier to
150 < measure than the flux, if unknown, and thus, is a preferable way to
151 < the forward NEMD methods. Although the momentum swapping approach for
152 < flux-imposing can be used for exchanging energy between particles of
153 < different identity, the kinetic energy transfer efficiency is affected
154 < by the mass difference between the particles, which limits its
113 < application on heterogeneous interfacial systems.
149 > the thermal response becomes easier to
150 > measure than the flux. Although M\"{u}ller-Plathe's original momentum
151 > swapping approach can be used for exchanging energy between particles
152 > of different identity, the kinetic energy transfer efficiency is
153 > affected by the mass difference between the particles, which limits
154 > its application on heterogeneous interfacial systems.
155  
156 < The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach in
157 < non-equilibrium MD simulations is able to impose relatively large
158 < kinetic energy flux without obvious perturbation to the velocity
159 < distribution of the simulated systems. Furthermore, this approach has
156 > The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach to
157 > non-equilibrium MD simulations is able to impose a wide range of
158 > kinetic energy fluxes without obvious perturbation to the velocity
159 > distributions of the simulated systems. Furthermore, this approach has
160   the advantage in heterogeneous interfaces in that kinetic energy flux
161   can be applied between regions of particles of arbitary identity, and
162 < the flux quantity is not restricted by particle mass difference.
162 > the flux will not be restricted by difference in particle mass.
163  
164   The NIVS algorithm scales the velocity vectors in two separate regions
165   of a simulation system with respective diagonal scaling matricies. To
166   determine these scaling factors in the matricies, a set of equations
167   including linear momentum conservation and kinetic energy conservation
168 < constraints and target momentum/energy flux satisfaction is
169 < solved. With the scaling operation applied to the system in a set
170 < frequency, corresponding momentum/temperature gradients can be built,
171 < which can be used for computing transportation properties and other
172 < applications related to momentum/temperature gradients. The NIVS
132 < algorithm conserves momenta and energy and does not depend on an
133 < external thermostat.
168 > constraints and target energy flux satisfaction is solved. With the
169 > scaling operation applied to the system in a set frequency, bulk
170 > temperature gradients can be easily established, and these can be used
171 > for computing thermal conductivities. The NIVS algorithm conserves
172 > momenta and energy and does not depend on an external thermostat.
173  
174   \subsection{Defining Interfacial Thermal Conductivity $G$}
175   For interfaces with a relatively low interfacial conductance, the bulk
# Line 148 | Line 187 | When the interfacial conductance is {\it not} small, t
187    T_\mathrm{cold}\rangle}$ are the average observed temperature of the
188   two separated phases.
189  
190 < When the interfacial conductance is {\it not} small, two ways can be
191 < used to define $G$.
190 > When the interfacial conductance is {\it not} small, there are two
191 > ways to define $G$.
192  
193 < One way is to assume the temperature is discretely different on two
194 < sides of the interface, $G$ can be calculated with the thermal flux
195 < applied $J$ and the maximum temperature difference measured along the
196 < thermal gradient max($\Delta T$), which occurs at the interface, as:
193 > One way is to assume the temperature is discrete on the two sides of
194 > the interface. $G$ can be calculated using the applied thermal flux
195 > $J$ and the maximum temperature difference measured along the thermal
196 > gradient max($\Delta T$), which occurs at the Gibbs deviding surface
197 > (Figure \ref{demoPic}):
198   \begin{equation}
199   G=\frac{J}{\Delta T}
200   \label{discreteG}
201   \end{equation}
202  
203 + \begin{figure}
204 + \includegraphics[width=\linewidth]{method}
205 + \caption{Interfacial conductance can be calculated by applying an
206 +  (unphysical) kinetic energy flux between two slabs, one located
207 +  within the metal and another on the edge of the periodic box.  The
208 +  system responds by forming a thermal response or a gradient.  In
209 +  bulk liquids, this gradient typically has a single slope, but in
210 +  interfacial systems, there are distinct thermal conductivity
211 +  domains.  The interfacial conductance, $G$ is found by measuring the
212 +  temperature gap at the Gibbs dividing surface, or by using second
213 +  derivatives of the thermal profile.}
214 + \label{demoPic}
215 + \end{figure}
216 +
217   The other approach is to assume a continuous temperature profile along
218   the thermal gradient axis (e.g. $z$) and define $G$ at the point where
219   the magnitude of thermal conductivity $\lambda$ change reach its
# Line 175 | Line 229 | difference method and thus calculate $G^\prime$.
229  
230   With the temperature profile obtained from simulations, one is able to
231   approximate the first and second derivatives of $T$ with finite
232 < difference method and thus calculate $G^\prime$.
232 > difference methods and thus calculate $G^\prime$.
233  
234 < In what follows, both definitions are used for calculation and comparison.
234 > In what follows, both definitions have been used for calculation and
235 > are compared in the results.
236  
237 < [IMPOSE G DEFINITION INTO OUR SYSTEMS]
238 < To facilitate the use of the above definitions in calculating $G$ and
239 < $G^\prime$, we have a metal slab with its (111) surfaces perpendicular
240 < to the $z$-axis of our simulation cells. With or withour capping
241 < agents on the surfaces, the metal slab is solvated with organic
187 < solvents, as illustrated in Figure \ref{demoPic}.
237 > To compare the above definitions ($G$ and $G^\prime$), we have modeled
238 > a metal slab with its (111) surfaces perpendicular to the $z$-axis of
239 > our simulation cells. Both with and without capping agents on the
240 > surfaces, the metal slab is solvated with simple organic solvents, as
241 > illustrated in Figure \ref{demoPic}.
242  
243 < \begin{figure}
244 < \includegraphics[width=\linewidth]{demoPic}
245 < \caption{A sample showing how a metal slab has its (111) surface
246 <  covered by capping agent molecules and solvated by hexane.}
247 < \label{demoPic}
248 < \end{figure}
243 > With the simulation cell described above, we are able to equilibrate
244 > the system and impose an unphysical thermal flux between the liquid
245 > and the metal phase using the NIVS algorithm. By periodically applying
246 > the unphysical flux, we are able to obtain a temperature profile and
247 > its spatial derivatives. These quantities enable the evaluation of the
248 > interfacial thermal conductance of a surface. Figure \ref{gradT} is an
249 > example how those applied thermal fluxes can be used to obtain the 1st
250 > and 2nd derivatives of the temperature profile.
251  
196 – With a simulation cell setup following the above manner, one is able
197 – to equilibrate the system and impose an unphysical thermal flux
198 – between the liquid and the metal phase with the NIVS algorithm. Under
199 – a stablized thermal gradient induced by periodically applying the
200 – unphysical flux, one is able to obtain a temperature profile and the
201 – physical thermal flux corresponding to it, which equals to the
202 – unphysical flux applied by NIVS. These data enables the evaluation of
203 – the interfacial thermal conductance of a surface. Figure \ref{gradT}
204 – is an example how those stablized thermal gradient can be used to
205 – obtain the 1st and 2nd derivatives of the temperature profile.
206 –
252   \begin{figure}
253   \includegraphics[width=\linewidth]{gradT}
254 < \caption{The 1st and 2nd derivatives of temperature profile can be
255 <  obtained with finite difference approximation.}
254 > \caption{A sample of Au-butanethiol/hexane interfacial system and the
255 >  temperature profile after a kinetic energy flux is imposed to
256 >  it. The 1st and 2nd derivatives of the temperature profile can be
257 >  obtained with finite difference approximation (lower panel).}
258   \label{gradT}
259   \end{figure}
260  
261   \section{Computational Details}
262 < \subsection{System Geometry}
263 < In our simulations, Au is used to construct a metal slab with bare
264 < (111) surface perpendicular to the $z$-axis. Different slab thickness
265 < (layer numbers of Au) are simulated. This metal slab is first
266 < equilibrated under normal pressure (1 atm) and a desired
267 < temperature. After equilibration, butanethiol is used as the capping
268 < agent molecule to cover the bare Au (111) surfaces evenly. The sulfur
269 < atoms in the butanethiol molecules would occupy the three-fold sites
270 < of the surfaces, and the maximal butanethiol capacity on Au surface is
271 < $1/3$ of the total number of surface Au atoms[CITATION]. A series of
272 < different coverage surfaces is investigated in order to study the
273 < relation between coverage and conductance.
227 <
228 < [COVERAGE DISCRIPTION] However, since the interactions between surface
229 < Au and butanethiol is non-bonded, the capping agent molecules are
230 < allowed to migrate to an empty neighbor three-fold site during a
231 < simulation. Therefore, the initial configuration would not severely
232 < affect the sampling of a variety of configurations of the same
233 < coverage, and the final conductance measurement would be an average
234 < effect of these configurations explored in the simulations. [MAY NEED FIGURES]
262 > \subsection{Simulation Protocol}
263 > The NIVS algorithm has been implemented in our MD simulation code,
264 > OpenMD\cite{Meineke:2005gd,openmd}, and was used for our
265 > simulations. Different slab thickness (layer numbers of Au) were
266 > simulated. Metal slabs were first equilibrated under atmospheric
267 > pressure (1 atm) and a desired temperature (e.g. 200K). After
268 > equilibration, butanethiol capping agents were placed at three-fold
269 > sites on the Au(111) surfaces. The maximum butanethiol capacity on Au
270 > surface is $1/3$ of the total number of surface Au
271 > atoms\cite{vlugt:cpc2007154}. A series of different coverages was
272 > investigated in order to study the relation between coverage and
273 > interfacial conductance.
274  
275 < After the modified Au-butanethiol surface systems are equilibrated
276 < under canonical ensemble, Packmol\cite{packmol} is used to pack
277 < organic solvent molecules in the previously vacuum part of the
278 < simulation cells, which guarantees that short range repulsive
279 < interactions do not disrupt the simulations. Two solvents are
280 < investigated, one which has little vibrational overlap with the
281 < alkanethiol and plane-like shape (toluene), and one which has similar
243 < vibrational frequencies and chain-like shape ({\it n}-hexane). The
244 < spacing filled by solvent molecules, i.e. the gap between periodically
245 < repeated Au-butanethiol surfaces should be carefully chosen so that it
246 < would not be too short to affect the liquid phase structure, nor too
247 < long, leading to over cooling (freezing) or heating (boiling) when a
248 < thermal flux is applied. In our simulations, this spacing is usually
249 < $35 \sim 60$\AA.
275 > The capping agent molecules were allowed to migrate during the
276 > simulations. They distributed themselves uniformly and sampled a
277 > number of three-fold sites throughout out study. Therefore, the
278 > initial configuration would not noticeably affect the sampling of a
279 > variety of configurations of the same coverage, and the final
280 > conductance measurement would be an average effect of these
281 > configurations explored in the simulations. [MAY NEED FIGURES]
282  
283 + After the modified Au-butanethiol surface systems were equilibrated
284 + under canonical ensemble, organic solvent molecules were packed in the
285 + previously empty part of the simulation cells\cite{packmol}. Two
286 + solvents were investigated, one which has little vibrational overlap
287 + with the alkanethiol and a planar shape (toluene), and one which has
288 + similar vibrational frequencies and chain-like shape ({\it n}-hexane).
289 +
290 + The space filled by solvent molecules, i.e. the gap between
291 + periodically repeated Au-butanethiol surfaces should be carefully
292 + chosen. A very long length scale for the thermal gradient axis ($z$)
293 + may cause excessively hot or cold temperatures in the middle of the
294 + solvent region and lead to undesired phenomena such as solvent boiling
295 + or freezing when a thermal flux is applied. Conversely, too few
296 + solvent molecules would change the normal behavior of the liquid
297 + phase. Therefore, our $N_{solvent}$ values were chosen to ensure that
298 + these extreme cases did not happen to our simulations. And the
299 + corresponding spacing is usually $35 \sim 75$\AA.
300 +
301   The initial configurations generated by Packmol are further
302   equilibrated with the $x$ and $y$ dimensions fixed, only allowing
303   length scale change in $z$ dimension. This is to ensure that the
# Line 277 | Line 327 | Our simulations include various components. Therefore,
327   \end{equation}
328  
329   \subsection{Force Field Parameters}
330 < Our simulations include various components. Therefore, force field
331 < parameter descriptions are needed for interactions both between the
332 < same type of particles and between particles of different species.
330 > Our simulations include various components. Figure \ref{demoMol}
331 > demonstrates the sites defined for both United-Atom and All-Atom
332 > models of the organic solvent and capping agent molecules in our
333 > simulations. Force field parameter descriptions are needed for
334 > interactions both between the same type of particles and between
335 > particles of different species.
336  
337 + \begin{figure}
338 + \includegraphics[width=\linewidth]{structures}
339 + \caption{Structures of the capping agent and solvents utilized in
340 +  these simulations. The chemically-distinct sites (a-e) are expanded
341 +  in terms of constituent atoms for both United Atom (UA) and All Atom
342 +  (AA) force fields.  Most parameters are from
343 +  Refs. \protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} (UA) and
344 +  \protect\cite{OPLSAA} (AA).  Cross-interactions with the Au atoms are given
345 +  in Table \ref{MnM}.}
346 + \label{demoMol}
347 + \end{figure}
348 +
349   The Au-Au interactions in metal lattice slab is described by the
350 < quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC
350 > quantum Sutton-Chen (QSC) formulation\cite{PhysRevB.59.3527}. The QSC
351   potentials include zero-point quantum corrections and are
352   reparametrized for accurate surface energies compared to the
353   Sutton-Chen potentials\cite{Chen90}.
# Line 291 | Line 356 | for our UA solvent molecules. In these models, pseudo-
356   toluene, United-Atom (UA) and All-Atom (AA) models are used
357   respectively. The TraPPE-UA
358   parameters\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} are used
359 < for our UA solvent molecules. In these models, pseudo-atoms are
360 < located at the carbon centers for alkyl groups. By eliminating
361 < explicit hydrogen atoms, these models are simple and computationally
362 < efficient, while maintains good accuracy. However, the TraPPE-UA for
363 < alkanes is known to predict a lower boiling point than experimental
299 < values. Considering that after an unphysical thermal flux is applied
300 < to a system, the temperature of ``hot'' area in the liquid phase would be
301 < significantly higher than the average, to prevent over heating and
302 < boiling of the liquid phase, the average temperature in our
303 < simulations should be much lower than the liquid boiling point. [NEED MORE DISCUSSION]
304 < For UA-toluene model, rigid body constraints are applied, so that the
305 < benzene ring and the methyl-C(aromatic) bond are kept rigid. This
306 < would save computational time.[MORE DETAILS NEEDED]
359 > for our UA solvent molecules. In these models, sites are located at
360 > the carbon centers for alkyl groups. Bonding interactions, including
361 > bond stretches and bends and torsions, were used for intra-molecular
362 > sites not separated by more than 3 bonds. Otherwise, for non-bonded
363 > interactions, Lennard-Jones potentials are used. [MORE CITATION?]
364  
365 + By eliminating explicit hydrogen atoms, these models are simple and
366 + computationally efficient, while maintains good accuracy. However, the
367 + TraPPE-UA for alkanes is known to predict a lower boiling point than
368 + experimental values. Considering that after an unphysical thermal flux
369 + is applied to a system, the temperature of ``hot'' area in the liquid
370 + phase would be significantly higher than the average, to prevent over
371 + heating and boiling of the liquid phase, the average temperature in
372 + our simulations should be much lower than the liquid boiling point.
373 +
374 + For UA-toluene model, the non-bonded potentials between
375 + inter-molecular sites have a similar Lennard-Jones formulation. For
376 + intra-molecular interactions, considering the stiffness of the benzene
377 + ring, rigid body constraints are applied for further computational
378 + efficiency. All bonds in the benzene ring and between the ring and the
379 + methyl group remain rigid during the progress of simulations.
380 +
381   Besides the TraPPE-UA models, AA models for both organic solvents are
382 < included in our studies as well. For hexane, the OPLS
383 < all-atom\cite{OPLSAA} force field is used. [MORE DETAILS]
384 < For toluene, the United Force Field developed by Rapp\'{e} {\it et
385 <  al.}\cite{doi:10.1021/ja00051a040} is adopted.[MORE DETAILS]
382 > included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA}
383 > force field is used. Additional explicit hydrogen sites were
384 > included. Besides bonding and non-bonded site-site interactions,
385 > partial charges and the electrostatic interactions were added to each
386 > CT and HC site. For toluene, the United Force Field developed by
387 > Rapp\'{e} {\it et al.}\cite{doi:10.1021/ja00051a040} is
388 > adopted. Without the rigid body constraints, bonding interactions were
389 > included. For the aromatic ring, improper torsions (inversions) were
390 > added as an extra potential for maintaining the planar shape.
391 > [MORE CITATION?]
392  
393   The capping agent in our simulations, the butanethiol molecules can
394   either use UA or AA model. The TraPPE-UA force fields includes
395 < parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used in
396 < our simulations corresponding to our TraPPE-UA models for solvent.
397 < and All-Atom models [NEED CITATIONS]
398 < However, the model choice (UA or AA) of capping agent can be different
399 < from the solvent. Regardless of model choice, the force field
400 < parameters for interactions between capping agent and solvent can be
401 < derived using Lorentz-Berthelot Mixing Rule.
395 > parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used for
396 > UA butanethiol model in our simulations. The OPLS-AA also provides
397 > parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111)
398 > surfaces do not have the hydrogen atom bonded to sulfur. To adapt this
399 > change and derive suitable parameters for butanethiol adsorbed on
400 > Au(111) surfaces, we adopt the S parameters from Luedtke and
401 > Landman\cite{landman:1998} and modify parameters for its neighbor C
402 > atom for charge balance in the molecule. Note that the model choice
403 > (UA or AA) of capping agent can be different from the
404 > solvent. Regardless of model choice, the force field parameters for
405 > interactions between capping agent and solvent can be derived using
406 > Lorentz-Berthelot Mixing Rule:
407 > \begin{eqnarray}
408 > \sigma_{ij} & = & \frac{1}{2} \left(\sigma_{ii} + \sigma_{jj}\right) \\
409 > \epsilon_{ij} & = & \sqrt{\epsilon_{ii}\epsilon_{jj}}
410 > \end{eqnarray}
411  
412   To describe the interactions between metal Au and non-metal capping
413 < agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive
414 < other interactions which are not yet finely parametrized. [can add
415 < hautman and klein's paper here and more discussion; need to put
416 < aromatic-metal interaction approximation here]\cite{doi:10.1021/jp034405s}
413 > agent and solvent particles, we refer to an adsorption study of alkyl
414 > thiols on gold surfaces by Vlugt {\it et
415 >  al.}\cite{vlugt:cpc2007154} They fitted an effective Lennard-Jones
416 > form of potential parameters for the interaction between Au and
417 > pseudo-atoms CH$_x$ and S based on a well-established and widely-used
418 > effective potential of Hautman and Klein\cite{hautman:4994} for the
419 > Au(111) surface. As our simulations require the gold lattice slab to
420 > be non-rigid so that it could accommodate kinetic energy for thermal
421 > transport study purpose, the pair-wise form of potentials is
422 > preferred.
423  
424 < [TABULATED FORCE FIELD PARAMETERS NEEDED]
424 > Besides, the potentials developed from {\it ab initio} calculations by
425 > Leng {\it et al.}\cite{doi:10.1021/jp034405s} are adopted for the
426 > interactions between Au and aromatic C/H atoms in toluene. A set of
427 > pseudo Lennard-Jones parameters were provided for Au in their force
428 > fields. By using the Mixing Rule, this can be used to derive pair-wise
429 > potentials for non-bonded interactions between Au and non-metal sites.
430  
431 + However, the Lennard-Jones parameters between Au and other types of
432 + particles, such as All-Atom normal alkanes in our simulations are not
433 + yet well-established. For these interactions, we attempt to derive
434 + their parameters using the Mixing Rule. To do this, Au pseudo
435 + Lennard-Jones parameters for ``Metal-non-Metal'' (MnM) interactions
436 + were first extracted from the Au-CH$_x$ parameters by applying the
437 + Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM''
438 + parameters in our simulations.
439  
440 < [SURFACE RECONSTRUCTION PREVENTS SIMULATION TEMP TO GO HIGHER]
440 > \begin{table*}
441 >  \begin{minipage}{\linewidth}
442 >    \begin{center}
443 >      \caption{Non-bonded interaction parameters (including cross
444 >        interactions with Au atoms) for both force fields used in this
445 >        work.}      
446 >      \begin{tabular}{lllllll}
447 >        \hline\hline
448 >        & Site  & $\sigma_{ii}$ & $\epsilon_{ii}$ & $q_i$ &
449 >        $\sigma_{Au-i}$ & $\epsilon_{Au-i}$ \\
450 >        & & (\AA) & (kcal/mol) & ($e$) & (\AA) & (kcal/mol) \\
451 >        \hline
452 >        United Atom (UA)
453 >        &CH3  & 3.75  & 0.1947  & -      & 3.54   & 0.2146  \\
454 >        &CH2  & 3.95  & 0.0914  & -      & 3.54   & 0.1749  \\
455 >        &CHar & 3.695 & 0.1003  & -      & 3.4625 & 0.1680  \\
456 >        &CRar & 3.88  & 0.04173 & -      & 3.555  & 0.1604  \\
457 >        \hline
458 >        All Atom (AA)
459 >        &CT3  & 3.50  & 0.066   & -0.18  & 3.365  & 0.1373  \\
460 >        &CT2  & 3.50  & 0.066   & -0.12  & 3.365  & 0.1373  \\
461 >        &CTT  & 3.50  & 0.066   & -0.065 & 3.365  & 0.1373  \\
462 >        &HC   & 2.50  & 0.030   &  0.06  & 2.865  & 0.09256 \\
463 >        &CA   & 3.55  & 0.070   & -0.115 & 3.173  & 0.0640  \\
464 >        &HA   & 2.42  & 0.030   &  0.115 & 2.746  & 0.0414  \\
465 >        \hline
466 >        Both UA and AA
467 >        & S   & 4.45  & 0.25    & -      & 2.40   & 8.465   \\
468 >        \hline\hline
469 >      \end{tabular}
470 >      \label{MnM}
471 >    \end{center}
472 >  \end{minipage}
473 > \end{table*}
474  
475  
476 < \section{Results}
477 < [REARRANGEMENT NEEDED]
478 < \subsection{Toluene Solvent}
476 > \section{Results and Discussions}
477 > [MAY HAVE A BRIEF SUMMARY]
478 > \subsection{How Simulation Parameters Affects $G$}
479 > [MAY NOT PUT AT FIRST]
480 > We have varied our protocol or other parameters of the simulations in
481 > order to investigate how these factors would affect the measurement of
482 > $G$'s. It turned out that while some of these parameters would not
483 > affect the results substantially, some other changes to the
484 > simulations would have a significant impact on the measurement
485 > results.
486  
487 < The results (Table \ref{AuThiolToluene}) show a
488 < significant conductance enhancement compared to the gold/water
489 < interface without capping agent and agree with available experimental
490 < data. This indicates that the metal-metal potential, though not
491 < predicting an accurate bulk metal thermal conductivity, does not
492 < greatly interfere with the simulation of the thermal conductance
493 < behavior across a non-metal interface. The solvent model is not
494 < particularly volatile, so the simulation cell does not expand
495 < significantly under higher temperature. We did not observe a
496 < significant conductance decrease when the temperature was increased to
497 < 300K. The results show that the two definitions used for $G$ yield
498 < comparable values, though $G^\prime$ tends to be smaller.
487 > In some of our simulations, we allowed $L_x$ and $L_y$ to change
488 > during equilibrating the liquid phase. Due to the stiffness of the
489 > crystalline Au structure, $L_x$ and $L_y$ would not change noticeably
490 > after equilibration. Although $L_z$ could fluctuate $\sim$1\% after a
491 > system is fully equilibrated in the NPT ensemble, this fluctuation, as
492 > well as those of $L_x$ and $L_y$ (which is significantly smaller),
493 > would not be magnified on the calculated $G$'s, as shown in Table
494 > \ref{AuThiolHexaneUA}. This insensivity to $L_i$ fluctuations allows
495 > reliable measurement of $G$'s without the necessity of extremely
496 > cautious equilibration process.
497 >
498 > As stated in our computational details, the spacing filled with
499 > solvent molecules can be chosen within a range. This allows some
500 > change of solvent molecule numbers for the same Au-butanethiol
501 > surfaces. We did this study on our Au-butanethiol/hexane
502 > simulations. Nevertheless, the results obtained from systems of
503 > different $N_{hexane}$ did not indicate that the measurement of $G$ is
504 > susceptible to this parameter. For computational efficiency concern,
505 > smaller system size would be preferable, given that the liquid phase
506 > structure is not affected.
507  
508 + Our NIVS algorithm allows change of unphysical thermal flux both in
509 + direction and in quantity. This feature extends our investigation of
510 + interfacial thermal conductance. However, the magnitude of this
511 + thermal flux is not arbitary if one aims to obtain a stable and
512 + reliable thermal gradient. A temperature profile would be
513 + substantially affected by noise when $|J_z|$ has a much too low
514 + magnitude; while an excessively large $|J_z|$ that overwhelms the
515 + conductance capacity of the interface would prevent a thermal gradient
516 + to reach a stablized steady state. NIVS has the advantage of allowing
517 + $J$ to vary in a wide range such that the optimal flux range for $G$
518 + measurement can generally be simulated by the algorithm. Within the
519 + optimal range, we were able to study how $G$ would change according to
520 + the thermal flux across the interface. For our simulations, we denote
521 + $J_z$ to be positive when the physical thermal flux is from the liquid
522 + to metal, and negative vice versa. The $G$'s measured under different
523 + $J_z$ is listed in Table \ref{AuThiolHexaneUA} and
524 + \ref{AuThiolToluene}. These results do not suggest that $G$ is
525 + dependent on $J_z$ within this flux range. The linear response of flux
526 + to thermal gradient simplifies our investigations in that we can rely
527 + on $G$ measurement with only a couple $J_z$'s and do not need to test
528 + a large series of fluxes.
529 +
530   \begin{table*}
531    \begin{minipage}{\linewidth}
532      \begin{center}
533        \caption{Computed interfacial thermal conductivity ($G$ and
534 <        $G^\prime$) values for the Au/butanethiol/toluene interface at
535 <        different temperatures using a range of energy fluxes.}
534 >        $G^\prime$) values for the 100\% covered Au-butanethiol/hexane
535 >        interfaces with UA model and different hexane molecule numbers
536 >        at different temperatures using a range of energy
537 >        fluxes. Error estimates indicated in parenthesis.}
538        
539 <      \begin{tabular}{cccc}
539 >      \begin{tabular}{ccccccc}
540          \hline\hline
541 <        $\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\
542 <        (K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
541 >        $\langle T\rangle$ & $N_{hexane}$ & Fixed & $\rho_{hexane}$ &
542 >        $J_z$ & $G$ & $G^\prime$ \\
543 >        (K) & & $L_x$ \& $L_y$? & (g/cm$^3$) & (GW/m$^2$) &
544 >        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
545          \hline
546 <        200 & 1.86 & 180 & 135 \\
547 <            & 2.15 & 204 & 113 \\
548 <            & 3.93 & 175 & 114 \\
549 <        300 & 1.91 & 143 & 125 \\
550 <            & 4.19 & 134 & 113 \\
546 >        200 & 266 & No  & 0.672 & -0.96 & 102(3)    & 80.0(0.8) \\
547 >            & 200 & Yes & 0.694 &  1.92 & 129(11)   & 87.3(0.3) \\
548 >            &     & Yes & 0.672 &  1.93 & 131(16)   & 78(13)    \\
549 >            &     & No  & 0.688 &  0.96 & 125(16)   & 90.2(15)  \\
550 >            &     &     &       &  1.91 & 139(10)   & 101(10)   \\
551 >            &     &     &       &  2.83 & 141(6)    & 89.9(9.8) \\
552 >            & 166 & Yes & 0.679 &  0.97 & 115(19)   & 69(18)    \\
553 >            &     &     &       &  1.94 & 125(9)    & 87.1(0.2) \\
554 >            &     & No  & 0.681 &  0.97 & 141(30)   & 78(22)    \\
555 >            &     &     &       &  1.92 & 138(4)    & 98.9(9.5) \\
556 >        \hline
557 >        250 & 200 & No  & 0.560 &  0.96 & 75(10)    & 61.8(7.3) \\
558 >            &     &     &       & -0.95 & 49.4(0.3) & 45.7(2.1) \\
559 >            & 166 & Yes & 0.570 &  0.98 & 79.0(3.5) & 62.9(3.0) \\
560 >            &     & No  & 0.569 &  0.97 & 80.3(0.6) & 67(11)    \\
561 >            &     &     &       &  1.44 & 76.2(5.0) & 64.8(3.8) \\
562 >            &     &     &       & -0.95 & 56.4(2.5) & 54.4(1.1) \\
563 >            &     &     &       & -1.85 & 47.8(1.1) & 53.5(1.5) \\
564          \hline\hline
565        \end{tabular}
566 <      \label{AuThiolToluene}
566 >      \label{AuThiolHexaneUA}
567      \end{center}
568    \end{minipage}
569   \end{table*}
570  
571 < \subsection{Hexane Solvent}
571 > Furthermore, we also attempted to increase system average temperatures
572 > to above 200K. These simulations are first equilibrated in the NPT
573 > ensemble under normal pressure. As stated above, the TraPPE-UA model
574 > for hexane tends to predict a lower boiling point. In our simulations,
575 > hexane had diffculty to remain in liquid phase when NPT equilibration
576 > temperature is higher than 250K. Additionally, the equilibrated liquid
577 > hexane density under 250K becomes lower than experimental value. This
578 > expanded liquid phase leads to lower contact between hexane and
579 > butanethiol as well.[MAY NEED SLAB DENSITY FIGURE]
580 > And this reduced contact would
581 > probably be accountable for a lower interfacial thermal conductance,
582 > as shown in Table \ref{AuThiolHexaneUA}.
583  
584 < Using the united-atom model, different coverages of capping agent,
585 < temperatures of simulations and numbers of solvent molecules were all
586 < investigated and Table \ref{AuThiolHexaneUA} shows the results of
587 < these computations. The number of hexane molecules in our simulations
588 < does not affect the calculations significantly. However, a very long
589 < length scale for the thermal gradient axis ($z$) may cause excessively
590 < hot or cold temperatures in the middle of the solvent region and lead
591 < to undesired phenomena such as solvent boiling or freezing, while too
592 < few solvent molecules would change the normal behavior of the liquid
593 < phase. Our $N_{hexane}$ values were chosen to ensure that these
389 < extreme cases did not happen to our simulations.
584 > A similar study for TraPPE-UA toluene agrees with the above result as
585 > well. Having a higher boiling point, toluene tends to remain liquid in
586 > our simulations even equilibrated under 300K in NPT
587 > ensembles. Furthermore, the expansion of the toluene liquid phase is
588 > not as significant as that of the hexane. This prevents severe
589 > decrease of liquid-capping agent contact and the results (Table
590 > \ref{AuThiolToluene}) show only a slightly decreased interface
591 > conductance. Therefore, solvent-capping agent contact should play an
592 > important role in the thermal transport process across the interface
593 > in that higher degree of contact could yield increased conductance.
594  
391 – Table \ref{AuThiolHexaneUA} enables direct comparison between
392 – different coverages of capping agent, when other system parameters are
393 – held constant. With high coverage of butanethiol on the gold surface,
394 – the interfacial thermal conductance is enhanced
395 – significantly. Interestingly, a slightly lower butanethiol coverage
396 – leads to a moderately higher conductivity. This is probably due to
397 – more solvent/capping agent contact when butanethiol molecules are
398 – not densely packed, which enhances the interactions between the two
399 – phases and lowers the thermal transfer barrier of this interface.
400 – % [COMPARE TO AU/WATER IN PAPER]
401 –
402 – It is also noted that the overall simulation temperature is another
403 – factor that affects the interfacial thermal conductance. One
404 – possibility of this effect may be rooted in the decrease in density of
405 – the liquid phase. We observed that when the average temperature
406 – increases from 200K to 250K, the bulk hexane density becomes lower
407 – than experimental value, as the system is equilibrated under NPT
408 – ensemble. This leads to lower contact between solvent and capping
409 – agent, and thus lower conductivity.
410 –
411 – Conductivity values are more difficult to obtain under higher
412 – temperatures. This is because the Au surface tends to undergo
413 – reconstructions in relatively high temperatures. Surface Au atoms can
414 – migrate outward to reach higher Au-S contact; and capping agent
415 – molecules can be embedded into the surface Au layer due to the same
416 – driving force. This phenomenon agrees with experimental
417 – results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. A surface
418 – fully covered in capping agent is more susceptible to reconstruction,
419 – possibly because fully coverage prevents other means of capping agent
420 – relaxation, such as migration to an empty neighbor three-fold site.
421 –
422 – %MAY ADD MORE DATA TO TABLE
595   \begin{table*}
596    \begin{minipage}{\linewidth}
597      \begin{center}
598        \caption{Computed interfacial thermal conductivity ($G$ and
599 <        $G^\prime$) values for the Au/butanethiol/hexane interface
600 <        with united-atom model and different capping agent coverage
601 <        and solvent molecule numbers at different temperatures using a
430 <        range of energy fluxes.}
599 >        $G^\prime$) values for a 90\% coverage Au-butanethiol/toluene
600 >        interface at different temperatures using a range of energy
601 >        fluxes. Error estimates indicated in parenthesis.}
602        
603 <      \begin{tabular}{cccccc}
603 >      \begin{tabular}{ccccc}
604          \hline\hline
605 <        Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\
606 <        coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) &
436 <        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
605 >        $\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\
606 >        (K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
607          \hline
608 <        0.0   & 200 & 200 & 0.96 & 43.3 & 42.7 \\
609 <              &     &     & 1.91 & 45.7 & 42.9 \\
610 <              &     & 166 & 0.96 & 43.1 & 53.4 \\
611 <        88.9  & 200 & 166 & 1.94 & 172  & 108  \\
612 <        100.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\
613 <              &     & 166 & 0.98 & 79.0 & 62.9 \\
444 <              &     &     & 1.44 & 76.2 & 64.8 \\
445 <              & 200 & 200 & 1.92 & 129  & 87.3 \\
446 <              &     &     & 1.93 & 131  & 77.5 \\
447 <              &     & 166 & 0.97 & 115  & 69.3 \\
448 <              &     &     & 1.94 & 125  & 87.1 \\
608 >        200 & 0.933 &  2.15 & 204(12) & 113(12) \\
609 >            &       & -1.86 & 180(3)  & 135(21) \\
610 >            &       & -3.93 & 176(5)  & 113(12) \\
611 >        \hline
612 >        300 & 0.855 & -1.91 & 143(5)  & 125(2)  \\
613 >            &       & -4.19 & 135(9)  & 113(12) \\
614          \hline\hline
615        \end{tabular}
616 <      \label{AuThiolHexaneUA}
616 >      \label{AuThiolToluene}
617      \end{center}
618    \end{minipage}
619   \end{table*}
620  
621 < For the all-atom model, the liquid hexane phase was not stable under NPT
622 < conditions. Therefore, the simulation length scale parameters are
623 < adopted from previous equilibration results of the united-atom model
624 < at 200K. Table \ref{AuThiolHexaneAA} shows the results of these
625 < simulations. The conductivity values calculated with full capping
626 < agent coverage are substantially larger than observed in the
627 < united-atom model, and is even higher than predicted by
628 < experiments. It is possible that our parameters for metal-non-metal
629 < particle interactions lead to an overestimate of the interfacial
630 < thermal conductivity, although the active C-H vibrations in the
631 < all-atom model (which should not be appreciably populated at normal
632 < temperatures) could also account for this high conductivity. The major
633 < thermal transfer barrier of Au/butanethiol/hexane interface is between
634 < the liquid phase and the capping agent, so extra degrees of freedom
635 < such as the C-H vibrations could enhance heat exchange between these
636 < two phases and result in a much higher conductivity.
621 > Besides lower interfacial thermal conductance, surfaces in relatively
622 > high temperatures are susceptible to reconstructions, when
623 > butanethiols have a full coverage on the Au(111) surface. These
624 > reconstructions include surface Au atoms migrated outward to the S
625 > atom layer, and butanethiol molecules embedded into the original
626 > surface Au layer. The driving force for this behavior is the strong
627 > Au-S interactions in our simulations. And these reconstructions lead
628 > to higher ratio of Au-S attraction and thus is energetically
629 > favorable. Furthermore, this phenomenon agrees with experimental
630 > results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt
631 > {\it et al.} had kept their Au(111) slab rigid so that their
632 > simulations can reach 300K without surface reconstructions. Without
633 > this practice, simulating 100\% thiol covered interfaces under higher
634 > temperatures could hardly avoid surface reconstructions. However, our
635 > measurement is based on assuming homogeneity on $x$ and $y$ dimensions
636 > so that measurement of $T$ at particular $z$ would be an effective
637 > average of the particles of the same type. Since surface
638 > reconstructions could eliminate the original $x$ and $y$ dimensional
639 > homogeneity, measurement of $G$ is more difficult to conduct under
640 > higher temperatures. Therefore, most of our measurements are
641 > undertaken at $\langle T\rangle\sim$200K.
642  
643 + However, when the surface is not completely covered by butanethiols,
644 + the simulated system is more resistent to the reconstruction
645 + above. Our Au-butanethiol/toluene system had the Au(111) surfaces 90\%
646 + covered by butanethiols, but did not see this above phenomena even at
647 + $\langle T\rangle\sim$300K. The empty three-fold sites not occupied by
648 + capping agents could help prevent surface reconstruction in that they
649 + provide other means of capping agent relaxation. It is observed that
650 + butanethiols can migrate to their neighbor empty sites during a
651 + simulation. Therefore, we were able to obtain $G$'s for these
652 + interfaces even at a relatively high temperature without being
653 + affected by surface reconstructions.
654 +
655 + \subsection{Influence of Capping Agent Coverage on $G$}
656 + To investigate the influence of butanethiol coverage on interfacial
657 + thermal conductance, a series of different coverage Au-butanethiol
658 + surfaces is prepared and solvated with various organic
659 + molecules. These systems are then equilibrated and their interfacial
660 + thermal conductivity are measured with our NIVS algorithm. Figure
661 + \ref{coverage} demonstrates the trend of conductance change with
662 + respect to different coverages of butanethiol. To study the isotope
663 + effect in interfacial thermal conductance, deuterated UA-hexane is
664 + included as well.
665 +
666 + It turned out that with partial covered butanethiol on the Au(111)
667 + surface, the derivative definition for $G^\prime$
668 + (Eq. \ref{derivativeG}) was difficult to apply, due to the difficulty
669 + in locating the maximum of change of $\lambda$. Instead, the discrete
670 + definition (Eq. \ref{discreteG}) is easier to apply, as the Gibbs
671 + deviding surface can still be well-defined. Therefore, $G$ (not
672 + $G^\prime$) was used for this section.
673 +
674 + From Figure \ref{coverage}, one can see the significance of the
675 + presence of capping agents. Even when a fraction of the Au(111)
676 + surface sites are covered with butanethiols, the conductivity would
677 + see an enhancement by at least a factor of 3. This indicates the
678 + important role cappping agent is playing for thermal transport
679 + phenomena on metal / organic solvent surfaces.
680 +
681 + Interestingly, as one could observe from our results, the maximum
682 + conductance enhancement (largest $G$) happens while the surfaces are
683 + about 75\% covered with butanethiols. This again indicates that
684 + solvent-capping agent contact has an important role of the thermal
685 + transport process. Slightly lower butanethiol coverage allows small
686 + gaps between butanethiols to form. And these gaps could be filled with
687 + solvent molecules, which acts like ``heat conductors'' on the
688 + surface. The higher degree of interaction between these solvent
689 + molecules and capping agents increases the enhancement effect and thus
690 + produces a higher $G$ than densely packed butanethiol arrays. However,
691 + once this maximum conductance enhancement is reached, $G$ decreases
692 + when butanethiol coverage continues to decrease. Each capping agent
693 + molecule reaches its maximum capacity for thermal
694 + conductance. Therefore, even higher solvent-capping agent contact
695 + would not offset this effect. Eventually, when butanethiol coverage
696 + continues to decrease, solvent-capping agent contact actually
697 + decreases with the disappearing of butanethiol molecules. In this
698 + case, $G$ decrease could not be offset but instead accelerated. [NEED
699 + SNAPSHOT SHOWING THE PHENOMENA]
700 +
701 + A comparison of the results obtained from differenet organic solvents
702 + can also provide useful information of the interfacial thermal
703 + transport process. The deuterated hexane (UA) results do not appear to
704 + be much different from those of normal hexane (UA), given that
705 + butanethiol (UA) is non-deuterated for both solvents. These UA model
706 + studies, even though eliminating C-H vibration samplings, still have
707 + C-C vibrational frequencies different from each other. However, these
708 + differences in the infrared range do not seem to produce an observable
709 + difference for the results of $G$. [MAY NEED SPECTRA FIGURE]
710 +
711 + Furthermore, results for rigid body toluene solvent, as well as other
712 + UA-hexane solvents, are reasonable within the general experimental
713 + ranges[CITATIONS]. This suggests that explicit hydrogen might not be a
714 + required factor for modeling thermal transport phenomena of systems
715 + such as Au-thiol/organic solvent.
716 +
717 + However, results for Au-butanethiol/toluene do not show an identical
718 + trend with those for Au-butanethiol/hexane in that $G$ remains at
719 + approximately the same magnitue when butanethiol coverage differs from
720 + 25\% to 75\%. This might be rooted in the molecule shape difference
721 + for planar toluene and chain-like {\it n}-hexane. Due to this
722 + difference, toluene molecules have more difficulty in occupying
723 + relatively small gaps among capping agents when their coverage is not
724 + too low. Therefore, the solvent-capping agent contact may keep
725 + increasing until the capping agent coverage reaches a relatively low
726 + level. This becomes an offset for decreasing butanethiol molecules on
727 + its effect to the process of interfacial thermal transport. Thus, one
728 + can see a plateau of $G$ vs. butanethiol coverage in our results.
729 +
730 + \begin{figure}
731 + \includegraphics[width=\linewidth]{coverage}
732 + \caption{Comparison of interfacial thermal conductivity ($G$) values
733 +  for the Au-butanethiol/solvent interface with various UA models and
734 +  different capping agent coverages at $\langle T\rangle\sim$200K
735 +  using certain energy flux respectively.}
736 + \label{coverage}
737 + \end{figure}
738 +
739 + \subsection{Influence of Chosen Molecule Model on $G$}
740 + [MAY COMBINE W MECHANISM STUDY]
741 +
742 + In addition to UA solvent/capping agent models, AA models are included
743 + in our simulations as well. Besides simulations of the same (UA or AA)
744 + model for solvent and capping agent, different models can be applied
745 + to different components. Furthermore, regardless of models chosen,
746 + either the solvent or the capping agent can be deuterated, similar to
747 + the previous section. Table \ref{modelTest} summarizes the results of
748 + these studies.
749 +
750   \begin{table*}
751    \begin{minipage}{\linewidth}
752      \begin{center}
753        
754        \caption{Computed interfacial thermal conductivity ($G$ and
755 <        $G^\prime$) values for the Au/butanethiol/hexane interface
756 <        with all-atom model and different capping agent coverage at
757 <        200K using a range of energy fluxes.}
755 >        $G^\prime$) values for interfaces using various models for
756 >        solvent and capping agent (or without capping agent) at
757 >        $\langle T\rangle\sim$200K. (D stands for deuterated solvent
758 >        or capping agent molecules; ``Avg.'' denotes results that are
759 >        averages of simulations under different $J_z$'s. Error
760 >        estimates indicated in parenthesis.)}
761        
762 <      \begin{tabular}{cccc}
762 >      \begin{tabular}{llccc}
763          \hline\hline
764 <        Thiol & $J_z$ & $G$ & $G^\prime$ \\
765 <        coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
764 >        Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\
765 >        (or bare surface) & model & (GW/m$^2$) &
766 >        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
767          \hline
768 <        0.0   & 0.95 & 28.5 & 27.2 \\
769 <              & 1.88 & 30.3 & 28.9 \\
770 <        100.0 & 2.87 & 551  & 294  \\
771 <              & 3.81 & 494  & 193  \\
768 >        UA    & UA hexane    & Avg. & 131(9)    & 87(10)    \\
769 >              & UA hexane(D) & 1.95 & 153(5)    & 136(13)   \\
770 >              & AA hexane    & Avg. & 131(6)    & 122(10)   \\
771 >              & UA toluene   & 1.96 & 187(16)   & 151(11)   \\
772 >              & AA toluene   & 1.89 & 200(36)   & 149(53)   \\
773 >        \hline
774 >        AA    & UA hexane    & 1.94 & 116(9)    & 129(8)    \\
775 >              & AA hexane    & Avg. & 442(14)   & 356(31)   \\
776 >              & AA hexane(D) & 1.93 & 222(12)   & 234(54)   \\
777 >              & UA toluene   & 1.98 & 125(25)   & 97(60)    \\
778 >              & AA toluene   & 3.79 & 487(56)   & 290(42)   \\
779 >        \hline
780 >        AA(D) & UA hexane    & 1.94 & 158(25)   & 172(4)    \\
781 >              & AA hexane    & 1.92 & 243(29)   & 191(11)   \\
782 >              & AA toluene   & 1.93 & 364(36)   & 322(67)   \\
783 >        \hline
784 >        bare  & UA hexane    & Avg. & 46.5(3.2) & 49.4(4.5) \\
785 >              & UA hexane(D) & 0.98 & 43.9(4.6) & 43.0(2.0) \\
786 >              & AA hexane    & 0.96 & 31.0(1.4) & 29.4(1.3) \\
787 >              & UA toluene   & 1.99 & 70.1(1.3) & 65.8(0.5) \\
788          \hline\hline
789        \end{tabular}
790 <      \label{AuThiolHexaneAA}
790 >      \label{modelTest}
791      \end{center}
792    \end{minipage}
793   \end{table*}
794  
795 < %subsubsection{Vibrational spectrum study on conductance mechanism}
795 > To facilitate direct comparison, the same system with differnt models
796 > for different components uses the same length scale for their
797 > simulation cells. Without the presence of capping agent, using
798 > different models for hexane yields similar results for both $G$ and
799 > $G^\prime$, and these two definitions agree with eath other very
800 > well. This indicates very weak interaction between the metal and the
801 > solvent, and is a typical case for acoustic impedance mismatch between
802 > these two phases.
803 >
804 > As for Au(111) surfaces completely covered by butanethiols, the choice
805 > of models for capping agent and solvent could impact the measurement
806 > of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane
807 > interfaces, using AA model for both butanethiol and hexane yields
808 > substantially higher conductivity values than using UA model for at
809 > least one component of the solvent and capping agent, which exceeds
810 > the general range of experimental measurement results. This is
811 > probably due to the classically treated C-H vibrations in the AA
812 > model, which should not be appreciably populated at normal
813 > temperatures. In comparison, once either the hexanes or the
814 > butanethiols are deuterated, one can see a significantly lower $G$ and
815 > $G^\prime$. In either of these cases, the C-H(D) vibrational overlap
816 > between the solvent and the capping agent is removed.
817 > [MAY NEED SPECTRA FIGURE] Conclusively, the
818 > improperly treated C-H vibration in the AA model produced
819 > over-predicted results accordingly. Compared to the AA model, the UA
820 > model yields more reasonable results with higher computational
821 > efficiency.
822 >
823 > However, for Au-butanethiol/toluene interfaces, having the AA
824 > butanethiol deuterated did not yield a significant change in the
825 > measurement results. Compared to the C-H vibrational overlap between
826 > hexane and butanethiol, both of which have alkyl chains, that overlap
827 > between toluene and butanethiol is not so significant and thus does
828 > not have as much contribution to the ``Intramolecular Vibration
829 > Redistribution''[CITE HASE]. Conversely, extra degrees of freedom such
830 > as the C-H vibrations could yield higher heat exchange rate between
831 > these two phases and result in a much higher conductivity.
832 >
833 > Although the QSC model for Au is known to predict an overly low value
834 > for bulk metal gold conductivity\cite{kuang:164101}, our computational
835 > results for $G$ and $G^\prime$ do not seem to be affected by this
836 > drawback of the model for metal. Instead, our results suggest that the
837 > modeling of interfacial thermal transport behavior relies mainly on
838 > the accuracy of the interaction descriptions between components
839 > occupying the interfaces.
840 >
841 > \subsection{Mechanism of Interfacial Thermal Conductance Enhancement
842 >  by Capping Agent}
843 > [OR: Vibrational Spectrum Study on Conductance Mechanism]
844 >
845 > [MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S]
846 >
847   To investigate the mechanism of this interfacial thermal conductance,
848   the vibrational spectra of various gold systems were obtained and are
849   shown as in the upper panel of Fig. \ref{vibration}. To obtain these
850   spectra, one first runs a simulation in the NVE ensemble and collects
851   snapshots of configurations; these configurations are used to compute
852   the velocity auto-correlation functions, which is used to construct a
853 < power spectrum via a Fourier transform. The gold surfaces covered by
854 < butanethiol molecules exhibit an additional peak observed at a
855 < frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration
856 < of the S-Au bond. This vibration enables efficient thermal transport
857 < from surface Au atoms to the capping agents. Simultaneously, as shown
858 < in the lower panel of Fig. \ref{vibration}, the large overlap of the
859 < vibration spectra of butanethiol and hexane in the all-atom model,
853 > power spectrum via a Fourier transform.
854 >
855 > [MAY RELATE TO HASE'S]
856 > The gold surfaces covered by butanethiol molecules, compared to bare
857 > gold surfaces, exhibit an additional peak observed at the frequency of
858 > $\sim$170cm$^{-1}$, which is attributed to the S-Au bonding
859 > vibration. This vibration enables efficient thermal transport from
860 > surface Au layer to the capping agents.
861 > [MAY PUT IN OTHER SECTION] Simultaneously, as shown in
862 > the lower panel of Fig. \ref{vibration}, the large overlap of the
863 > vibration spectra of butanethiol and hexane in the All-Atom model,
864   including the C-H vibration, also suggests high thermal exchange
865   efficiency. The combination of these two effects produces the drastic
866 < interfacial thermal conductance enhancement in the all-atom model.
866 > interfacial thermal conductance enhancement in the All-Atom model.
867  
868 + [NEED SEPARATE FIGURE. MAY NEED TO CONVERT TO JPEG]
869   \begin{figure}
870   \includegraphics[width=\linewidth]{vibration}
871   \caption{Vibrational spectra obtained for gold in different
872 <  environments (upper panel) and for Au/thiol/hexane simulation in
520 <  all-atom model (lower panel).}
872 >  environments.}
873   \label{vibration}
874   \end{figure}
523 – % 600dpi, letter size. too large?
875  
876 + [MAY ADD COMPARISON OF G AND G', AU SLAB WIDTHS, ETC]
877 + % The results show that the two definitions used for $G$ yield
878 + % comparable values, though $G^\prime$ tends to be smaller.
879  
880 + \section{Conclusions}
881 + The NIVS algorithm we developed has been applied to simulations of
882 + Au-butanethiol surfaces with organic solvents. This algorithm allows
883 + effective unphysical thermal flux transferred between the metal and
884 + the liquid phase. With the flux applied, we were able to measure the
885 + corresponding thermal gradient and to obtain interfacial thermal
886 + conductivities. Our simulations have seen significant conductance
887 + enhancement with the presence of capping agent, compared to the bare
888 + gold / liquid interfaces. The acoustic impedance mismatch between the
889 + metal and the liquid phase is effectively eliminated by proper capping
890 + agent. Furthermore, the coverage precentage of the capping agent plays
891 + an important role in the interfacial thermal transport process.
892 +
893 + Our measurement results, particularly of the UA models, agree with
894 + available experimental data. This indicates that our force field
895 + parameters have a nice description of the interactions between the
896 + particles at the interfaces. AA models tend to overestimate the
897 + interfacial thermal conductance in that the classically treated C-H
898 + vibration would be overly sampled. Compared to the AA models, the UA
899 + models have higher computational efficiency with satisfactory
900 + accuracy, and thus are preferable in interfacial thermal transport
901 + modelings.
902 +
903 + Vlugt {\it et al.} has investigated the surface thiol structures for
904 + nanocrystal gold and pointed out that they differs from those of the
905 + Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to
906 + change of interfacial thermal transport behavior as well. To
907 + investigate this problem, an effective means to introduce thermal flux
908 + and measure the corresponding thermal gradient is desirable for
909 + simulating structures with spherical symmetry.
910 +
911 +
912   \section{Acknowledgments}
913   Support for this project was provided by the National Science
914   Foundation under grant CHE-0848243. Computational time was provided by
915   the Center for Research Computing (CRC) at the University of Notre
916 < Dame.  \newpage
916 > Dame. \newpage
917  
918   \bibliography{interfacial}
919  

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