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22   \setlength{\abovecaptionskip}{20 pt}
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24  
25 < %\renewcommand\citemid{\ } % no comma in optional referenc note
25 > %\renewcommand\citemid{\ } % no comma in optional reference note
26   \bibpunct{[}{]}{,}{s}{}{;}
27   \bibliographystyle{aip}
28  
# 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 –
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 < There have been many algorithms for computing thermal conductivity
141 < using molecular dynamics simulations. However, interfacial conductance
142 < is at least an order of magnitude smaller. This would make the
143 < calculation even more difficult for those slowly-converging
144 < 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
112 < 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
131 < algorithm conserves momenta and energy and does not depend on an
132 < 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 < (wondering how much detail of algorithm should be put here...)
174 > \subsection{Defining Interfacial Thermal Conductivity $G$}
175 > For interfaces with a relatively low interfacial conductance, the bulk
176 > regions on either side of an interface rapidly come to a state in
177 > which the two phases have relatively homogeneous (but distinct)
178 > temperatures. The interfacial thermal conductivity $G$ can therefore
179 > be approximated as:
180 > \begin{equation}
181 > G = \frac{E_{total}}{2 t L_x L_y \left( \langle T_\mathrm{hot}\rangle -
182 >    \langle T_\mathrm{cold}\rangle \right)}
183 > \label{lowG}
184 > \end{equation}
185 > where ${E_{total}}$ is the imposed non-physical kinetic energy
186 > transfer and ${\langle T_\mathrm{hot}\rangle}$ and ${\langle
187 >  T_\mathrm{cold}\rangle}$ are the average observed temperature of the
188 > two separated phases.
189  
136 – \subsection{Force Field Parameters}
137 – Our simulation systems consists of metal gold lattice slab solvated by
138 – organic solvents. In order to study the role of capping agents in
139 – interfacial thermal conductance, butanethiol is chosen to cover gold
140 – surfaces in comparison to no capping agent present.
141 –
142 – The Au-Au interactions in metal lattice slab is described by the
143 – quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC
144 – potentials include zero-point quantum corrections and are
145 – reparametrized for accurate surface energies compared to the
146 – Sutton-Chen potentials\cite{Chen90}.
147 –
148 – Straight chain {\it n}-hexane and aromatic toluene are respectively
149 – used as solvents. For hexane, both United-Atom\cite{TraPPE-UA.alkanes}
150 – and All-Atom\cite{OPLSAA} force fields are used for comparison; for
151 – toluene, United-Atom\cite{TraPPE-UA.alkylbenzenes} force fields are
152 – used with rigid body constraints applied. (maybe needs more details
153 – about rigid body)
154 –
155 – Buatnethiol molecules are used as capping agent for some of our
156 – simulations. United-Atom\cite{TraPPE-UA.thiols} and All-Atom models
157 – are respectively used corresponding to the force field type of
158 – solvent.
159 –
160 – To describe the interactions between metal Au and non-metal capping
161 – agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive
162 – other interactions which are not parametrized in their work. (can add
163 – hautman and klein's paper here and more discussion; need to put
164 – aromatic-metal interaction approximation here)
165 –
166 – [TABULATED FORCE FIELD PARAMETERS NEEDED]
167 –
168 – \section{Computational Details}
169 – \subsection{System Geometry}
170 – Our simulation systems consists of a lattice Au slab with the (111)
171 – surface perpendicular to the $z$-axis, and a solvent layer between the
172 – periodic Au slabs along the $z$-axis. To set up the interfacial
173 – system, the Au slab is first equilibrated without solvent under room
174 – pressure and a desired temperature. After the metal slab is
175 – equilibrated, United-Atom or All-Atom butanethiols are replicated on
176 – the Au surface, each occupying the (??) among three Au atoms, and is
177 – equilibrated under NVT ensemble. According to (CITATION), the maximal
178 – thiol capacity on Au surface is $1/3$ of the total number of surface
179 – Au atoms.
180 –
181 – \cite{packmol}
182 –
183 – \subsection{Simulation Parameters}
184 –
190   When the interfacial conductance is {\it not} small, there are two
191 < ways to define $G$. If we assume the temperature is discretely
192 < different on two sides of the interface, $G$ can be calculated with
193 < the thermal flux applied $J$ and the temperature difference measured
194 < $\Delta T$ as:
191 > ways to define $G$.
192 >
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 > as:
198   \begin{equation}
199   G=\frac{J}{\Delta T}
200   \label{discreteG}
201   \end{equation}
202 < We can as well assume a continuous temperature profile along the
203 < thermal gradient axis $z$ and define $G$ as the change of bulk thermal
204 < conductivity $\lambda$ at a defined interfacial point:
202 >
203 > The other approach is to assume a continuous temperature profile along
204 > the thermal gradient axis (e.g. $z$) and define $G$ at the point where
205 > the magnitude of thermal conductivity $\lambda$ change reach its
206 > maximum, given that $\lambda$ is well-defined throughout the space:
207   \begin{equation}
208   G^\prime = \Big|\frac{\partial\lambda}{\partial z}\Big|
209           = \Big|\frac{\partial}{\partial z}\left(-J_z\Big/
210             \left(\frac{\partial T}{\partial z}\right)\right)\Big|
211 <         = J_z\Big|\frac{\partial^2 T}{\partial z^2}\Big|
211 >         = |J_z|\Big|\frac{\partial^2 T}{\partial z^2}\Big|
212           \Big/\left(\frac{\partial T}{\partial z}\right)^2
213   \label{derivativeG}
214   \end{equation}
215 +
216   With the temperature profile obtained from simulations, one is able to
217   approximate the first and second derivatives of $T$ with finite
218 < difference method and thus calculate $G^\prime$.
218 > difference methods and thus calculate $G^\prime$.
219  
220 < In what follows, both definitions are used for calculation and comparison.
220 > In what follows, both definitions have been used for calculation and
221 > are compared in the results.
222  
223 < \section{Results}
224 < \subsection{Toluene Solvent}
223 > To compare the above definitions ($G$ and $G^\prime$), we have modeled
224 > a metal slab with its (111) surfaces perpendicular to the $z$-axis of
225 > our simulation cells. Both with and withour capping agents on the
226 > surfaces, the metal slab is solvated with simple organic solvents, as
227 > illustrated in Figure \ref{demoPic}.
228  
229 < The simulations follow a protocol similar to the previous gold/water
230 < interfacial systems. The results (Table \ref{AuThiolToluene}) show a
231 < significant conductance enhancement compared to the gold/water
232 < interface without capping agent and agree with available experimental
233 < data. This indicates that the metal-metal potential, though not
234 < predicting an accurate bulk metal thermal conductivity, does not
220 < greatly interfere with the simulation of the thermal conductance
221 < behavior across a non-metal interface. The solvent model is not
222 < particularly volatile, so the simulation cell does not expand
223 < significantly under higher temperature. We did not observe a
224 < significant conductance decrease when the temperature was increased to
225 < 300K. The results show that the two definitions used for $G$ yield
226 < comparable values, though $G^\prime$ tends to be smaller.
229 > \begin{figure}
230 > \includegraphics[width=\linewidth]{demoPic}
231 > \caption{A sample showing how a metal slab has its (111) surface
232 >  covered by capping agent molecules and solvated by hexane.}
233 > \label{demoPic}
234 > \end{figure}
235  
236 + With the simulation cell described above, we are able to equilibrate
237 + the system and impose an unphysical thermal flux between the liquid
238 + and the metal phase using the NIVS algorithm. By periodically applying
239 + the unphysical flux, we are able to obtain a temperature profile and
240 + its spatial derivatives. These quantities enable the evaluation of the
241 + interfacial thermal conductance of a surface. Figure \ref{gradT} is an
242 + example how those applied thermal fluxes can be used to obtain the 1st
243 + and 2nd derivatives of the temperature profile.
244 +
245 + \begin{figure}
246 + \includegraphics[width=\linewidth]{gradT}
247 + \caption{The 1st and 2nd derivatives of temperature profile can be
248 +  obtained with finite difference approximation.}
249 + \label{gradT}
250 + \end{figure}
251 +
252 + \section{Computational Details}
253 + \subsection{Simulation Protocol}
254 + The NIVS algorithm has been implemented in our MD simulation code,
255 + OpenMD\cite{Meineke:2005gd,openmd}, and was used for our
256 + simulations. Different slab thickness (layer numbers of Au) were
257 + simulated. Metal slabs were first equilibrated under atmospheric
258 + pressure (1 atm) and a desired temperature (e.g. 200K). After
259 + equilibration, butanethiol capping agents were placed at three-fold
260 + sites on the Au(111) surfaces. The maximum butanethiol capacity on Au
261 + surface is $1/3$ of the total number of surface Au
262 + atoms\cite{vlugt:cpc2007154}. A series of different coverages was
263 + investigated in order to study the relation between coverage and
264 + interfacial conductance.
265 +
266 + The capping agent molecules were allowed to migrate during the
267 + simulations. They distributed themselves uniformly and sampled a
268 + number of three-fold sites throughout out study. Therefore, the
269 + initial configuration would not noticeably affect the sampling of a
270 + variety of configurations of the same coverage, and the final
271 + conductance measurement would be an average effect of these
272 + configurations explored in the simulations. [MAY NEED FIGURES]
273 +
274 + After the modified Au-butanethiol surface systems were equilibrated
275 + under canonical ensemble, organic solvent molecules were packed in the
276 + previously empty part of the simulation cells\cite{packmol}. Two
277 + solvents were investigated, one which has little vibrational overlap
278 + with the alkanethiol and a planar shape (toluene), and one which has
279 + similar vibrational frequencies and chain-like shape ({\it n}-hexane).
280 +
281 + The space filled by solvent molecules, i.e. the gap between
282 + periodically repeated Au-butanethiol surfaces should be carefully
283 + chosen. A very long length scale for the thermal gradient axis ($z$)
284 + may cause excessively hot or cold temperatures in the middle of the
285 + solvent region and lead to undesired phenomena such as solvent boiling
286 + or freezing when a thermal flux is applied. Conversely, too few
287 + solvent molecules would change the normal behavior of the liquid
288 + phase. Therefore, our $N_{solvent}$ values were chosen to ensure that
289 + these extreme cases did not happen to our simulations. And the
290 + corresponding spacing is usually $35 \sim 60$\AA.
291 +
292 + The initial configurations generated by Packmol are further
293 + equilibrated with the $x$ and $y$ dimensions fixed, only allowing
294 + length scale change in $z$ dimension. This is to ensure that the
295 + equilibration of liquid phase does not affect the metal crystal
296 + structure in $x$ and $y$ dimensions. Further equilibration are run
297 + under NVT and then NVE ensembles.
298 +
299 + After the systems reach equilibrium, NIVS is implemented to impose a
300 + periodic unphysical thermal flux between the metal and the liquid
301 + phase. Most of our simulations are under an average temperature of
302 + $\sim$200K. Therefore, this flux usually comes from the metal to the
303 + liquid so that the liquid has a higher temperature and would not
304 + freeze due to excessively low temperature. This induced temperature
305 + gradient is stablized and the simulation cell is devided evenly into
306 + N slabs along the $z$-axis and the temperatures of each slab are
307 + recorded. When the slab width $d$ of each slab is the same, the
308 + derivatives of $T$ with respect to slab number $n$ can be directly
309 + used for $G^\prime$ calculations:
310 + \begin{equation}
311 + G^\prime = |J_z|\Big|\frac{\partial^2 T}{\partial z^2}\Big|
312 +         \Big/\left(\frac{\partial T}{\partial z}\right)^2
313 +         = |J_z|\Big|\frac{1}{d^2}\frac{\partial^2 T}{\partial n^2}\Big|
314 +         \Big/\left(\frac{1}{d}\frac{\partial T}{\partial n}\right)^2
315 +         = |J_z|\Big|\frac{\partial^2 T}{\partial n^2}\Big|
316 +         \Big/\left(\frac{\partial T}{\partial n}\right)^2
317 + \label{derivativeG2}
318 + \end{equation}
319 +
320 + \subsection{Force Field Parameters}
321 + Our simulations include various components. Therefore, force field
322 + parameter descriptions are needed for interactions both between the
323 + same type of particles and between particles of different species.
324 +
325 + The Au-Au interactions in metal lattice slab is described by the
326 + quantum Sutton-Chen (QSC) formulation\cite{PhysRevB.59.3527}. The QSC
327 + potentials include zero-point quantum corrections and are
328 + reparametrized for accurate surface energies compared to the
329 + Sutton-Chen potentials\cite{Chen90}.
330 +
331 + Figure \ref{demoMol} demonstrates how we name our pseudo-atoms of the
332 + organic solvent molecules in our simulations.
333 +
334 + \begin{figure}
335 + \includegraphics[width=\linewidth]{demoMol}
336 + \caption{Denomination of atoms or pseudo-atoms in our simulations: a)
337 +  UA-hexane; b) AA-hexane; c) UA-toluene; d) AA-toluene.}
338 + \label{demoMol}
339 + \end{figure}
340 +
341 + For both solvent molecules, straight chain {\it n}-hexane and aromatic
342 + toluene, United-Atom (UA) and All-Atom (AA) models are used
343 + respectively. The TraPPE-UA
344 + parameters\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} are used
345 + for our UA solvent molecules. In these models, pseudo-atoms are
346 + located at the carbon centers for alkyl groups. By eliminating
347 + explicit hydrogen atoms, these models are simple and computationally
348 + efficient, while maintains good accuracy. However, the TraPPE-UA for
349 + alkanes is known to predict a lower boiling point than experimental
350 + values. Considering that after an unphysical thermal flux is applied
351 + to a system, the temperature of ``hot'' area in the liquid phase would be
352 + significantly higher than the average, to prevent over heating and
353 + boiling of the liquid phase, the average temperature in our
354 + simulations should be much lower than the liquid boiling point. [MORE DISCUSSION]
355 + For UA-toluene model, rigid body constraints are applied, so that the
356 + benzene ring and the methyl-CRar bond are kept rigid. This would save
357 + computational time.[MORE DETAILS]
358 +
359 + Besides the TraPPE-UA models, AA models for both organic solvents are
360 + included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA}
361 + force field is used. [MORE DETAILS]
362 + For toluene, the United Force Field developed by Rapp\'{e} {\it et
363 +  al.}\cite{doi:10.1021/ja00051a040} is adopted.[MORE DETAILS]
364 +
365 + The capping agent in our simulations, the butanethiol molecules can
366 + either use UA or AA model. The TraPPE-UA force fields includes
367 + parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used for
368 + UA butanethiol model in our simulations. The OPLS-AA also provides
369 + parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111)
370 + surfaces do not have the hydrogen atom bonded to sulfur. To adapt this
371 + change and derive suitable parameters for butanethiol adsorbed on
372 + Au(111) surfaces, we adopt the S parameters from Luedtke and
373 + Landman\cite{landman:1998} and modify parameters for its neighbor C
374 + atom for charge balance in the molecule. Note that the model choice
375 + (UA or AA) of capping agent can be different from the
376 + solvent. Regardless of model choice, the force field parameters for
377 + interactions between capping agent and solvent can be derived using
378 + Lorentz-Berthelot Mixing Rule:
379 + \begin{eqnarray}
380 + \sigma_{IJ} & = & \frac{1}{2} \left(\sigma_{II} + \sigma_{JJ}\right) \\
381 + \epsilon_{IJ} & = & \sqrt{\epsilon_{II}\epsilon_{JJ}}
382 + \end{eqnarray}
383 +
384 + To describe the interactions between metal Au and non-metal capping
385 + agent and solvent particles, we refer to an adsorption study of alkyl
386 + thiols on gold surfaces by Vlugt {\it et
387 +  al.}\cite{vlugt:cpc2007154} They fitted an effective Lennard-Jones
388 + form of potential parameters for the interaction between Au and
389 + pseudo-atoms CH$_x$ and S based on a well-established and widely-used
390 + effective potential of Hautman and Klein\cite{hautman:4994} for the
391 + Au(111) surface. As our simulations require the gold lattice slab to
392 + be non-rigid so that it could accommodate kinetic energy for thermal
393 + transport study purpose, the pair-wise form of potentials is
394 + preferred.
395 +
396 + Besides, the potentials developed from {\it ab initio} calculations by
397 + Leng {\it et al.}\cite{doi:10.1021/jp034405s} are adopted for the
398 + interactions between Au and aromatic C/H atoms in toluene.[MORE DETAILS]
399 +
400 + However, the Lennard-Jones parameters between Au and other types of
401 + particles in our simulations are not yet well-established. For these
402 + interactions, we attempt to derive their parameters using the Mixing
403 + Rule. To do this, the ``Metal-non-Metal'' (MnM) interaction parameters
404 + for Au is first extracted from the Au-CH$_x$ parameters by applying
405 + the Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM''
406 + parameters in our simulations.
407 +
408   \begin{table*}
409    \begin{minipage}{\linewidth}
410      \begin{center}
411 <      \caption{Computed interfacial thermal conductivity ($G$ and
412 <        $G^\prime$) values for the Au/butanethiol/toluene interface at
413 <        different temperatures using a range of energy fluxes.}
411 >      \caption{Non-bonded interaction paramters for non-metal
412 >        particles and metal-non-metal interactions in our
413 >        simulations.}
414        
415 <      \begin{tabular}{cccc}
415 >      \begin{tabular}{cccccc}
416          \hline\hline
417 <        $\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\
418 <        (K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
417 >        Non-metal atom $I$ & $\sigma_{II}$ & $\epsilon_{II}$ & $q_I$ &
418 >        $\sigma_{AuI}$ & $\epsilon_{AuI}$ \\
419 >        (or pseudo-atom) & \AA & kcal/mol & & \AA & kcal/mol \\
420          \hline
421 <        200 & 1.86 & 180 & 135 \\
422 <            & 2.15 & 204 & 113 \\
423 <            & 3.93 & 175 & 114 \\
424 <        300 & 1.91 & 143 & 125 \\
425 <            & 4.19 & 134 & 113 \\
421 >        CH3  & 3.75  & 0.1947  & -      & 3.54   & 0.2146  \\
422 >        CH2  & 3.95  & 0.0914  & -      & 3.54   & 0.1749  \\
423 >        CHar & 3.695 & 0.1003  & -      & 3.4625 & 0.1680  \\
424 >        CRar & 3.88  & 0.04173 & -      & 3.555  & 0.1604  \\
425 >        S    & 4.45  & 0.25    & -      & 2.40   & 8.465   \\
426 >        CT3  & 3.50  & 0.066   & -0.18  & 3.365  & 0.1373  \\
427 >        CT2  & 3.50  & 0.066   & -0.12  & 3.365  & 0.1373  \\
428 >        CTT  & 3.50  & 0.066   & -0.065 & 3.365  & 0.1373  \\
429 >        HC   & 2.50  & 0.030   &  0.06  & 2.865  & 0.09256 \\
430 >        CA   & 3.55  & 0.070   & -0.115 & 3.173  & 0.0640  \\
431 >        HA   & 2.42  & 0.030   &  0.115 & 2.746  & 0.0414  \\
432          \hline\hline
433        \end{tabular}
434 <      \label{AuThiolToluene}
434 >      \label{MnM}
435      \end{center}
436    \end{minipage}
437   \end{table*}
438  
252 – \subsection{Hexane Solvent}
439  
440 < Using the united-atom model, different coverages of capping agent,
441 < temperatures of simulations and numbers of solvent molecules were all
442 < investigated and Table \ref{AuThiolHexaneUA} shows the results of
443 < these computations. The number of hexane molecules in our simulations
444 < does not affect the calculations significantly. However, a very long
445 < length scale for the thermal gradient axis ($z$) may cause excessively
446 < hot or cold temperatures in the middle of the solvent region and lead
447 < to undesired phenomena such as solvent boiling or freezing, while too
448 < few solvent molecules would change the normal behavior of the liquid
449 < phase. Our $N_{hexane}$ values were chosen to ensure that these
264 < extreme cases did not happen to our simulations.
440 > \section{Results and Discussions}
441 > [MAY HAVE A BRIEF SUMMARY]
442 > \subsection{How Simulation Parameters Affects $G$}
443 > [MAY NOT PUT AT FIRST]
444 > We have varied our protocol or other parameters of the simulations in
445 > order to investigate how these factors would affect the measurement of
446 > $G$'s. It turned out that while some of these parameters would not
447 > affect the results substantially, some other changes to the
448 > simulations would have a significant impact on the measurement
449 > results.
450  
451 < Table \ref{AuThiolHexaneUA} enables direct comparison between
452 < different coverages of capping agent, when other system parameters are
453 < held constant. With high coverage of butanethiol on the gold surface,
454 < the interfacial thermal conductance is enhanced
455 < significantly. Interestingly, a slightly lower butanethiol coverage
456 < leads to a moderately higher conductivity. This is probably due to
457 < more solvent/capping agent contact when butanethiol molecules are
458 < not densely packed, which enhances the interactions between the two
459 < phases and lowers the thermal transfer barrier of this interface.
275 < % [COMPARE TO AU/WATER IN PAPER]
451 > In some of our simulations, we allowed $L_x$ and $L_y$ to change
452 > during equilibrating the liquid phase. Due to the stiffness of the Au
453 > slab, $L_x$ and $L_y$ would not change noticeably after
454 > equilibration. Although $L_z$ could fluctuate $\sim$1\% after a system
455 > is fully equilibrated in the NPT ensemble, this fluctuation, as well
456 > as those comparably smaller to $L_x$ and $L_y$, would not be magnified
457 > on the calculated $G$'s, as shown in Table \ref{AuThiolHexaneUA}. This
458 > insensivity to $L_i$ fluctuations allows reliable measurement of $G$'s
459 > without the necessity of extremely cautious equilibration process.
460  
461 < It is also noted that the overall simulation temperature is another
462 < factor that affects the interfacial thermal conductance. One
463 < possibility of this effect may be rooted in the decrease in density of
464 < the liquid phase. We observed that when the average temperature
465 < increases from 200K to 250K, the bulk hexane density becomes lower
466 < than experimental value, as the system is equilibrated under NPT
467 < ensemble. This leads to lower contact between solvent and capping
468 < agent, and thus lower conductivity.
461 > As stated in our computational details, the spacing filled with
462 > solvent molecules can be chosen within a range. This allows some
463 > change of solvent molecule numbers for the same Au-butanethiol
464 > surfaces. We did this study on our Au-butanethiol/hexane
465 > simulations. Nevertheless, the results obtained from systems of
466 > different $N_{hexane}$ did not indicate that the measurement of $G$ is
467 > susceptible to this parameter. For computational efficiency concern,
468 > smaller system size would be preferable, given that the liquid phase
469 > structure is not affected.
470  
471 < Conductivity values are more difficult to obtain under higher
472 < temperatures. This is because the Au surface tends to undergo
473 < reconstructions in relatively high temperatures. Surface Au atoms can
474 < migrate outward to reach higher Au-S contact; and capping agent
475 < molecules can be embedded into the surface Au layer due to the same
476 < driving force. This phenomenon agrees with experimental
477 < results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. A surface
478 < fully covered in capping agent is more susceptible to reconstruction,
479 < possibly because fully coverage prevents other means of capping agent
480 < relaxation, such as migration to an empty neighbor three-fold site.
471 > Our NIVS algorithm allows change of unphysical thermal flux both in
472 > direction and in quantity. This feature extends our investigation of
473 > interfacial thermal conductance. However, the magnitude of this
474 > thermal flux is not arbitary if one aims to obtain a stable and
475 > reliable thermal gradient. A temperature profile would be
476 > substantially affected by noise when $|J_z|$ has a much too low
477 > magnitude; while an excessively large $|J_z|$ that overwhelms the
478 > conductance capacity of the interface would prevent a thermal gradient
479 > to reach a stablized steady state. NIVS has the advantage of allowing
480 > $J$ to vary in a wide range such that the optimal flux range for $G$
481 > measurement can generally be simulated by the algorithm. Within the
482 > optimal range, we were able to study how $G$ would change according to
483 > the thermal flux across the interface. For our simulations, we denote
484 > $J_z$ to be positive when the physical thermal flux is from the liquid
485 > to metal, and negative vice versa. The $G$'s measured under different
486 > $J_z$ is listed in Table \ref{AuThiolHexaneUA} and [REF]. These
487 > results do not suggest that $G$ is dependent on $J_z$ within this flux
488 > range. The linear response of flux to thermal gradient simplifies our
489 > investigations in that we can rely on $G$ measurement with only a
490 > couple $J_z$'s and do not need to test a large series of fluxes.
491  
492 < %MAY ADD MORE DATA TO TABLE
492 > %ADD MORE TO TABLE
493   \begin{table*}
494    \begin{minipage}{\linewidth}
495      \begin{center}
496        \caption{Computed interfacial thermal conductivity ($G$ and
497 <        $G^\prime$) values for the Au/butanethiol/hexane interface
498 <        with united-atom model and different capping agent coverage
499 <        and solvent molecule numbers at different temperatures using a
305 <        range of energy fluxes.}
497 >        $G^\prime$) values for the 100\% covered Au-butanethiol/hexane
498 >        interfaces with UA model and different hexane molecule numbers
499 >        at different temperatures using a range of energy fluxes.}
500        
501 <      \begin{tabular}{cccccc}
501 >      \begin{tabular}{ccccccc}
502          \hline\hline
503 <        Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\
504 <        coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) &
503 >        $\langle T\rangle$ & $N_{hexane}$ & Fixed & $\rho_{hexane}$ &
504 >        $J_z$ & $G$ & $G^\prime$ \\
505 >        (K) & & $L_x$ \& $L_y$? & (g/cm$^3$) & (GW/m$^2$) &
506          \multicolumn{2}{c}{(MW/m$^2$/K)} \\
507          \hline
508 <        0.0   & 200 & 200 & 0.96 & 43.3 & 42.7 \\
509 <              &     &     & 1.91 & 45.7 & 42.9 \\
510 <              &     & 166 & 0.96 & 43.1 & 53.4 \\
511 <        88.9  & 200 & 166 & 1.94 & 172  & 108  \\
512 <        100.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\
513 <              &     & 166 & 0.98 & 79.0 & 62.9 \\
514 <              &     &     & 1.44 & 76.2 & 64.8 \\
515 <              & 200 & 200 & 1.92 & 129  & 87.3 \\
516 <              &     &     & 1.93 & 131  & 77.5 \\
517 <              &     & 166 & 0.97 & 115  & 69.3 \\
518 <              &     &     & 1.94 & 125  & 87.1 \\
508 >        200 & 266 & No  & 0.672 & -0.96 & 102()  & 80.0() \\
509 >            & 200 & Yes & 0.694 &  1.92 & 129()  & 87.3() \\
510 >            &     & Yes & 0.672 &  1.93 & 131()  & 77.5() \\
511 >
512 >            & 166 & Yes & 0.679 &  0.97 & 115()  & 69.3() \\
513 >            &     & Yes & 0.679 &  1.94 & 125()  & 87.1() \\
514 >
515 >        250 & 200 & No  & 0.560 &  0.96 & 81.8() & 67.0() \\
516 >
517 >            & 166 & Yes & 0.570 &  0.98 & 79.0() & 62.9() \\
518 >
519 >            &     & No  & 0.569 &  1.44 & 76.2() & 64.8() \\
520 >
521          \hline\hline
522        \end{tabular}
523        \label{AuThiolHexaneUA}
# Line 328 | Line 525 | For the all-atom model, the liquid hexane phase was no
525    \end{minipage}
526   \end{table*}
527  
528 < For the all-atom model, the liquid hexane phase was not stable under NPT
529 < conditions. Therefore, the simulation length scale parameters are
530 < adopted from previous equilibration results of the united-atom model
531 < at 200K. Table \ref{AuThiolHexaneAA} shows the results of these
532 < simulations. The conductivity values calculated with full capping
533 < agent coverage are substantially larger than observed in the
534 < united-atom model, and is even higher than predicted by
535 < experiments. It is possible that our parameters for metal-non-metal
536 < particle interactions lead to an overestimate of the interfacial
537 < thermal conductivity, although the active C-H vibrations in the
538 < all-atom model (which should not be appreciably populated at normal
342 < temperatures) could also account for this high conductivity. The major
343 < thermal transfer barrier of Au/butanethiol/hexane interface is between
344 < the liquid phase and the capping agent, so extra degrees of freedom
345 < such as the C-H vibrations could enhance heat exchange between these
346 < two phases and result in a much higher conductivity.
528 > Furthermore, we also attempted to increase system average temperatures
529 > to above 200K. These simulations are first equilibrated in the NPT
530 > ensemble under normal pressure. As stated above, the TraPPE-UA model
531 > for hexane tends to predict a lower boiling point. In our simulations,
532 > hexane had diffculty to remain in liquid phase when NPT equilibration
533 > temperature is higher than 250K. Additionally, the equilibrated liquid
534 > hexane density under 250K becomes lower than experimental value. This
535 > expanded liquid phase leads to lower contact between hexane and
536 > butanethiol as well.[MAY NEED FIGURE] And this reduced contact would
537 > probably be accountable for a lower interfacial thermal conductance,
538 > as shown in Table \ref{AuThiolHexaneUA}.
539  
540 + A similar study for TraPPE-UA toluene agrees with the above result as
541 + well. Having a higher boiling point, toluene tends to remain liquid in
542 + our simulations even equilibrated under 300K in NPT
543 + ensembles. Furthermore, the expansion of the toluene liquid phase is
544 + not as significant as that of the hexane. This prevents severe
545 + decrease of liquid-capping agent contact and the results (Table
546 + \ref{AuThiolToluene}) show only a slightly decreased interface
547 + conductance. Therefore, solvent-capping agent contact should play an
548 + important role in the thermal transport process across the interface
549 + in that higher degree of contact could yield increased conductance.
550 +
551 + [ADD ERROR ESTIMATE TO TABLE]
552   \begin{table*}
553    \begin{minipage}{\linewidth}
554      \begin{center}
351 –      
555        \caption{Computed interfacial thermal conductivity ($G$ and
556 <        $G^\prime$) values for the Au/butanethiol/hexane interface
557 <        with all-atom model and different capping agent coverage at
558 <        200K using a range of energy fluxes.}
556 >        $G^\prime$) values for a 90\% coverage Au-butanethiol/toluene
557 >        interface at different temperatures using a range of energy
558 >        fluxes.}
559        
560 <      \begin{tabular}{cccc}
560 >      \begin{tabular}{ccccc}
561          \hline\hline
562 <        Thiol & $J_z$ & $G$ & $G^\prime$ \\
563 <        coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
562 >        $\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\
563 >        (K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
564          \hline
565 <        0.0   & 0.95 & 28.5 & 27.2 \\
566 <              & 1.88 & 30.3 & 28.9 \\
567 <        100.0 & 2.87 & 551  & 294  \\
568 <              & 3.81 & 494  & 193  \\
565 >        200 & 0.933 & -1.86 & 180() & 135() \\
566 >            &       &  2.15 & 204() & 113() \\
567 >            &       & -3.93 & 175() & 114() \\
568 >        \hline
569 >        300 & 0.855 & -1.91 & 143() & 125() \\
570 >            &       & -4.19 & 134() & 113() \\
571          \hline\hline
572        \end{tabular}
573 <      \label{AuThiolHexaneAA}
573 >      \label{AuThiolToluene}
574      \end{center}
575    \end{minipage}
576   \end{table*}
577  
578 < %subsubsection{Vibrational spectrum study on conductance mechanism}
578 > Besides lower interfacial thermal conductance, surfaces in relatively
579 > high temperatures are susceptible to reconstructions, when
580 > butanethiols have a full coverage on the Au(111) surface. These
581 > reconstructions include surface Au atoms migrated outward to the S
582 > atom layer, and butanethiol molecules embedded into the original
583 > surface Au layer. The driving force for this behavior is the strong
584 > Au-S interactions in our simulations. And these reconstructions lead
585 > to higher ratio of Au-S attraction and thus is energetically
586 > favorable. Furthermore, this phenomenon agrees with experimental
587 > results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt
588 > {\it et al.} had kept their Au(111) slab rigid so that their
589 > simulations can reach 300K without surface reconstructions. Without
590 > this practice, simulating 100\% thiol covered interfaces under higher
591 > temperatures could hardly avoid surface reconstructions. However, our
592 > measurement is based on assuming homogeneity on $x$ and $y$ dimensions
593 > so that measurement of $T$ at particular $z$ would be an effective
594 > average of the particles of the same type. Since surface
595 > reconstructions could eliminate the original $x$ and $y$ dimensional
596 > homogeneity, measurement of $G$ is more difficult to conduct under
597 > higher temperatures. Therefore, most of our measurements are
598 > undertaken at $\langle T\rangle\sim$200K.
599 >
600 > However, when the surface is not completely covered by butanethiols,
601 > the simulated system is more resistent to the reconstruction
602 > above. Our Au-butanethiol/toluene system did not see this phenomena
603 > even at $\langle T\rangle\sim$300K. The Au(111) surfaces have a 90\%
604 > coverage of butanethiols and have empty three-fold sites. These empty
605 > sites could help prevent surface reconstruction in that they provide
606 > other means of capping agent relaxation. It is observed that
607 > butanethiols can migrate to their neighbor empty sites during a
608 > simulation. Therefore, we were able to obtain $G$'s for these
609 > interfaces even at a relatively high temperature without being
610 > affected by surface reconstructions.
611 >
612 > \subsection{Influence of Capping Agent Coverage on $G$}
613 > To investigate the influence of butanethiol coverage on interfacial
614 > thermal conductance, a series of different coverage Au-butanethiol
615 > surfaces is prepared and solvated with various organic
616 > molecules. These systems are then equilibrated and their interfacial
617 > thermal conductivity are measured with our NIVS algorithm. Table
618 > \ref{tlnUhxnUhxnD} lists these results for direct comparison between
619 > different coverages of butanethiol. To study the isotope effect in
620 > interfacial thermal conductance, deuterated UA-hexane is included as
621 > well.
622 >
623 > It turned out that with partial covered butanethiol on the Au(111)
624 > surface, the derivative definition for $G$ (Eq. \ref{derivativeG}) has
625 > difficulty to apply, due to the difficulty in locating the maximum of
626 > change of $\lambda$. Instead, the discrete definition
627 > (Eq. \ref{discreteG}) is easier to apply, as max($\Delta T$) can still
628 > be well-defined. Therefore, $G$'s (not $G^\prime$) are used for this
629 > section.
630 >
631 > From Table \ref{tlnUhxnUhxnD}, one can see the significance of the
632 > presence of capping agents. Even when a fraction of the Au(111)
633 > surface sites are covered with butanethiols, the conductivity would
634 > see an enhancement by at least a factor of 3. This indicates the
635 > important role cappping agent is playing for thermal transport
636 > phenomena on metal/organic solvent surfaces.
637 >
638 > Interestingly, as one could observe from our results, the maximum
639 > conductance enhancement (largest $G$) happens while the surfaces are
640 > about 75\% covered with butanethiols. This again indicates that
641 > solvent-capping agent contact has an important role of the thermal
642 > transport process. Slightly lower butanethiol coverage allows small
643 > gaps between butanethiols to form. And these gaps could be filled with
644 > solvent molecules, which acts like ``heat conductors'' on the
645 > surface. The higher degree of interaction between these solvent
646 > molecules and capping agents increases the enhancement effect and thus
647 > produces a higher $G$ than densely packed butanethiol arrays. However,
648 > once this maximum conductance enhancement is reached, $G$ decreases
649 > when butanethiol coverage continues to decrease. Each capping agent
650 > molecule reaches its maximum capacity for thermal
651 > conductance. Therefore, even higher solvent-capping agent contact
652 > would not offset this effect. Eventually, when butanethiol coverage
653 > continues to decrease, solvent-capping agent contact actually
654 > decreases with the disappearing of butanethiol molecules. In this
655 > case, $G$ decrease could not be offset but instead accelerated.
656 >
657 > A comparison of the results obtained from differenet organic solvents
658 > can also provide useful information of the interfacial thermal
659 > transport process. The deuterated hexane (UA) results do not appear to
660 > be much different from those of normal hexane (UA), given that
661 > butanethiol (UA) is non-deuterated for both solvents. These UA model
662 > studies, even though eliminating C-H vibration samplings, still have
663 > C-C vibrational frequencies different from each other. However, these
664 > differences in the infrared range do not seem to produce an observable
665 > difference for the results of $G$. [MAY NEED FIGURE]
666 >
667 > Furthermore, results for rigid body toluene solvent, as well as other
668 > UA-hexane solvents, are reasonable within the general experimental
669 > ranges[CITATIONS]. This suggests that explicit hydrogen might not be a
670 > required factor for modeling thermal transport phenomena of systems
671 > such as Au-thiol/organic solvent.
672 >
673 > However, results for Au-butanethiol/toluene do not show an identical
674 > trend with those for Au-butanethiol/hexane in that $G$'s remain at
675 > approximately the same magnitue when butanethiol coverage differs from
676 > 25\% to 75\%. This might be rooted in the molecule shape difference
677 > for plane-like toluene and chain-like {\it n}-hexane. Due to this
678 > difference, toluene molecules have more difficulty in occupying
679 > relatively small gaps among capping agents when their coverage is not
680 > too low. Therefore, the solvent-capping agent contact may keep
681 > increasing until the capping agent coverage reaches a relatively low
682 > level. This becomes an offset for decreasing butanethiol molecules on
683 > its effect to the process of interfacial thermal transport. Thus, one
684 > can see a plateau of $G$ vs. butanethiol coverage in our results.
685 >
686 > [NEED ERROR ESTIMATE, CONVERT TO FIGURE]
687 > \begin{table*}
688 >  \begin{minipage}{\linewidth}
689 >    \begin{center}
690 >      \caption{Computed interfacial thermal conductivity ($G$) values
691 >        for the Au-butanethiol/solvent interface with various UA
692 >        models and different capping agent coverages at $\langle
693 >        T\rangle\sim$200K using certain energy flux respectively.}
694 >      
695 >      \begin{tabular}{cccc}
696 >        \hline\hline
697 >        Thiol & \multicolumn{3}{c}{$G$(MW/m$^2$/K)} \\
698 >        coverage (\%) & hexane & hexane(D) & toluene \\
699 >        \hline
700 >        0.0   & 46.5() & 43.9() & 70.1() \\
701 >        25.0  & 151()  & 153()  & 249()  \\
702 >        50.0  & 172()  & 182()  & 214()  \\
703 >        75.0  & 242()  & 229()  & 244()  \\
704 >        88.9  & 178()  & -      & -      \\
705 >        100.0 & 137()  & 153()  & 187()  \\
706 >        \hline\hline
707 >      \end{tabular}
708 >      \label{tlnUhxnUhxnD}
709 >    \end{center}
710 >  \end{minipage}
711 > \end{table*}
712 >
713 > \subsection{Influence of Chosen Molecule Model on $G$}
714 > [MAY COMBINE W MECHANISM STUDY]
715 >
716 > In addition to UA solvent/capping agent models, AA models are included
717 > in our simulations as well. Besides simulations of the same (UA or AA)
718 > model for solvent and capping agent, different models can be applied
719 > to different components. Furthermore, regardless of models chosen,
720 > either the solvent or the capping agent can be deuterated, similar to
721 > the previous section. Table \ref{modelTest} summarizes the results of
722 > these studies.
723 >
724 > [MORE DATA; ERROR ESTIMATE]
725 > \begin{table*}
726 >  \begin{minipage}{\linewidth}
727 >    \begin{center}
728 >      
729 >      \caption{Computed interfacial thermal conductivity ($G$ and
730 >        $G^\prime$) values for interfaces using various models for
731 >        solvent and capping agent (or without capping agent) at
732 >        $\langle T\rangle\sim$200K.}
733 >      
734 >      \begin{tabular}{ccccc}
735 >        \hline\hline
736 >        Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\
737 >        (or bare surface) & model & (GW/m$^2$) &
738 >        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
739 >        \hline
740 >        UA    & AA hexane  & 1.94 & 135()  & 129()  \\
741 >              &            & 2.86 & 126()  & 115()  \\
742 >              & AA toluene & 1.89 & 200()  & 149()  \\
743 >        AA    & UA hexane  & 1.94 & 116()  & 129()  \\
744 >              & AA hexane  & 3.76 & 451()  & 378()  \\
745 >              &            & 4.71 & 432()  & 334()  \\
746 >              & AA toluene & 3.79 & 487()  & 290()  \\
747 >        AA(D) & UA hexane  & 1.94 & 158()  & 172()  \\
748 >        bare  & AA hexane  & 0.96 & 31.0() & 29.4() \\
749 >        \hline\hline
750 >      \end{tabular}
751 >      \label{modelTest}
752 >    \end{center}
753 >  \end{minipage}
754 > \end{table*}
755 >
756 > To facilitate direct comparison, the same system with differnt models
757 > for different components uses the same length scale for their
758 > simulation cells. Without the presence of capping agent, using
759 > different models for hexane yields similar results for both $G$ and
760 > $G^\prime$, and these two definitions agree with eath other very
761 > well. This indicates very weak interaction between the metal and the
762 > solvent, and is a typical case for acoustic impedance mismatch between
763 > these two phases.
764 >
765 > As for Au(111) surfaces completely covered by butanethiols, the choice
766 > of models for capping agent and solvent could impact the measurement
767 > of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane
768 > interfaces, using AA model for both butanethiol and hexane yields
769 > substantially higher conductivity values than using UA model for at
770 > least one component of the solvent and capping agent, which exceeds
771 > the upper bond of experimental value range. This is probably due to
772 > the classically treated C-H vibrations in the AA model, which should
773 > not be appreciably populated at normal temperatures. In comparison,
774 > once either the hexanes or the butanethiols are deuterated, one can
775 > see a significantly lower $G$ and $G^\prime$. In either of these
776 > cases, the C-H(D) vibrational overlap between the solvent and the
777 > capping agent is removed. [MAY NEED FIGURE] Conclusively, the
778 > improperly treated C-H vibration in the AA model produced
779 > over-predicted results accordingly. Compared to the AA model, the UA
780 > model yields more reasonable results with higher computational
781 > efficiency.
782 >
783 > However, for Au-butanethiol/toluene interfaces, having the AA
784 > butanethiol deuterated did not yield a significant change in the
785 > measurement results.
786 > . , so extra degrees of freedom
787 > such as the C-H vibrations could enhance heat exchange between these
788 > two phases and result in a much higher conductivity.
789 >
790 >
791 > Although the QSC model for Au is known to predict an overly low value
792 > for bulk metal gold conductivity\cite{kuang:164101}, our computational
793 > results for $G$ and $G^\prime$ do not seem to be affected by this
794 > drawback of the model for metal. Instead, the modeling of interfacial
795 > thermal transport behavior relies mainly on an accurate description of
796 > the interactions between components occupying the interfaces.
797 >
798 > \subsection{Mechanism of Interfacial Thermal Conductance Enhancement
799 >  by Capping Agent}
800 > %OR\subsection{Vibrational spectrum study on conductance mechanism}
801 >
802 > [MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S]
803 >
804   To investigate the mechanism of this interfacial thermal conductance,
805   the vibrational spectra of various gold systems were obtained and are
806   shown as in the upper panel of Fig. \ref{vibration}. To obtain these
807   spectra, one first runs a simulation in the NVE ensemble and collects
808   snapshots of configurations; these configurations are used to compute
809   the velocity auto-correlation functions, which is used to construct a
810 < power spectrum via a Fourier transform. The gold surfaces covered by
381 < butanethiol molecules exhibit an additional peak observed at a
382 < frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration
383 < of the S-Au bond. This vibration enables efficient thermal transport
384 < from surface Au atoms to the capping agents. Simultaneously, as shown
385 < in the lower panel of Fig. \ref{vibration}, the large overlap of the
386 < vibration spectra of butanethiol and hexane in the all-atom model,
387 < including the C-H vibration, also suggests high thermal exchange
388 < efficiency. The combination of these two effects produces the drastic
389 < interfacial thermal conductance enhancement in the all-atom model.
810 > power spectrum via a Fourier transform.
811  
812 + The gold surfaces covered by
813 + butanethiol molecules, compared to bare gold surfaces, exhibit an
814 + additional peak observed at a frequency of $\sim$170cm$^{-1}$, which
815 + is attributed to the vibration of the S-Au bond. This vibration
816 + enables efficient thermal transport from surface Au atoms to the
817 + capping agents. Simultaneously, as shown in the lower panel of
818 + Fig. \ref{vibration}, the large overlap of the vibration spectra of
819 + butanethiol and hexane in the all-atom model, including the C-H
820 + vibration, also suggests high thermal exchange efficiency. The
821 + combination of these two effects produces the drastic interfacial
822 + thermal conductance enhancement in the all-atom model.
823 +
824 + [MAY NEED TO CONVERT TO JPEG]
825   \begin{figure}
826   \includegraphics[width=\linewidth]{vibration}
827   \caption{Vibrational spectra obtained for gold in different
# Line 395 | Line 829 | interfacial thermal conductance enhancement in the all
829    all-atom model (lower panel).}
830   \label{vibration}
831   \end{figure}
398 – % 600dpi, letter size. too large?
832  
833 + [COMPARISON OF TWO G'S; AU SLAB WIDTHS; ETC]
834 + % The results show that the two definitions used for $G$ yield
835 + % comparable values, though $G^\prime$ tends to be smaller.
836  
837 + \section{Conclusions}
838 + The NIVS algorithm we developed has been applied to simulations of
839 + Au-butanethiol surfaces with organic solvents. This algorithm allows
840 + effective unphysical thermal flux transferred between the metal and
841 + the liquid phase. With the flux applied, we were able to measure the
842 + corresponding thermal gradient and to obtain interfacial thermal
843 + conductivities. Our simulations have seen significant conductance
844 + enhancement with the presence of capping agent, compared to the bare
845 + gold/liquid interfaces. The acoustic impedance mismatch between the
846 + metal and the liquid phase is effectively eliminated by proper capping
847 + agent. Furthermore, the coverage precentage of the capping agent plays
848 + an important role in the interfacial thermal transport process.
849 +
850 + Our measurement results, particularly of the UA models, agree with
851 + available experimental data. This indicates that our force field
852 + parameters have a nice description of the interactions between the
853 + particles at the interfaces. AA models tend to overestimate the
854 + interfacial thermal conductance in that the classically treated C-H
855 + vibration would be overly sampled. Compared to the AA models, the UA
856 + models have higher computational efficiency with satisfactory
857 + accuracy, and thus are preferable in interfacial thermal transport
858 + modelings.
859 +
860 + Vlugt {\it et al.} has investigated the surface thiol structures for
861 + nanocrystal gold and pointed out that they differs from those of the
862 + Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to
863 + change of interfacial thermal transport behavior as well. To
864 + investigate this problem, an effective means to introduce thermal flux
865 + and measure the corresponding thermal gradient is desirable for
866 + simulating structures with spherical symmetry.
867 +
868 +
869   \section{Acknowledgments}
870   Support for this project was provided by the National Science
871   Foundation under grant CHE-0848243. Computational time was provided by
872   the Center for Research Computing (CRC) at the University of Notre
873 < Dame.  \newpage
873 > Dame. \newpage
874  
875   \bibliography{interfacial}
876  

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