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# Line 45 | Line 45 | We have developed a Non-Isotropic Velocity Scaling alg
45  
46   \begin{abstract}
47  
48 < We have developed a Non-Isotropic Velocity Scaling algorithm for
49 < setting up and maintaining stable thermal gradients in non-equilibrium
50 < molecular dynamics simulations. This approach effectively imposes
51 < unphysical thermal flux even between particles of different
52 < identities, conserves linear momentum and kinetic energy, and
53 < minimally perturbs the velocity profile of a system when compared with
54 < previous RNEMD methods. We have used this method to simulate thermal
55 < conductance at metal / organic solvent interfaces both with and
56 < without the presence of thiol-based capping agents.  We obtained
57 < values comparable with experimental values, and observed significant
58 < conductance enhancement with the presence of capping agents. Computed
59 < power spectra indicate the acoustic impedance mismatch between metal
60 < and liquid phase is greatly reduced by the capping agents and thus
61 < leads to higher interfacial thermal transfer efficiency.
48 > With the Non-Isotropic Velocity Scaling algorithm (NIVS) we have
49 > developed, an unphysical thermal flux can be effectively set up even
50 > for non-homogeneous systems like interfaces in non-equilibrium
51 > molecular dynamics simulations. In this work, this algorithm is
52 > applied for simulating thermal conductance at metal / organic solvent
53 > interfaces with various coverages of butanethiol capping
54 > agents. Different solvents and force field models were tested. Our
55 > results suggest that the United-Atom models are able to provide an
56 > estimate of the interfacial thermal conductivity comparable to
57 > experiments in our simulations with satisfactory computational
58 > efficiency. From our results, the acoustic impedance mismatch between
59 > metal and liquid phase is effectively reduced by the capping
60 > agents, and thus leads to interfacial thermal conductance
61 > enhancement. Furthermore, this effect is closely related to the
62 > capping agent coverage on the metal surfaces and the type of solvent
63 > molecules, and is affected by the models used in the simulations.
64  
65   \end{abstract}
66  
# Line 71 | Line 73 | leads to higher interfacial thermal transfer efficienc
73   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
74  
75   \section{Introduction}
74 – [BACKGROUND FOR INTERFACIAL THERMAL CONDUCTANCE PROBLEM]
76   Interfacial thermal conductance is extensively studied both
77 < experimentally and computationally, and systems with interfaces
78 < present are generally heterogeneous. Although interfaces are commonly
79 < barriers to heat transfer, it has been
80 < reported\cite{doi:10.1021/la904855s} that under specific circustances,
81 < e.g. with certain capping agents present on the surface, interfacial
82 < conductance can be significantly enhanced. However, heat conductance
83 < of molecular and nano-scale interfaces will be affected by the
84 < chemical details of the surface and is challenging to
85 < experimentalist. The lower thermal flux through interfaces is even
85 < more difficult to measure with EMD and forward NEMD simulation
86 < methods. Therefore, developing good simulation methods will be
87 < desirable in order to investigate thermal transport across interfaces.
77 > experimentally and computationally\cite{cahill:793}, due to its
78 > importance in nanoscale science and technology. Reliability of
79 > nanoscale devices depends on their thermal transport
80 > properties. Unlike bulk homogeneous materials, nanoscale materials
81 > features significant presence of interfaces, and these interfaces
82 > could dominate the heat transfer behavior of these
83 > materials. Furthermore, these materials are generally heterogeneous,
84 > which challenges traditional research methods for homogeneous
85 > systems.
86  
87 + Heat conductance of molecular and nano-scale interfaces will be
88 + affected by the chemical details of the surface. Experimentally,
89 + various interfaces have been investigated for their thermal
90 + conductance properties. Wang {\it et al.} studied heat transport
91 + through long-chain hydrocarbon monolayers on gold substrate at
92 + individual molecular level\cite{Wang10082007}; Schmidt {\it et al.}
93 + studied the role of CTAB on thermal transport between gold nanorods
94 + and solvent\cite{doi:10.1021/jp8051888}; Juv\'e {\it et al.} studied
95 + the cooling dynamics, which is controlled by thermal interface
96 + resistence of glass-embedded metal
97 + nanoparticles\cite{PhysRevB.80.195406}. Although interfaces are
98 + commonly barriers for heat transport, Alper {\it et al.} suggested
99 + that specific ligands (capping agents) could completely eliminate this
100 + barrier ($G\rightarrow\infty$)\cite{doi:10.1021/la904855s}.
101 +
102 + Theoretical and computational models have also been used to study the
103 + interfacial thermal transport in order to gain an understanding of
104 + this phenomena at the molecular level. Recently, Hase and coworkers
105 + employed Non-Equilibrium Molecular Dynamics (NEMD) simulations to
106 + study thermal transport from hot Au(111) substrate to a self-assembled
107 + monolayer of alkylthiol with relatively long chain (8-20 carbon
108 + atoms)\cite{hase:2010,hase:2011}. However, ensemble averaged
109 + measurements for heat conductance of interfaces between the capping
110 + monolayer on Au and a solvent phase has yet to be studied.
111 + The comparatively low thermal flux through interfaces is
112 + difficult to measure with Equilibrium MD or forward NEMD simulation
113 + methods. Therefore, the Reverse NEMD (RNEMD) methods would have the
114 + advantage of having this difficult to measure flux known when studying
115 + the thermal transport across interfaces, given that the simulation
116 + methods being able to effectively apply an unphysical flux in
117 + non-homogeneous systems.
118 +
119   Recently, we have developed the Non-Isotropic Velocity Scaling (NIVS)
120   algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm
121   retains the desirable features of RNEMD (conservation of linear
122   momentum and total energy, compatibility with periodic boundary
123   conditions) while establishing true thermal distributions in each of
124 < the two slabs. Furthermore, it allows more effective thermal exchange
125 < between particles of different identities, and thus enables extensive
126 < study of interfacial conductance.
124 > the two slabs. Furthermore, it allows effective thermal exchange
125 > between particles of different identities, and thus makes the study of
126 > interfacial conductance much simpler.
127  
128 + The work presented here deals with the Au(111) surface covered to
129 + varying degrees by butanethiol, a capping agent with short carbon
130 + chain, and solvated with organic solvents of different molecular
131 + properties. Different models were used for both the capping agent and
132 + the solvent force field parameters. Using the NIVS algorithm, the
133 + thermal transport across these interfaces was studied and the
134 + underlying mechanism for this phenomena was investigated.
135 +
136 + [MAY ADD WHY STUDY AU-THIOL SURFACE; CITE SHAOYI JIANG]
137 +
138   \section{Methodology}
139 < \subsection{Algorithm}
140 < [BACKGROUND FOR MD METHODS]
141 < There have been many algorithms for computing thermal conductivity
142 < using molecular dynamics simulations. However, interfacial conductance
143 < is at least an order of magnitude smaller. This would make the
144 < calculation even more difficult for those slowly-converging
145 < equilibrium methods. Imposed-flux non-equilibrium
139 > \subsection{Imposd-Flux Methods in MD Simulations}
140 > For systems with low interfacial conductivity one must have a method
141 > capable of generating relatively small fluxes, compared to those
142 > required for bulk conductivity. This requirement makes the calculation
143 > even more difficult for those slowly-converging equilibrium
144 > methods\cite{Viscardy:2007lq}.
145 > Forward methods impose gradient, but in interfacail conditions it is
146 > not clear what behavior to impose at the boundary...
147 > Imposed-flux reverse non-equilibrium
148   methods\cite{MullerPlathe:1997xw} have the flux set {\it a priori} and
149 < the response of temperature or momentum gradients are easier to
150 < measure than the flux, if unknown, and thus, is a preferable way to
151 < the forward NEMD methods. Although the momentum swapping approach for
152 < flux-imposing can be used for exchanging energy between particles of
153 < different identity, the kinetic energy transfer efficiency is affected
154 < by the mass difference between the particles, which limits its
113 < application on heterogeneous interfacial systems.
149 > the thermal response becomes easier to
150 > measure than the flux. Although M\"{u}ller-Plathe's original momentum
151 > swapping approach can be used for exchanging energy between particles
152 > of different identity, the kinetic energy transfer efficiency is
153 > affected by the mass difference between the particles, which limits
154 > its application on heterogeneous interfacial systems.
155  
156 < The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach in
157 < non-equilibrium MD simulations is able to impose relatively large
158 < kinetic energy flux without obvious perturbation to the velocity
159 < distribution of the simulated systems. Furthermore, this approach has
156 > The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach to
157 > non-equilibrium MD simulations is able to impose a wide range of
158 > kinetic energy fluxes without obvious perturbation to the velocity
159 > distributions of the simulated systems. Furthermore, this approach has
160   the advantage in heterogeneous interfaces in that kinetic energy flux
161   can be applied between regions of particles of arbitary identity, and
162 < the flux quantity is not restricted by particle mass difference.
162 > the flux will not be restricted by difference in particle mass.
163  
164   The NIVS algorithm scales the velocity vectors in two separate regions
165   of a simulation system with respective diagonal scaling matricies. To
166   determine these scaling factors in the matricies, a set of equations
167   including linear momentum conservation and kinetic energy conservation
168 < constraints and target momentum/energy flux satisfaction is
169 < solved. With the scaling operation applied to the system in a set
170 < frequency, corresponding momentum/temperature gradients can be built,
171 < which can be used for computing transportation properties and other
172 < applications related to momentum/temperature gradients. The NIVS
132 < algorithm conserves momenta and energy and does not depend on an
133 < external thermostat.
168 > constraints and target energy flux satisfaction is solved. With the
169 > scaling operation applied to the system in a set frequency, bulk
170 > temperature gradients can be easily established, and these can be used
171 > for computing thermal conductivities. The NIVS algorithm conserves
172 > momenta and energy and does not depend on an external thermostat.
173  
174   \subsection{Defining Interfacial Thermal Conductivity $G$}
175   For interfaces with a relatively low interfacial conductance, the bulk
# Line 148 | Line 187 | When the interfacial conductance is {\it not} small, t
187    T_\mathrm{cold}\rangle}$ are the average observed temperature of the
188   two separated phases.
189  
190 < When the interfacial conductance is {\it not} small, two ways can be
191 < used to define $G$.
190 > When the interfacial conductance is {\it not} small, there are two
191 > ways to define $G$.
192  
193 < One way is to assume the temperature is discretely different on two
194 < sides of the interface, $G$ can be calculated with the thermal flux
195 < applied $J$ and the maximum temperature difference measured along the
196 < thermal gradient max($\Delta T$), which occurs at the interface, as:
193 > One way is to assume the temperature is discrete on the two sides of
194 > the interface. $G$ can be calculated using the applied thermal flux
195 > $J$ and the maximum temperature difference measured along the thermal
196 > gradient max($\Delta T$), which occurs at the Gibbs deviding surface,
197 > as:
198   \begin{equation}
199   G=\frac{J}{\Delta T}
200   \label{discreteG}
# Line 175 | Line 215 | difference method and thus calculate $G^\prime$.
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 < [IMPOSE G DEFINITION INTO OUR SYSTEMS]
224 < To facilitate the use of the above definitions in calculating $G$ and
225 < $G^\prime$, we have a metal slab with its (111) surfaces perpendicular
226 < to the $z$-axis of our simulation cells. With or withour capping
227 < agents on the surfaces, the metal slab is solvated with organic
187 < solvents, as illustrated in Figure \ref{demoPic}.
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   \begin{figure}
230   \includegraphics[width=\linewidth]{demoPic}
# Line 193 | Line 233 | With a simulation cell setup following the above manne
233   \label{demoPic}
234   \end{figure}
235  
236 < With a simulation cell setup following the above manner, one is able
237 < to equilibrate the system and impose an unphysical thermal flux
238 < between the liquid and the metal phase with the NIVS algorithm. Under
239 < a stablized thermal gradient induced by periodically applying the
240 < unphysical flux, one is able to obtain a temperature profile and the
241 < physical thermal flux corresponding to it, which equals to the
242 < unphysical flux applied by NIVS. These data enables the evaluation of
243 < 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.
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}
# Line 212 | Line 250 | obtain the 1st and 2nd derivatives of the temperature
250   \end{figure}
251  
252   \section{Computational Details}
253 < \subsection{System Geometry}
254 < In our simulations, Au is used to construct a metal slab with bare
255 < (111) surface perpendicular to the $z$-axis. Different slab thickness
256 < (layer numbers of Au) are simulated. This metal slab is first
257 < equilibrated under normal pressure (1 atm) and a desired
258 < temperature. After equilibration, butanethiol is used as the capping
259 < agent molecule to cover the bare Au (111) surfaces evenly. The sulfur
260 < atoms in the butanethiol molecules would occupy the three-fold sites
261 < of the surfaces, and the maximal butanethiol capacity on Au surface is
262 < $1/3$ of the total number of surface Au atoms[CITATION]. A series of
263 < different coverage surfaces is investigated in order to study the
264 < relation between coverage and conductance.
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 < [COVERAGE DISCRIPTION] However, since the interactions between surface
267 < Au and butanethiol is non-bonded, the capping agent molecules are
268 < allowed to migrate to an empty neighbor three-fold site during a
269 < simulation. Therefore, the initial configuration would not severely
270 < affect the sampling of a variety of configurations of the same
271 < coverage, and the final conductance measurement would be an average
272 < effect of these configurations explored in the simulations. [MAY NEED FIGURES]
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 are equilibrated
275 < under canonical ensemble, Packmol\cite{packmol} is used to pack
276 < organic solvent molecules in the previously vacuum part of the
277 < simulation cells, which guarantees that short range repulsive
278 < interactions do not disrupt the simulations. Two solvents are
279 < investigated, one which has little vibrational overlap with the
242 < 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.
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
# Line 282 | Line 323 | quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.5
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
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
# Line 294 | Line 345 | efficient, while maintains good accuracy. [LOW BOILING
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. [LOW BOILING POINT IS A
349 < KNOWN PROBLEM FOR TRAPPE-UA ALKANES, NEED MORE DISCUSSION]
350 < for
351 < toluene,  force fields are
352 < used with rigid body constraints applied.[MORE DETAILS NEEDED]
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 are included in our studies as
360 < well. For hexane, the OPLS all-atom\cite{OPLSAA} force field is
361 < used. [MORE DETAILS]
362 < For toluene,
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 < Buatnethiol molecules are used as capping agent for some of our
366 < simulations. United-Atom\cite{TraPPE-UA.thiols} and All-Atom models
367 < are respectively used corresponding to the force field type of
368 < solvent.
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, we refer to Vlugt\cite{vlugt:cpc2007154} and derive
386 < other interactions which are not parametrized in their work. (can add
387 < hautman and klein's paper here and more discussion; need to put
388 < aromatic-metal interaction approximation here)
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 < [TABULATED FORCE FIELD PARAMETERS NEEDED]
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 < \section{Results}
401 < \subsection{Toluene Solvent}
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  
324 – The results (Table \ref{AuThiolToluene}) show a
325 – significant conductance enhancement compared to the gold/water
326 – interface without capping agent and agree with available experimental
327 – data. This indicates that the metal-metal potential, though not
328 – predicting an accurate bulk metal thermal conductivity, does not
329 – 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.
336 –
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  
361 – \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
373 < 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.
384 < % [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
414 <        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 >            &     & No  & 0.688 &  0.96 & 125()  & 90.2() \\
512 >            &     &     &       &  1.91 & 139()  & 101()  \\
513 >            &     &     &       &  2.83 & 141()  & 89.9() \\
514 >            & 166 & Yes & 0.679 &  0.97 & 115()  & 69.3() \\
515 >            &     &     &       &  1.94 & 125()  & 87.1() \\
516 >            &     & No  & 0.681 &  0.97 & 141()  & 77.7() \\
517 >            &     &     &       &  1.92 & 138()  & 98.9() \\
518 >        \hline
519 >        250 & 200 & No  & 0.560 &  0.96 & 74.8() & 61.8() \\
520 >            &     &     &       & -0.95 & 49.4() & 45.7() \\
521 >            & 166 & Yes & 0.570 &  0.98 & 79.0() & 62.9() \\
522 >            &     & No  & 0.569 &  0.97 & 80.3() & 67.1() \\
523 >            &     &     &       &  1.44 & 76.2() & 64.8() \\
524 >            &     &     &       & -0.95 & 56.4() & 54.4() \\
525 >            &     &     &       & -1.85 & 47.8() & 53.5() \\
526          \hline\hline
527        \end{tabular}
528        \label{AuThiolHexaneUA}
# Line 437 | Line 530 | For the all-atom model, the liquid hexane phase was no
530    \end{minipage}
531   \end{table*}
532  
533 < For the all-atom model, the liquid hexane phase was not stable under NPT
534 < conditions. Therefore, the simulation length scale parameters are
535 < adopted from previous equilibration results of the united-atom model
536 < at 200K. Table \ref{AuThiolHexaneAA} shows the results of these
537 < simulations. The conductivity values calculated with full capping
538 < agent coverage are substantially larger than observed in the
539 < united-atom model, and is even higher than predicted by
540 < experiments. It is possible that our parameters for metal-non-metal
541 < particle interactions lead to an overestimate of the interfacial
542 < thermal conductivity, although the active C-H vibrations in the
543 < all-atom model (which should not be appreciably populated at normal
451 < 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.
533 > Furthermore, we also attempted to increase system average temperatures
534 > to above 200K. These simulations are first equilibrated in the NPT
535 > ensemble under normal pressure. As stated above, the TraPPE-UA model
536 > for hexane tends to predict a lower boiling point. In our simulations,
537 > hexane had diffculty to remain in liquid phase when NPT equilibration
538 > temperature is higher than 250K. Additionally, the equilibrated liquid
539 > hexane density under 250K becomes lower than experimental value. This
540 > expanded liquid phase leads to lower contact between hexane and
541 > butanethiol as well.[MAY NEED FIGURE] And this reduced contact would
542 > probably be accountable for a lower interfacial thermal conductance,
543 > as shown in Table \ref{AuThiolHexaneUA}.
544  
545 + A similar study for TraPPE-UA toluene agrees with the above result as
546 + well. Having a higher boiling point, toluene tends to remain liquid in
547 + our simulations even equilibrated under 300K in NPT
548 + ensembles. Furthermore, the expansion of the toluene liquid phase is
549 + not as significant as that of the hexane. This prevents severe
550 + decrease of liquid-capping agent contact and the results (Table
551 + \ref{AuThiolToluene}) show only a slightly decreased interface
552 + conductance. Therefore, solvent-capping agent contact should play an
553 + important role in the thermal transport process across the interface
554 + in that higher degree of contact could yield increased conductance.
555 +
556 + [ADD ERROR ESTIMATE TO TABLE]
557   \begin{table*}
558    \begin{minipage}{\linewidth}
559      \begin{center}
460 –      
560        \caption{Computed interfacial thermal conductivity ($G$ and
561 <        $G^\prime$) values for the Au/butanethiol/hexane interface
562 <        with all-atom model and different capping agent coverage at
563 <        200K using a range of energy fluxes.}
561 >        $G^\prime$) values for a 90\% coverage Au-butanethiol/toluene
562 >        interface at different temperatures using a range of energy
563 >        fluxes.}
564        
565 <      \begin{tabular}{cccc}
565 >      \begin{tabular}{ccccc}
566          \hline\hline
567 <        Thiol & $J_z$ & $G$ & $G^\prime$ \\
568 <        coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
567 >        $\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\
568 >        (K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
569          \hline
570 <        0.0   & 0.95 & 28.5 & 27.2 \\
571 <              & 1.88 & 30.3 & 28.9 \\
572 <        100.0 & 2.87 & 551  & 294  \\
573 <              & 3.81 & 494  & 193  \\
570 >        200 & 0.933 & -1.86 & 180() & 135() \\
571 >            &       &  2.15 & 204() & 113() \\
572 >            &       & -3.93 & 175() & 114() \\
573 >        \hline
574 >        300 & 0.855 & -1.91 & 143() & 125() \\
575 >            &       & -4.19 & 134() & 113() \\
576          \hline\hline
577        \end{tabular}
578 <      \label{AuThiolHexaneAA}
578 >      \label{AuThiolToluene}
579      \end{center}
580    \end{minipage}
581   \end{table*}
582  
583 < %subsubsection{Vibrational spectrum study on conductance mechanism}
583 > Besides lower interfacial thermal conductance, surfaces in relatively
584 > high temperatures are susceptible to reconstructions, when
585 > butanethiols have a full coverage on the Au(111) surface. These
586 > reconstructions include surface Au atoms migrated outward to the S
587 > atom layer, and butanethiol molecules embedded into the original
588 > surface Au layer. The driving force for this behavior is the strong
589 > Au-S interactions in our simulations. And these reconstructions lead
590 > to higher ratio of Au-S attraction and thus is energetically
591 > favorable. Furthermore, this phenomenon agrees with experimental
592 > results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt
593 > {\it et al.} had kept their Au(111) slab rigid so that their
594 > simulations can reach 300K without surface reconstructions. Without
595 > this practice, simulating 100\% thiol covered interfaces under higher
596 > temperatures could hardly avoid surface reconstructions. However, our
597 > measurement is based on assuming homogeneity on $x$ and $y$ dimensions
598 > so that measurement of $T$ at particular $z$ would be an effective
599 > average of the particles of the same type. Since surface
600 > reconstructions could eliminate the original $x$ and $y$ dimensional
601 > homogeneity, measurement of $G$ is more difficult to conduct under
602 > higher temperatures. Therefore, most of our measurements are
603 > undertaken at $\langle T\rangle\sim$200K.
604 >
605 > However, when the surface is not completely covered by butanethiols,
606 > the simulated system is more resistent to the reconstruction
607 > above. Our Au-butanethiol/toluene system did not see this phenomena
608 > even at $\langle T\rangle\sim$300K. The Au(111) surfaces have a 90\%
609 > coverage of butanethiols and have empty three-fold sites. These empty
610 > sites could help prevent surface reconstruction in that they provide
611 > other means of capping agent relaxation. It is observed that
612 > butanethiols can migrate to their neighbor empty sites during a
613 > simulation. Therefore, we were able to obtain $G$'s for these
614 > interfaces even at a relatively high temperature without being
615 > affected by surface reconstructions.
616 >
617 > \subsection{Influence of Capping Agent Coverage on $G$}
618 > To investigate the influence of butanethiol coverage on interfacial
619 > thermal conductance, a series of different coverage Au-butanethiol
620 > surfaces is prepared and solvated with various organic
621 > molecules. These systems are then equilibrated and their interfacial
622 > thermal conductivity are measured with our NIVS algorithm. Table
623 > \ref{tlnUhxnUhxnD} lists these results for direct comparison between
624 > different coverages of butanethiol. To study the isotope effect in
625 > interfacial thermal conductance, deuterated UA-hexane is included as
626 > well.
627 >
628 > It turned out that with partial covered butanethiol on the Au(111)
629 > surface, the derivative definition for $G$ (Eq. \ref{derivativeG}) has
630 > difficulty to apply, due to the difficulty in locating the maximum of
631 > change of $\lambda$. Instead, the discrete definition
632 > (Eq. \ref{discreteG}) is easier to apply, as max($\Delta T$) can still
633 > be well-defined. Therefore, $G$'s (not $G^\prime$) are used for this
634 > section.
635 >
636 > From Table \ref{tlnUhxnUhxnD}, one can see the significance of the
637 > presence of capping agents. Even when a fraction of the Au(111)
638 > surface sites are covered with butanethiols, the conductivity would
639 > see an enhancement by at least a factor of 3. This indicates the
640 > important role cappping agent is playing for thermal transport
641 > phenomena on metal/organic solvent surfaces.
642 >
643 > Interestingly, as one could observe from our results, the maximum
644 > conductance enhancement (largest $G$) happens while the surfaces are
645 > about 75\% covered with butanethiols. This again indicates that
646 > solvent-capping agent contact has an important role of the thermal
647 > transport process. Slightly lower butanethiol coverage allows small
648 > gaps between butanethiols to form. And these gaps could be filled with
649 > solvent molecules, which acts like ``heat conductors'' on the
650 > surface. The higher degree of interaction between these solvent
651 > molecules and capping agents increases the enhancement effect and thus
652 > produces a higher $G$ than densely packed butanethiol arrays. However,
653 > once this maximum conductance enhancement is reached, $G$ decreases
654 > when butanethiol coverage continues to decrease. Each capping agent
655 > molecule reaches its maximum capacity for thermal
656 > conductance. Therefore, even higher solvent-capping agent contact
657 > would not offset this effect. Eventually, when butanethiol coverage
658 > continues to decrease, solvent-capping agent contact actually
659 > decreases with the disappearing of butanethiol molecules. In this
660 > case, $G$ decrease could not be offset but instead accelerated.
661 >
662 > A comparison of the results obtained from differenet organic solvents
663 > can also provide useful information of the interfacial thermal
664 > transport process. The deuterated hexane (UA) results do not appear to
665 > be much different from those of normal hexane (UA), given that
666 > butanethiol (UA) is non-deuterated for both solvents. These UA model
667 > studies, even though eliminating C-H vibration samplings, still have
668 > C-C vibrational frequencies different from each other. However, these
669 > differences in the infrared range do not seem to produce an observable
670 > difference for the results of $G$. [MAY NEED FIGURE]
671 >
672 > Furthermore, results for rigid body toluene solvent, as well as other
673 > UA-hexane solvents, are reasonable within the general experimental
674 > ranges[CITATIONS]. This suggests that explicit hydrogen might not be a
675 > required factor for modeling thermal transport phenomena of systems
676 > such as Au-thiol/organic solvent.
677 >
678 > However, results for Au-butanethiol/toluene do not show an identical
679 > trend with those for Au-butanethiol/hexane in that $G$'s remain at
680 > approximately the same magnitue when butanethiol coverage differs from
681 > 25\% to 75\%. This might be rooted in the molecule shape difference
682 > for plane-like toluene and chain-like {\it n}-hexane. Due to this
683 > difference, toluene molecules have more difficulty in occupying
684 > relatively small gaps among capping agents when their coverage is not
685 > too low. Therefore, the solvent-capping agent contact may keep
686 > increasing until the capping agent coverage reaches a relatively low
687 > level. This becomes an offset for decreasing butanethiol molecules on
688 > its effect to the process of interfacial thermal transport. Thus, one
689 > can see a plateau of $G$ vs. butanethiol coverage in our results.
690 >
691 > [NEED ERROR ESTIMATE]
692 > \begin{figure}
693 > \includegraphics[width=\linewidth]{coverage}
694 > \caption{Comparison of interfacial thermal conductivity ($G$) values
695 >  for the Au-butanethiol/solvent interface with various UA models and
696 >  different capping agent coverages at $\langle T\rangle\sim$200K
697 >  using certain energy flux respectively.}
698 > \label{coverage}
699 > \end{figure}
700 >
701 > \subsection{Influence of Chosen Molecule Model on $G$}
702 > [MAY COMBINE W MECHANISM STUDY]
703 >
704 > In addition to UA solvent/capping agent models, AA models are included
705 > in our simulations as well. Besides simulations of the same (UA or AA)
706 > model for solvent and capping agent, different models can be applied
707 > to different components. Furthermore, regardless of models chosen,
708 > either the solvent or the capping agent can be deuterated, similar to
709 > the previous section. Table \ref{modelTest} summarizes the results of
710 > these studies.
711 >
712 > [MORE DATA; ERROR ESTIMATE]
713 > \begin{table*}
714 >  \begin{minipage}{\linewidth}
715 >    \begin{center}
716 >      
717 >      \caption{Computed interfacial thermal conductivity ($G$ and
718 >        $G^\prime$) values for interfaces using various models for
719 >        solvent and capping agent (or without capping agent) at
720 >        $\langle T\rangle\sim$200K. (D stands for deuterated solvent
721 >        or capping agent molecules; ``Avg.'' denotes results that are
722 >        averages of several simulations.)}
723 >      
724 >      \begin{tabular}{ccccc}
725 >        \hline\hline
726 >        Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\
727 >        (or bare surface) & model & (GW/m$^2$) &
728 >        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
729 >        \hline
730 >        UA    & UA hexane    & Avg. & 131()  & 86.5() \\
731 >              & UA hexane(D) & 1.95 & 153()  & 136()  \\
732 >              & AA hexane    & 1.94 & 135()  & 129()  \\
733 >              &              & 2.86 & 126()  & 115()  \\
734 >              & UA toluene   & 1.96 & 187()  & 151()  \\
735 >              & AA toluene   & 1.89 & 200()  & 149()  \\
736 >        \hline
737 >        AA    & UA hexane    & 1.94 & 116()  & 129()  \\
738 >              & AA hexane    & Avg. & 442()  & 356()  \\
739 >              & AA hexane(D) & 1.93 & 222()  & 234()  \\
740 >              & UA toluene   & 1.98 & 125()  & 96.5() \\
741 >              & AA toluene   & 3.79 & 487()  & 290()  \\
742 >        \hline
743 >        AA(D) & UA hexane    & 1.94 & 158()  & 172()  \\
744 >              & AA hexane    & 1.92 & 243()  & 191()  \\
745 >              & AA toluene   & 1.93 & 364()  & 322()  \\
746 >        \hline
747 >        bare  & UA hexane    & Avg. & 46.5() & 49.4() \\
748 >              & UA hexane(D) & 0.98 & 43.9() & 43.0() \\
749 >              & AA hexane    & 0.96 & 31.0() & 29.4() \\
750 >              & UA toluene   & 1.99 & 70.1() & 65.8() \\
751 >        \hline\hline
752 >      \end{tabular}
753 >      \label{modelTest}
754 >    \end{center}
755 >  \end{minipage}
756 > \end{table*}
757 >
758 > To facilitate direct comparison, the same system with differnt models
759 > for different components uses the same length scale for their
760 > simulation cells. Without the presence of capping agent, using
761 > different models for hexane yields similar results for both $G$ and
762 > $G^\prime$, and these two definitions agree with eath other very
763 > well. This indicates very weak interaction between the metal and the
764 > solvent, and is a typical case for acoustic impedance mismatch between
765 > these two phases.
766 >
767 > As for Au(111) surfaces completely covered by butanethiols, the choice
768 > of models for capping agent and solvent could impact the measurement
769 > of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane
770 > interfaces, using AA model for both butanethiol and hexane yields
771 > substantially higher conductivity values than using UA model for at
772 > least one component of the solvent and capping agent, which exceeds
773 > the upper bond of experimental value range. This is probably due to
774 > the classically treated C-H vibrations in the AA model, which should
775 > not be appreciably populated at normal temperatures. In comparison,
776 > once either the hexanes or the butanethiols are deuterated, one can
777 > see a significantly lower $G$ and $G^\prime$. In either of these
778 > cases, the C-H(D) vibrational overlap between the solvent and the
779 > capping agent is removed. [MAY NEED FIGURE] Conclusively, the
780 > improperly treated C-H vibration in the AA model produced
781 > over-predicted results accordingly. Compared to the AA model, the UA
782 > model yields more reasonable results with higher computational
783 > efficiency.
784 >
785 > However, for Au-butanethiol/toluene interfaces, having the AA
786 > butanethiol deuterated did not yield a significant change in the
787 > measurement results. Compared to the C-H vibrational overlap between
788 > hexane and butanethiol, both of which have alkyl chains, that overlap
789 > between toluene and butanethiol is not so significant and thus does
790 > not have as much contribution to the ``Intramolecular Vibration
791 > Redistribution''[CITE HASE]. Conversely, extra degrees of freedom such
792 > as the C-H vibrations could yield higher heat exchange rate between
793 > these two phases and result in a much higher conductivity.
794 >
795 > Although the QSC model for Au is known to predict an overly low value
796 > for bulk metal gold conductivity\cite{kuang:164101}, our computational
797 > results for $G$ and $G^\prime$ do not seem to be affected by this
798 > drawback of the model for metal. Instead, our results suggest that the
799 > modeling of interfacial thermal transport behavior relies mainly on
800 > the accuracy of the interaction descriptions between components
801 > occupying the interfaces.
802 >
803 > \subsection{Mechanism of Interfacial Thermal Conductance Enhancement
804 >  by Capping Agent}
805 > %OR\subsection{Vibrational spectrum study on conductance mechanism}
806 >
807 > [MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S]
808 >
809   To investigate the mechanism of this interfacial thermal conductance,
810   the vibrational spectra of various gold systems were obtained and are
811   shown as in the upper panel of Fig. \ref{vibration}. To obtain these
812   spectra, one first runs a simulation in the NVE ensemble and collects
813   snapshots of configurations; these configurations are used to compute
814   the velocity auto-correlation functions, which is used to construct a
815 < power spectrum via a Fourier transform. The gold surfaces covered by
490 < butanethiol molecules exhibit an additional peak observed at a
491 < frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration
492 < of the S-Au bond. This vibration enables efficient thermal transport
493 < from surface Au atoms to the capping agents. Simultaneously, as shown
494 < 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,
496 < including the C-H vibration, also suggests high thermal exchange
497 < efficiency. The combination of these two effects produces the drastic
498 < interfacial thermal conductance enhancement in the all-atom model.
815 > power spectrum via a Fourier transform.
816  
817 + [MAY RELATE TO HASE'S]
818 + The gold surfaces covered by
819 + butanethiol molecules, compared to bare gold surfaces, exhibit an
820 + additional peak observed at a frequency of $\sim$170cm$^{-1}$, which
821 + is attributed to the vibration of the S-Au bond. This vibration
822 + enables efficient thermal transport from surface Au atoms to the
823 + capping agents. Simultaneously, as shown in the lower panel of
824 + Fig. \ref{vibration}, the large overlap of the vibration spectra of
825 + butanethiol and hexane in the all-atom model, including the C-H
826 + vibration, also suggests high thermal exchange efficiency. The
827 + combination of these two effects produces the drastic interfacial
828 + thermal conductance enhancement in the all-atom model.
829 +
830 + [REDO. MAY NEED TO CONVERT TO JPEG]
831   \begin{figure}
832   \includegraphics[width=\linewidth]{vibration}
833   \caption{Vibrational spectra obtained for gold in different
# Line 504 | Line 835 | interfacial thermal conductance enhancement in the all
835    all-atom model (lower panel).}
836   \label{vibration}
837   \end{figure}
507 – % 600dpi, letter size. too large?
838  
839 + [COMPARISON OF TWO G'S; AU SLAB WIDTHS; ETC]
840 + % The results show that the two definitions used for $G$ yield
841 + % comparable values, though $G^\prime$ tends to be smaller.
842  
843 + \section{Conclusions}
844 + The NIVS algorithm we developed has been applied to simulations of
845 + Au-butanethiol surfaces with organic solvents. This algorithm allows
846 + effective unphysical thermal flux transferred between the metal and
847 + the liquid phase. With the flux applied, we were able to measure the
848 + corresponding thermal gradient and to obtain interfacial thermal
849 + conductivities. Our simulations have seen significant conductance
850 + enhancement with the presence of capping agent, compared to the bare
851 + gold/liquid interfaces. The acoustic impedance mismatch between the
852 + metal and the liquid phase is effectively eliminated by proper capping
853 + agent. Furthermore, the coverage precentage of the capping agent plays
854 + an important role in the interfacial thermal transport process.
855 +
856 + Our measurement results, particularly of the UA models, agree with
857 + available experimental data. This indicates that our force field
858 + parameters have a nice description of the interactions between the
859 + particles at the interfaces. AA models tend to overestimate the
860 + interfacial thermal conductance in that the classically treated C-H
861 + vibration would be overly sampled. Compared to the AA models, the UA
862 + models have higher computational efficiency with satisfactory
863 + accuracy, and thus are preferable in interfacial thermal transport
864 + modelings.
865 +
866 + Vlugt {\it et al.} has investigated the surface thiol structures for
867 + nanocrystal gold and pointed out that they differs from those of the
868 + Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to
869 + change of interfacial thermal transport behavior as well. To
870 + investigate this problem, an effective means to introduce thermal flux
871 + and measure the corresponding thermal gradient is desirable for
872 + simulating structures with spherical symmetry.
873 +
874 +
875   \section{Acknowledgments}
876   Support for this project was provided by the National Science
877   Foundation under grant CHE-0848243. Computational time was provided by
878   the Center for Research Computing (CRC) at the University of Notre
879 < Dame.  \newpage
879 > Dame. \newpage
880  
881   \bibliography{interfacial}
882  

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