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Revision 3746 by skuang, Fri Jul 22 03:35:19 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 interfacial 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{gradT}.
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.
274 <
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 metal 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}[CITE CHEM REV].
272 > A series of different coverages was
273 > investigated in order to study the relation between coverage and
274 > interfacial conductance.
275  
276 < After the modified Au-butanethiol surface systems are equilibrated
277 < under canonical ensemble, Packmol\cite{packmol} is used to pack
278 < organic solvent molecules in the previously vacuum part of the
279 < simulation cells, which guarantees that short range repulsive
280 < interactions do not disrupt the simulations. Two solvents are
281 < investigated, one which has little vibrational overlap with the
282 < 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.
276 > The capping agent molecules were allowed to migrate during the
277 > simulations. They distributed themselves uniformly and sampled a
278 > number of three-fold sites throughout out study. Therefore, the
279 > initial configuration would not noticeably affect the sampling of a
280 > variety of configurations of the same coverage, and the final
281 > conductance measurement would be an average effect of these
282 > configurations explored in the simulations. [MAY NEED SNAPSHOTS]
283  
284 < The initial configurations generated by Packmol are further
285 < equilibrated with the $x$ and $y$ dimensions fixed, only allowing
286 < length scale change in $z$ dimension. This is to ensure that the
287 < equilibration of liquid phase does not affect the metal crystal
288 < structure in $x$ and $y$ dimensions. Further equilibration are run
289 < under NVT and then NVE ensembles.
284 > After the modified Au-butanethiol surface systems were equilibrated
285 > under canonical ensemble, organic solvent molecules were packed in the
286 > previously empty part of the simulation cells\cite{packmol}. Two
287 > solvents were investigated, one which has little vibrational overlap
288 > with the alkanethiol and a planar shape (toluene), and one which has
289 > similar vibrational frequencies and chain-like shape ({\it n}-hexane).
290  
291 + The space filled by solvent molecules, i.e. the gap between
292 + periodically repeated Au-butanethiol surfaces should be carefully
293 + chosen. A very long length scale for the thermal gradient axis ($z$)
294 + may cause excessively hot or cold temperatures in the middle of the
295 + solvent region and lead to undesired phenomena such as solvent boiling
296 + or freezing when a thermal flux is applied. Conversely, too few
297 + solvent molecules would change the normal behavior of the liquid
298 + phase. Therefore, our $N_{solvent}$ values were chosen to ensure that
299 + these extreme cases did not happen to our simulations. And the
300 + corresponding spacing is usually $35[?] \sim 75$\AA.
301 +
302 + The initial configurations generated are further equilibrated with the
303 + $x$ and $y$ dimensions fixed, only allowing length scale change in $z$
304 + dimension. This is to ensure that the equilibration of liquid phase
305 + does not affect the metal crystal structure in $x$ and $y$ dimensions.
306 + To investigate this effect, comparisons were made with simulations
307 + allowed to change $L_x$ and $L_y$ during NPT equilibration, and the
308 + results are shown in later sections. After ensuring the liquid phase
309 + reaches equilibrium at atmospheric pressure (1 atm), further
310 + equilibration are followed under NVT and then NVE ensembles.
311 +
312   After the systems reach equilibrium, NIVS is implemented to impose a
313   periodic unphysical thermal flux between the metal and the liquid
314   phase. Most of our simulations are under an average temperature of
# Line 277 | Line 331 | Our simulations include various components. Therefore,
331   \end{equation}
332  
333   \subsection{Force Field Parameters}
334 < Our simulations include various components. Therefore, force field
335 < parameter descriptions are needed for interactions both between the
336 < same type of particles and between particles of different species.
334 > Our simulations include various components. Figure \ref{demoMol}
335 > demonstrates the sites defined for both United-Atom and All-Atom
336 > models of the organic solvent and capping agent molecules in our
337 > simulations. Force field parameter descriptions are needed for
338 > interactions both between the same type of particles and between
339 > particles of different species.
340  
341 + \begin{figure}
342 + \includegraphics[width=\linewidth]{structures}
343 + \caption{Structures of the capping agent and solvents utilized in
344 +  these simulations. The chemically-distinct sites (a-e) are expanded
345 +  in terms of constituent atoms for both United Atom (UA) and All Atom
346 +  (AA) force fields.  Most parameters are from
347 +  Refs. \protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} (UA) and
348 +  \protect\cite{OPLSAA} (AA).  Cross-interactions with the Au atoms are given
349 +  in Table \ref{MnM}.}
350 + \label{demoMol}
351 + \end{figure}
352 +
353   The Au-Au interactions in metal lattice slab is described by the
354 < quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC
354 > quantum Sutton-Chen (QSC) formulation\cite{PhysRevB.59.3527}. The QSC
355   potentials include zero-point quantum corrections and are
356   reparametrized for accurate surface energies compared to the
357   Sutton-Chen potentials\cite{Chen90}.
# Line 291 | Line 360 | for our UA solvent molecules. In these models, pseudo-
360   toluene, United-Atom (UA) and All-Atom (AA) models are used
361   respectively. The TraPPE-UA
362   parameters\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} are used
363 < for our UA solvent molecules. In these models, pseudo-atoms are
364 < located at the carbon centers for alkyl groups. By eliminating
365 < explicit hydrogen atoms, these models are simple and computationally
366 < efficient, while maintains good accuracy. [LOW BOILING POINT IS A
367 < KNOWN PROBLEM FOR TRAPPE-UA ALKANES, NEED MORE DISCUSSION]
299 < for
300 < toluene,  force fields are
301 < used with rigid body constraints applied.[MORE DETAILS NEEDED]
363 > for our UA solvent molecules. In these models, sites are located at
364 > the carbon centers for alkyl groups. Bonding interactions, including
365 > bond stretches and bends and torsions, were used for intra-molecular
366 > sites not separated by more than 3 bonds. Otherwise, for non-bonded
367 > interactions, Lennard-Jones potentials are used. [MORE CITATION?]
368  
369 < Besides the TraPPE-UA models, AA models are included in our studies as
370 < well. For hexane, the OPLS all-atom\cite{OPLSAA} force field is
371 < used. [MORE DETAILS]
372 < For toluene,
369 > By eliminating explicit hydrogen atoms, these models are simple and
370 > computationally efficient, while maintains good accuracy. However, the
371 > TraPPE-UA for alkanes is known to predict a lower boiling point than
372 > experimental values. Considering that after an unphysical thermal flux
373 > is applied to a system, the temperature of ``hot'' area in the liquid
374 > phase would be significantly higher than the average, to prevent over
375 > heating and boiling of the liquid phase, the average temperature in
376 > our simulations should be much lower than the liquid boiling point.
377  
378 < Buatnethiol molecules are used as capping agent for some of our
379 < simulations. United-Atom\cite{TraPPE-UA.thiols} and All-Atom models
380 < are respectively used corresponding to the force field type of
381 < solvent.
378 > For UA-toluene model, the non-bonded potentials between
379 > inter-molecular sites have a similar Lennard-Jones formulation. For
380 > intra-molecular interactions, considering the stiffness of the benzene
381 > ring, rigid body constraints are applied for further computational
382 > efficiency. All bonds in the benzene ring and between the ring and the
383 > methyl group remain rigid during the progress of simulations.
384  
385 < To describe the interactions between metal Au and non-metal capping
386 < agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive
387 < other interactions which are not parametrized in their work. (can add
388 < hautman and klein's paper here and more discussion; need to put
389 < aromatic-metal interaction approximation here)
385 > Besides the TraPPE-UA models, AA models for both organic solvents are
386 > included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA}
387 > force field is used. Additional explicit hydrogen sites were
388 > included. Besides bonding and non-bonded site-site interactions,
389 > partial charges and the electrostatic interactions were added to each
390 > CT and HC site. For toluene, the United Force Field developed by
391 > Rapp\'{e} {\it et al.}\cite{doi:10.1021/ja00051a040} is
392 > adopted. Without the rigid body constraints, bonding interactions were
393 > included. For the aromatic ring, improper torsions (inversions) were
394 > added as an extra potential for maintaining the planar shape.
395 > [MORE CITATION?]
396  
397 < [TABULATED FORCE FIELD PARAMETERS NEEDED]
397 > The capping agent in our simulations, the butanethiol molecules can
398 > either use UA or AA model. The TraPPE-UA force fields includes
399 > parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used for
400 > UA butanethiol model in our simulations. The OPLS-AA also provides
401 > parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111)
402 > surfaces do not have the hydrogen atom bonded to sulfur. To adapt this
403 > change and derive suitable parameters for butanethiol adsorbed on
404 > Au(111) surfaces, we adopt the S parameters from Luedtke and
405 > Landman\cite{landman:1998} and modify parameters for its neighbor C
406 > atom for charge balance in the molecule. Note that the model choice
407 > (UA or AA) of capping agent can be different from the
408 > solvent. Regardless of model choice, the force field parameters for
409 > interactions between capping agent and solvent can be derived using
410 > Lorentz-Berthelot Mixing Rule:
411 > \begin{eqnarray}
412 > \sigma_{ij} & = & \frac{1}{2} \left(\sigma_{ii} + \sigma_{jj}\right) \\
413 > \epsilon_{ij} & = & \sqrt{\epsilon_{ii}\epsilon_{jj}}
414 > \end{eqnarray}
415  
416 < \section{Results}
417 < \subsection{Toluene Solvent}
416 > To describe the interactions between metal Au and non-metal capping
417 > agent and solvent particles, we refer to an adsorption study of alkyl
418 > thiols on gold surfaces by Vlugt {\it et
419 >  al.}\cite{vlugt:cpc2007154} They fitted an effective Lennard-Jones
420 > form of potential parameters for the interaction between Au and
421 > pseudo-atoms CH$_x$ and S based on a well-established and widely-used
422 > effective potential of Hautman and Klein\cite{hautman:4994} for the
423 > Au(111) surface. As our simulations require the gold lattice slab to
424 > be non-rigid so that it could accommodate kinetic energy for thermal
425 > transport study purpose, the pair-wise form of potentials is
426 > preferred.
427  
428 < The results (Table \ref{AuThiolToluene}) show a
429 < significant conductance enhancement compared to the gold/water
430 < interface without capping agent and agree with available experimental
431 < data. This indicates that the metal-metal potential, though not
432 < predicting an accurate bulk metal thermal conductivity, does not
433 < greatly interfere with the simulation of the thermal conductance
330 < behavior across a non-metal interface. The solvent model is not
331 < particularly volatile, so the simulation cell does not expand
332 < significantly under higher temperature. We did not observe a
333 < significant conductance decrease when the temperature was increased to
334 < 300K. The results show that the two definitions used for $G$ yield
335 < comparable values, though $G^\prime$ tends to be smaller.
428 > Besides, the potentials developed from {\it ab initio} calculations by
429 > Leng {\it et al.}\cite{doi:10.1021/jp034405s} are adopted for the
430 > interactions between Au and aromatic C/H atoms in toluene. A set of
431 > pseudo Lennard-Jones parameters were provided for Au in their force
432 > fields. By using the Mixing Rule, this can be used to derive pair-wise
433 > potentials for non-bonded interactions between Au and non-metal sites.
434  
435 + However, the Lennard-Jones parameters between Au and other types of
436 + particles, such as All-Atom normal alkanes in our simulations are not
437 + yet well-established. For these interactions, we attempt to derive
438 + their parameters using the Mixing Rule. To do this, Au pseudo
439 + Lennard-Jones parameters for ``Metal-non-Metal'' (MnM) interactions
440 + were first extracted from the Au-CH$_x$ parameters by applying the
441 + Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM''
442 + parameters in our simulations.
443 +
444   \begin{table*}
445    \begin{minipage}{\linewidth}
446      \begin{center}
447 <      \caption{Computed interfacial thermal conductivity ($G$ and
448 <        $G^\prime$) values for the Au/butanethiol/toluene interface at
449 <        different temperatures using a range of energy fluxes.}
450 <      
344 <      \begin{tabular}{cccc}
447 >      \caption{Non-bonded interaction parameters (including cross
448 >        interactions with Au atoms) for both force fields used in this
449 >        work.}      
450 >      \begin{tabular}{lllllll}
451          \hline\hline
452 <        $\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\
453 <        (K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
452 >        & Site  & $\sigma_{ii}$ & $\epsilon_{ii}$ & $q_i$ &
453 >        $\sigma_{Au-i}$ & $\epsilon_{Au-i}$ \\
454 >        & & (\AA) & (kcal/mol) & ($e$) & (\AA) & (kcal/mol) \\
455          \hline
456 <        200 & 1.86 & 180 & 135 \\
457 <            & 2.15 & 204 & 113 \\
458 <            & 3.93 & 175 & 114 \\
459 <        300 & 1.91 & 143 & 125 \\
460 <            & 4.19 & 134 & 113 \\
456 >        United Atom (UA)
457 >        &CH3  & 3.75  & 0.1947  & -      & 3.54   & 0.2146  \\
458 >        &CH2  & 3.95  & 0.0914  & -      & 3.54   & 0.1749  \\
459 >        &CHar & 3.695 & 0.1003  & -      & 3.4625 & 0.1680  \\
460 >        &CRar & 3.88  & 0.04173 & -      & 3.555  & 0.1604  \\
461 >        \hline
462 >        All Atom (AA)
463 >        &CT3  & 3.50  & 0.066   & -0.18  & 3.365  & 0.1373  \\
464 >        &CT2  & 3.50  & 0.066   & -0.12  & 3.365  & 0.1373  \\
465 >        &CTT  & 3.50  & 0.066   & -0.065 & 3.365  & 0.1373  \\
466 >        &HC   & 2.50  & 0.030   &  0.06  & 2.865  & 0.09256 \\
467 >        &CA   & 3.55  & 0.070   & -0.115 & 3.173  & 0.0640  \\
468 >        &HA   & 2.42  & 0.030   &  0.115 & 2.746  & 0.0414  \\
469 >        \hline
470 >        Both UA and AA
471 >        & S   & 4.45  & 0.25    & -      & 2.40   & 8.465   \\
472          \hline\hline
473        \end{tabular}
474 <      \label{AuThiolToluene}
474 >      \label{MnM}
475      \end{center}
476    \end{minipage}
477   \end{table*}
478  
479 < \subsection{Hexane Solvent}
479 > \subsection{Vibrational Spectrum}
480  
481 < Using the united-atom model, different coverages of capping agent,
482 < temperatures of simulations and numbers of solvent molecules were all
483 < investigated and Table \ref{AuThiolHexaneUA} shows the results of
484 < these computations. The number of hexane molecules in our simulations
485 < does not affect the calculations significantly. However, a very long
486 < length scale for the thermal gradient axis ($z$) may cause excessively
369 < hot or cold temperatures in the middle of the solvent region and lead
370 < to undesired phenomena such as solvent boiling or freezing, while too
371 < few solvent molecules would change the normal behavior of the liquid
372 < phase. Our $N_{hexane}$ values were chosen to ensure that these
373 < extreme cases did not happen to our simulations.
481 > [MAY ADD EQN'S]
482 > To obtain these
483 > spectra, one first runs a simulation in the NVE ensemble and collects
484 > snapshots of configurations; these configurations are used to compute
485 > the velocity auto-correlation functions, which is used to construct a
486 > power spectrum via a Fourier transform.
487  
488 < Table \ref{AuThiolHexaneUA} enables direct comparison between
489 < different coverages of capping agent, when other system parameters are
490 < held constant. With high coverage of butanethiol on the gold surface,
491 < the interfacial thermal conductance is enhanced
492 < significantly. Interestingly, a slightly lower butanethiol coverage
493 < leads to a moderately higher conductivity. This is probably due to
494 < more solvent/capping agent contact when butanethiol molecules are
495 < not densely packed, which enhances the interactions between the two
496 < phases and lowers the thermal transfer barrier of this interface.
497 < % [COMPARE TO AU/WATER IN PAPER]
488 > \section{Results and Discussions}
489 > [MAY HAVE A BRIEF SUMMARY]
490 > \subsection{How Simulation Parameters Affects $G$}
491 > [MAY NOT PUT AT FIRST]
492 > We have varied our protocol or other parameters of the simulations in
493 > order to investigate how these factors would affect the measurement of
494 > $G$'s. It turned out that while some of these parameters would not
495 > affect the results substantially, some other changes to the
496 > simulations would have a significant impact on the measurement
497 > results.
498  
499 < It is also noted that the overall simulation temperature is another
500 < factor that affects the interfacial thermal conductance. One
501 < possibility of this effect may be rooted in the decrease in density of
502 < the liquid phase. We observed that when the average temperature
503 < increases from 200K to 250K, the bulk hexane density becomes lower
504 < than experimental value, as the system is equilibrated under NPT
505 < ensemble. This leads to lower contact between solvent and capping
506 < agent, and thus lower conductivity.
499 > In some of our simulations, we allowed $L_x$ and $L_y$ to change
500 > during equilibrating the liquid phase. Due to the stiffness of the
501 > crystalline Au structure, $L_x$ and $L_y$ would not change noticeably
502 > after equilibration. Although $L_z$ could fluctuate $\sim$1\% after a
503 > system is fully equilibrated in the NPT ensemble, this fluctuation, as
504 > well as those of $L_x$ and $L_y$ (which is significantly smaller),
505 > would not be magnified on the calculated $G$'s, as shown in Table
506 > \ref{AuThiolHexaneUA}. This insensivity to $L_i$ fluctuations allows
507 > reliable measurement of $G$'s without the necessity of extremely
508 > cautious equilibration process.
509  
510 < Conductivity values are more difficult to obtain under higher
511 < temperatures. This is because the Au surface tends to undergo
512 < reconstructions in relatively high temperatures. Surface Au atoms can
513 < migrate outward to reach higher Au-S contact; and capping agent
514 < molecules can be embedded into the surface Au layer due to the same
515 < driving force. This phenomenon agrees with experimental
516 < results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. A surface
517 < fully covered in capping agent is more susceptible to reconstruction,
518 < possibly because fully coverage prevents other means of capping agent
404 < relaxation, such as migration to an empty neighbor three-fold site.
510 > As stated in our computational details, the spacing filled with
511 > solvent molecules can be chosen within a range. This allows some
512 > change of solvent molecule numbers for the same Au-butanethiol
513 > surfaces. We did this study on our Au-butanethiol/hexane
514 > simulations. Nevertheless, the results obtained from systems of
515 > different $N_{hexane}$ did not indicate that the measurement of $G$ is
516 > susceptible to this parameter. For computational efficiency concern,
517 > smaller system size would be preferable, given that the liquid phase
518 > structure is not affected.
519  
520 < %MAY ADD MORE DATA TO TABLE
520 > Our NIVS algorithm allows change of unphysical thermal flux both in
521 > direction and in quantity. This feature extends our investigation of
522 > interfacial thermal conductance. However, the magnitude of this
523 > thermal flux is not arbitary if one aims to obtain a stable and
524 > reliable thermal gradient. A temperature profile would be
525 > substantially affected by noise when $|J_z|$ has a much too low
526 > magnitude; while an excessively large $|J_z|$ that overwhelms the
527 > conductance capacity of the interface would prevent a thermal gradient
528 > to reach a stablized steady state. NIVS has the advantage of allowing
529 > $J$ to vary in a wide range such that the optimal flux range for $G$
530 > measurement can generally be simulated by the algorithm. Within the
531 > optimal range, we were able to study how $G$ would change according to
532 > the thermal flux across the interface. For our simulations, we denote
533 > $J_z$ to be positive when the physical thermal flux is from the liquid
534 > to metal, and negative vice versa. The $G$'s measured under different
535 > $J_z$ is listed in Table \ref{AuThiolHexaneUA} and
536 > \ref{AuThiolToluene}. These results do not suggest that $G$ is
537 > dependent on $J_z$ within this flux range. The linear response of flux
538 > to thermal gradient simplifies our investigations in that we can rely
539 > on $G$ measurement with only a couple $J_z$'s and do not need to test
540 > a large series of fluxes.
541 >
542   \begin{table*}
543    \begin{minipage}{\linewidth}
544      \begin{center}
545        \caption{Computed interfacial thermal conductivity ($G$ and
546 <        $G^\prime$) values for the Au/butanethiol/hexane interface
547 <        with united-atom model and different capping agent coverage
548 <        and solvent molecule numbers at different temperatures using a
549 <        range of energy fluxes.}
546 >        $G^\prime$) values for the 100\% covered Au-butanethiol/hexane
547 >        interfaces with UA model and different hexane molecule numbers
548 >        at different temperatures using a range of energy
549 >        fluxes. Error estimates indicated in parenthesis.}
550        
551 <      \begin{tabular}{cccccc}
551 >      \begin{tabular}{ccccccc}
552          \hline\hline
553 <        Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\
554 <        coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) &
553 >        $\langle T\rangle$ & $N_{hexane}$ & Fixed & $\rho_{hexane}$ &
554 >        $J_z$ & $G$ & $G^\prime$ \\
555 >        (K) & & $L_x$ \& $L_y$? & (g/cm$^3$) & (GW/m$^2$) &
556          \multicolumn{2}{c}{(MW/m$^2$/K)} \\
557          \hline
558 <        0.0   & 200 & 200 & 0.96 & 43.3 & 42.7 \\
559 <              &     &     & 1.91 & 45.7 & 42.9 \\
560 <              &     & 166 & 0.96 & 43.1 & 53.4 \\
561 <        88.9  & 200 & 166 & 1.94 & 172  & 108  \\
562 <        100.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\
563 <              &     & 166 & 0.98 & 79.0 & 62.9 \\
564 <              &     &     & 1.44 & 76.2 & 64.8 \\
565 <              & 200 & 200 & 1.92 & 129  & 87.3 \\
566 <              &     &     & 1.93 & 131  & 77.5 \\
567 <              &     & 166 & 0.97 & 115  & 69.3 \\
568 <              &     &     & 1.94 & 125  & 87.1 \\
558 >        200 & 266 & No  & 0.672 & -0.96 & 102(3)    & 80.0(0.8) \\
559 >            & 200 & Yes & 0.694 &  1.92 & 129(11)   & 87.3(0.3) \\
560 >            &     & Yes & 0.672 &  1.93 & 131(16)   & 78(13)    \\
561 >            &     & No  & 0.688 &  0.96 & 125(16)   & 90.2(15)  \\
562 >            &     &     &       &  1.91 & 139(10)   & 101(10)   \\
563 >            &     &     &       &  2.83 & 141(6)    & 89.9(9.8) \\
564 >            & 166 & Yes & 0.679 &  0.97 & 115(19)   & 69(18)    \\
565 >            &     &     &       &  1.94 & 125(9)    & 87.1(0.2) \\
566 >            &     & No  & 0.681 &  0.97 & 141(30)   & 78(22)    \\
567 >            &     &     &       &  1.92 & 138(4)    & 98.9(9.5) \\
568 >        \hline
569 >        250 & 200 & No  & 0.560 &  0.96 & 75(10)    & 61.8(7.3) \\
570 >            &     &     &       & -0.95 & 49.4(0.3) & 45.7(2.1) \\
571 >            & 166 & Yes & 0.570 &  0.98 & 79.0(3.5) & 62.9(3.0) \\
572 >            &     & No  & 0.569 &  0.97 & 80.3(0.6) & 67(11)    \\
573 >            &     &     &       &  1.44 & 76.2(5.0) & 64.8(3.8) \\
574 >            &     &     &       & -0.95 & 56.4(2.5) & 54.4(1.1) \\
575 >            &     &     &       & -1.85 & 47.8(1.1) & 53.5(1.5) \\
576          \hline\hline
577        \end{tabular}
578        \label{AuThiolHexaneUA}
# Line 437 | Line 580 | For the all-atom model, the liquid hexane phase was no
580    \end{minipage}
581   \end{table*}
582  
583 < For the all-atom model, the liquid hexane phase was not stable under NPT
584 < conditions. Therefore, the simulation length scale parameters are
585 < adopted from previous equilibration results of the united-atom model
586 < at 200K. Table \ref{AuThiolHexaneAA} shows the results of these
587 < simulations. The conductivity values calculated with full capping
588 < agent coverage are substantially larger than observed in the
589 < united-atom model, and is even higher than predicted by
590 < experiments. It is possible that our parameters for metal-non-metal
591 < particle interactions lead to an overestimate of the interfacial
592 < thermal conductivity, although the active C-H vibrations in the
593 < all-atom model (which should not be appreciably populated at normal
594 < temperatures) could also account for this high conductivity. The major
452 < thermal transfer barrier of Au/butanethiol/hexane interface is between
453 < the liquid phase and the capping agent, so extra degrees of freedom
454 < such as the C-H vibrations could enhance heat exchange between these
455 < two phases and result in a much higher conductivity.
583 > Furthermore, we also attempted to increase system average temperatures
584 > to above 200K. These simulations are first equilibrated in the NPT
585 > ensemble under normal pressure. As stated above, the TraPPE-UA model
586 > for hexane tends to predict a lower boiling point. In our simulations,
587 > hexane had diffculty to remain in liquid phase when NPT equilibration
588 > temperature is higher than 250K. Additionally, the equilibrated liquid
589 > hexane density under 250K becomes lower than experimental value. This
590 > expanded liquid phase leads to lower contact between hexane and
591 > butanethiol as well.[MAY NEED SLAB DENSITY FIGURE]
592 > And this reduced contact would
593 > probably be accountable for a lower interfacial thermal conductance,
594 > as shown in Table \ref{AuThiolHexaneUA}.
595  
596 + A similar study for TraPPE-UA toluene agrees with the above result as
597 + well. Having a higher boiling point, toluene tends to remain liquid in
598 + our simulations even equilibrated under 300K in NPT
599 + ensembles. Furthermore, the expansion of the toluene liquid phase is
600 + not as significant as that of the hexane. This prevents severe
601 + decrease of liquid-capping agent contact and the results (Table
602 + \ref{AuThiolToluene}) show only a slightly decreased interface
603 + conductance. Therefore, solvent-capping agent contact should play an
604 + important role in the thermal transport process across the interface
605 + in that higher degree of contact could yield increased conductance.
606 +
607   \begin{table*}
608    \begin{minipage}{\linewidth}
609      \begin{center}
460 –      
610        \caption{Computed interfacial thermal conductivity ($G$ and
611 <        $G^\prime$) values for the Au/butanethiol/hexane interface
612 <        with all-atom model and different capping agent coverage at
613 <        200K using a range of energy fluxes.}
611 >        $G^\prime$) values for a 90\% coverage Au-butanethiol/toluene
612 >        interface at different temperatures using a range of energy
613 >        fluxes. Error estimates indicated in parenthesis.}
614        
615 <      \begin{tabular}{cccc}
615 >      \begin{tabular}{ccccc}
616          \hline\hline
617 <        Thiol & $J_z$ & $G$ & $G^\prime$ \\
618 <        coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
617 >        $\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\
618 >        (K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
619          \hline
620 <        0.0   & 0.95 & 28.5 & 27.2 \\
621 <              & 1.88 & 30.3 & 28.9 \\
622 <        100.0 & 2.87 & 551  & 294  \\
623 <              & 3.81 & 494  & 193  \\
620 >        200 & 0.933 &  2.15 & 204(12) & 113(12) \\
621 >            &       & -1.86 & 180(3)  & 135(21) \\
622 >            &       & -3.93 & 176(5)  & 113(12) \\
623 >        \hline
624 >        300 & 0.855 & -1.91 & 143(5)  & 125(2)  \\
625 >            &       & -4.19 & 135(9)  & 113(12) \\
626          \hline\hline
627        \end{tabular}
628 <      \label{AuThiolHexaneAA}
628 >      \label{AuThiolToluene}
629      \end{center}
630    \end{minipage}
631   \end{table*}
632  
633 < %subsubsection{Vibrational spectrum study on conductance mechanism}
633 > Besides lower interfacial thermal conductance, surfaces in relatively
634 > high temperatures are susceptible to reconstructions, when
635 > butanethiols have a full coverage on the Au(111) surface. These
636 > reconstructions include surface Au atoms migrated outward to the S
637 > atom layer, and butanethiol molecules embedded into the original
638 > surface Au layer. The driving force for this behavior is the strong
639 > Au-S interactions in our simulations. And these reconstructions lead
640 > to higher ratio of Au-S attraction and thus is energetically
641 > favorable. Furthermore, this phenomenon agrees with experimental
642 > results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt
643 > {\it et al.} had kept their Au(111) slab rigid so that their
644 > simulations can reach 300K without surface reconstructions. Without
645 > this practice, simulating 100\% thiol covered interfaces under higher
646 > temperatures could hardly avoid surface reconstructions. However, our
647 > measurement is based on assuming homogeneity on $x$ and $y$ dimensions
648 > so that measurement of $T$ at particular $z$ would be an effective
649 > average of the particles of the same type. Since surface
650 > reconstructions could eliminate the original $x$ and $y$ dimensional
651 > homogeneity, measurement of $G$ is more difficult to conduct under
652 > higher temperatures. Therefore, most of our measurements are
653 > undertaken at $\langle T\rangle\sim$200K.
654 >
655 > However, when the surface is not completely covered by butanethiols,
656 > the simulated system is more resistent to the reconstruction
657 > above. Our Au-butanethiol/toluene system had the Au(111) surfaces 90\%
658 > covered by butanethiols, but did not see this above phenomena even at
659 > $\langle T\rangle\sim$300K. The empty three-fold sites not occupied by
660 > capping agents could help prevent surface reconstruction in that they
661 > provide other means of capping agent relaxation. It is observed that
662 > butanethiols can migrate to their neighbor empty sites during a
663 > simulation. Therefore, we were able to obtain $G$'s for these
664 > interfaces even at a relatively high temperature without being
665 > affected by surface reconstructions.
666 >
667 > \subsection{Influence of Capping Agent Coverage on $G$}
668 > To investigate the influence of butanethiol coverage on interfacial
669 > thermal conductance, a series of different coverage Au-butanethiol
670 > surfaces is prepared and solvated with various organic
671 > molecules. These systems are then equilibrated and their interfacial
672 > thermal conductivity are measured with our NIVS algorithm. Figure
673 > \ref{coverage} demonstrates the trend of conductance change with
674 > respect to different coverages of butanethiol. To study the isotope
675 > effect in interfacial thermal conductance, deuterated UA-hexane is
676 > included as well.
677 >
678 > It turned out that with partial covered butanethiol on the Au(111)
679 > surface, the derivative definition for $G^\prime$
680 > (Eq. \ref{derivativeG}) was difficult to apply, due to the difficulty
681 > in locating the maximum of change of $\lambda$. Instead, the discrete
682 > definition (Eq. \ref{discreteG}) is easier to apply, as the Gibbs
683 > deviding surface can still be well-defined. Therefore, $G$ (not
684 > $G^\prime$) was used for this section.
685 >
686 > From Figure \ref{coverage}, one can see the significance of the
687 > presence of capping agents. Even when a fraction of the Au(111)
688 > surface sites are covered with butanethiols, the conductivity would
689 > see an enhancement by at least a factor of 3. This indicates the
690 > important role cappping agent is playing for thermal transport
691 > phenomena on metal / organic solvent surfaces.
692 >
693 > Interestingly, as one could observe from our results, the maximum
694 > conductance enhancement (largest $G$) happens while the surfaces are
695 > about 75\% covered with butanethiols. This again indicates that
696 > solvent-capping agent contact has an important role of the thermal
697 > transport process. Slightly lower butanethiol coverage allows small
698 > gaps between butanethiols to form. And these gaps could be filled with
699 > solvent molecules, which acts like ``heat conductors'' on the
700 > surface. The higher degree of interaction between these solvent
701 > molecules and capping agents increases the enhancement effect and thus
702 > produces a higher $G$ than densely packed butanethiol arrays. However,
703 > once this maximum conductance enhancement is reached, $G$ decreases
704 > when butanethiol coverage continues to decrease. Each capping agent
705 > molecule reaches its maximum capacity for thermal
706 > conductance. Therefore, even higher solvent-capping agent contact
707 > would not offset this effect. Eventually, when butanethiol coverage
708 > continues to decrease, solvent-capping agent contact actually
709 > decreases with the disappearing of butanethiol molecules. In this
710 > case, $G$ decrease could not be offset but instead accelerated. [NEED
711 > SNAPSHOT SHOWING THE PHENOMENA / SLAB DENSITY ANALYSIS]
712 >
713 > A comparison of the results obtained from differenet organic solvents
714 > can also provide useful information of the interfacial thermal
715 > transport process. The deuterated hexane (UA) results do not appear to
716 > be much different from those of normal hexane (UA), given that
717 > butanethiol (UA) is non-deuterated for both solvents. These UA model
718 > studies, even though eliminating C-H vibration samplings, still have
719 > C-C vibrational frequencies different from each other. However, these
720 > differences in the infrared range do not seem to produce an observable
721 > difference for the results of $G$. [MAY NEED SPECTRA FIGURE]
722 >
723 > Furthermore, results for rigid body toluene solvent, as well as other
724 > UA-hexane solvents, are reasonable within the general experimental
725 > ranges[CITATIONS]. This suggests that explicit hydrogen might not be a
726 > required factor for modeling thermal transport phenomena of systems
727 > such as Au-thiol/organic solvent.
728 >
729 > However, results for Au-butanethiol/toluene do not show an identical
730 > trend with those for Au-butanethiol/hexane in that $G$ remains at
731 > approximately the same magnitue when butanethiol coverage differs from
732 > 25\% to 75\%. This might be rooted in the molecule shape difference
733 > for planar toluene and chain-like {\it n}-hexane. Due to this
734 > difference, toluene molecules have more difficulty in occupying
735 > relatively small gaps among capping agents when their coverage is not
736 > too low. Therefore, the solvent-capping agent contact may keep
737 > increasing until the capping agent coverage reaches a relatively low
738 > level. This becomes an offset for decreasing butanethiol molecules on
739 > its effect to the process of interfacial thermal transport. Thus, one
740 > can see a plateau of $G$ vs. butanethiol coverage in our results.
741 >
742 > \begin{figure}
743 > \includegraphics[width=\linewidth]{coverage}
744 > \caption{Comparison of interfacial thermal conductivity ($G$) values
745 >  for the Au-butanethiol/solvent interface with various UA models and
746 >  different capping agent coverages at $\langle T\rangle\sim$200K
747 >  using certain energy flux respectively.}
748 > \label{coverage}
749 > \end{figure}
750 >
751 > \subsection{Influence of Chosen Molecule Model on $G$}
752 > In addition to UA solvent/capping agent models, AA models are included
753 > in our simulations as well. Besides simulations of the same (UA or AA)
754 > model for solvent and capping agent, different models can be applied
755 > to different components. Furthermore, regardless of models chosen,
756 > either the solvent or the capping agent can be deuterated, similar to
757 > the previous section. Table \ref{modelTest} summarizes the results of
758 > these studies.
759 >
760 > \begin{table*}
761 >  \begin{minipage}{\linewidth}
762 >    \begin{center}
763 >      
764 >      \caption{Computed interfacial thermal conductivity ($G$ and
765 >        $G^\prime$) values for interfaces using various models for
766 >        solvent and capping agent (or without capping agent) at
767 >        $\langle T\rangle\sim$200K. (D stands for deuterated solvent
768 >        or capping agent molecules; ``Avg.'' denotes results that are
769 >        averages of simulations under different $J_z$'s. Error
770 >        estimates indicated in parenthesis.)}
771 >      
772 >      \begin{tabular}{llccc}
773 >        \hline\hline
774 >        Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\
775 >        (or bare surface) & model & (GW/m$^2$) &
776 >        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
777 >        \hline
778 >        UA    & UA hexane    & Avg. & 131(9)    & 87(10)    \\
779 >              & UA hexane(D) & 1.95 & 153(5)    & 136(13)   \\
780 >              & AA hexane    & Avg. & 131(6)    & 122(10)   \\
781 >              & UA toluene   & 1.96 & 187(16)   & 151(11)   \\
782 >              & AA toluene   & 1.89 & 200(36)   & 149(53)   \\
783 >        \hline
784 >        AA    & UA hexane    & 1.94 & 116(9)    & 129(8)    \\
785 >              & AA hexane    & Avg. & 442(14)   & 356(31)   \\
786 >              & AA hexane(D) & 1.93 & 222(12)   & 234(54)   \\
787 >              & UA toluene   & 1.98 & 125(25)   & 97(60)    \\
788 >              & AA toluene   & 3.79 & 487(56)   & 290(42)   \\
789 >        \hline
790 >        AA(D) & UA hexane    & 1.94 & 158(25)   & 172(4)    \\
791 >              & AA hexane    & 1.92 & 243(29)   & 191(11)   \\
792 >              & AA toluene   & 1.93 & 364(36)   & 322(67)   \\
793 >        \hline
794 >        bare  & UA hexane    & Avg. & 46.5(3.2) & 49.4(4.5) \\
795 >              & UA hexane(D) & 0.98 & 43.9(4.6) & 43.0(2.0) \\
796 >              & AA hexane    & 0.96 & 31.0(1.4) & 29.4(1.3) \\
797 >              & UA toluene   & 1.99 & 70.1(1.3) & 65.8(0.5) \\
798 >        \hline\hline
799 >      \end{tabular}
800 >      \label{modelTest}
801 >    \end{center}
802 >  \end{minipage}
803 > \end{table*}
804 >
805 > To facilitate direct comparison, the same system with differnt models
806 > for different components uses the same length scale for their
807 > simulation cells. Without the presence of capping agent, using
808 > different models for hexane yields similar results for both $G$ and
809 > $G^\prime$, and these two definitions agree with eath other very
810 > well. This indicates very weak interaction between the metal and the
811 > solvent, and is a typical case for acoustic impedance mismatch between
812 > these two phases.
813 >
814 > As for Au(111) surfaces completely covered by butanethiols, the choice
815 > of models for capping agent and solvent could impact the measurement
816 > of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane
817 > interfaces, using AA model for both butanethiol and hexane yields
818 > substantially higher conductivity values than using UA model for at
819 > least one component of the solvent and capping agent, which exceeds
820 > the general range of experimental measurement results. This is
821 > probably due to the classically treated C-H vibrations in the AA
822 > model, which should not be appreciably populated at normal
823 > temperatures. In comparison, once either the hexanes or the
824 > butanethiols are deuterated, one can see a significantly lower $G$ and
825 > $G^\prime$. In either of these cases, the C-H(D) vibrational overlap
826 > between the solvent and the capping agent is removed.
827 > [MAY NEED SPECTRA FIGURE] Conclusively, the
828 > improperly treated C-H vibration in the AA model produced
829 > over-predicted results accordingly. Compared to the AA model, the UA
830 > model yields more reasonable results with higher computational
831 > efficiency.
832 >
833 > However, for Au-butanethiol/toluene interfaces, having the AA
834 > butanethiol deuterated did not yield a significant change in the
835 > measurement results. Compared to the C-H vibrational overlap between
836 > hexane and butanethiol, both of which have alkyl chains, that overlap
837 > between toluene and butanethiol is not so significant and thus does
838 > not have as much contribution to the ``Intramolecular Vibration
839 > Redistribution''[CITE HASE]. Conversely, extra degrees of freedom such
840 > as the C-H vibrations could yield higher heat exchange rate between
841 > these two phases and result in a much higher conductivity.
842 >
843 > Although the QSC model for Au is known to predict an overly low value
844 > for bulk metal gold conductivity\cite{kuang:164101}, our computational
845 > results for $G$ and $G^\prime$ do not seem to be affected by this
846 > drawback of the model for metal. Instead, our results suggest that the
847 > modeling of interfacial thermal transport behavior relies mainly on
848 > the accuracy of the interaction descriptions between components
849 > occupying the interfaces.
850 >
851 > \subsection{Role of Capping Agent in Interfacial Thermal Conductance}
852   To investigate the mechanism of this interfacial thermal conductance,
853   the vibrational spectra of various gold systems were obtained and are
854 < shown as in the upper panel of Fig. \ref{vibration}. To obtain these
855 < spectra, one first runs a simulation in the NVE ensemble and collects
856 < snapshots of configurations; these configurations are used to compute
857 < the velocity auto-correlation functions, which is used to construct a
858 < power spectrum via a Fourier transform. The gold surfaces covered by
859 < butanethiol molecules exhibit an additional peak observed at a
860 < frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration
861 < of the S-Au bond. This vibration enables efficient thermal transport
862 < from surface Au atoms to the capping agents. Simultaneously, as shown
863 < in the lower panel of Fig. \ref{vibration}, the large overlap of the
495 < vibration spectra of butanethiol and hexane in the all-atom model,
854 > shown as in Fig. \ref{vibration}.
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
504 <  all-atom model (lower panel).}
872 >  environments.}
873   \label{vibration}
874   \end{figure}
507 – % 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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