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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
83 < chemical details of the surface and is challenging to
84 < 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, due to its importance in nanoscale
78 > science and technology. Reliability of nanoscale devices depends on
79 > their thermal transport properties. Unlike bulk homogeneous materials,
80 > nanoscale materials features significant presence of interfaces, and
81 > these interfaces could dominate the heat transfer behavior of these
82 > materials. Furthermore, these materials are generally heterogeneous,
83 > which challenges traditional research methods for homogeneous systems.
84  
85 + Heat conductance of molecular and nano-scale interfaces will be
86 + affected by the chemical details of the surface. Experimentally,
87 + various interfaces have been investigated for their thermal
88 + conductance properties. Wang {\it et al.} studied heat transport
89 + through long-chain hydrocarbon monolayers on gold substrate at
90 + individual molecular level\cite{Wang10082007}; Schmidt {\it et al.}
91 + studied the role of CTAB on thermal transport between gold nanorods
92 + and solvent\cite{doi:10.1021/jp8051888}; Juv\'e {\it et al.} studied
93 + the cooling dynamics, which is controlled by thermal interface
94 + resistence of glass-embedded metal
95 + nanoparticles\cite{PhysRevB.80.195406}. Although interfaces are
96 + commonly barriers for heat transport, Alper {\it et al.} suggested
97 + that specific ligands (capping agents) could completely eliminate this
98 + barrier ($G\rightarrow\infty$)\cite{doi:10.1021/la904855s}.
99 +
100 + Theoretical and computational studies were also engaged in the
101 + interfacial thermal transport research in order to gain an
102 + understanding of this phenomena at the molecular level. Hase and
103 + coworkers employed Non-Equilibrium Molecular Dynamics (NEMD)
104 + simulations to study thermal transport from hot Au(111) substrate to a
105 + self-assembled monolayer of alkylthiolate with relatively long chain
106 + (8-20 carbon atoms)[CITE TWO PAPERS]. However, emsemble average measurements for heat
107 + conductance of interfaces between the capping monolayer on Au and a
108 + solvent phase has yet to be studied. The relatively low thermal flux
109 + through interfaces is difficult to measure with Equilibrium MD or
110 + forward NEMD simulation methods. Therefore, the Reverse NEMD (RNEMD)
111 + methods would have the advantage of having this difficult to measure
112 + flux known when studying the thermal transport
113 + across interfaces, given that the simulation
114 + methods being able to effectively apply an unphysical flux in
115 + non-homogeneous systems.
116 +
117   Recently, we have developed the Non-Isotropic Velocity Scaling (NIVS)
118   algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm
119   retains the desirable features of RNEMD (conservation of linear
# Line 93 | Line 121 | study of interfacial conductance.
121   conditions) while establishing true thermal distributions in each of
122   the two slabs. Furthermore, it allows more effective thermal exchange
123   between particles of different identities, and thus enables extensive
124 < study of interfacial conductance.
124 > study of interfacial conductance under steady states.
125  
126 + Our work presented here investigated the Au(111) surface with various
127 + coverage of butanethiol, a capping agent with shorter carbon chain,
128 + solvated with organic solvents of different molecular shapes. And
129 + different models were used for both the capping agent and the solvent
130 + force field parameters. With the NIVS algorithm applied, the thermal
131 + transport through these interfacial systems was studied and the
132 + underlying mechanism for this phenomena was investigated.
133 +
134 + [WHY STUDY AU-THIOL SURFACE; MAY CITE SHAOYI JIANG]
135 +
136   \section{Methodology}
137   \subsection{Algorithm}
138   [BACKGROUND FOR MD METHODS]
# Line 211 | Line 249 | obtain the 1st and 2nd derivatives of the temperature
249   \label{gradT}
250   \end{figure}
251  
252 + [MAY INCLUDE POWER SPECTRUM PROTOCOL]
253 +
254   \section{Computational Details}
255 < \subsection{System Geometry}
255 > \subsection{Simulation Protocol}
256   In our simulations, Au is used to construct a metal slab with bare
257   (111) surface perpendicular to the $z$-axis. Different slab thickness
258   (layer numbers of Au) are simulated. This metal slab is first
# Line 240 | Line 280 | vibrational frequencies and chain-like shape ({\it n}-
280   interactions do not disrupt the simulations. Two solvents are
281   investigated, one which has little vibrational overlap with the
282   alkanethiol and plane-like shape (toluene), and one which has similar
283 < vibrational frequencies and chain-like shape ({\it n}-hexane). The
284 < 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.
283 > vibrational frequencies and chain-like shape ({\it n}-hexane). [MAY
284 > EXPLAIN WHY WE CHOOSE THEM]
285  
286 + The spacing filled by solvent molecules, i.e. the gap between
287 + periodically repeated Au-butanethiol surfaces should be carefully
288 + chosen. A very long length scale for the thermal gradient axis ($z$)
289 + may cause excessively hot or cold temperatures in the middle of the
290 + solvent region and lead to undesired phenomena such as solvent boiling
291 + or freezing when a thermal flux is applied. Conversely, too few
292 + solvent molecules would change the normal behavior of the liquid
293 + phase. Therefore, our $N_{solvent}$ values were chosen to ensure that
294 + these extreme cases did not happen to our simulations. And the
295 + corresponding spacing is usually $35 \sim 60$\AA.
296 +
297   The initial configurations generated by Packmol are further
298   equilibrated with the $x$ and $y$ dimensions fixed, only allowing
299   length scale change in $z$ dimension. This is to ensure that the
# Line 287 | Line 333 | For both solvent molecules, straight chain {\it n}-hex
333   reparametrized for accurate surface energies compared to the
334   Sutton-Chen potentials\cite{Chen90}.
335  
336 + Figure [REF] demonstrates how we name our pseudo-atoms of the
337 + molecules in our simulations.
338 + [FIGURE FOR MOLECULE NOMENCLATURE]
339 +
340   For both solvent molecules, straight chain {\it n}-hexane and aromatic
341   toluene, United-Atom (UA) and All-Atom (AA) models are used
342   respectively. The TraPPE-UA
# Line 300 | Line 350 | simulations should be much lower than the liquid boili
350   to a system, the temperature of ``hot'' area in the liquid phase would be
351   significantly higher than the average, to prevent over heating and
352   boiling of the liquid phase, the average temperature in our
353 < simulations should be much lower than the liquid boiling point. [NEED MORE DISCUSSION]
353 > simulations should be much lower than the liquid boiling point. [MORE DISCUSSION]
354   For UA-toluene model, rigid body constraints are applied, so that the
355 < benzene ring and the methyl-C(aromatic) bond are kept rigid. This
356 < would save computational time.[MORE DETAILS NEEDED]
355 > benzene ring and the methyl-CRar bond are kept rigid. This would save
356 > computational time.[MORE DETAILS]
357  
358   Besides the TraPPE-UA models, AA models for both organic solvents are
359 < included in our studies as well. For hexane, the OPLS
360 < all-atom\cite{OPLSAA} force field is used. [MORE DETAILS]
359 > included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA}
360 > force field is used. [MORE DETAILS]
361   For toluene, the United Force Field developed by Rapp\'{e} {\it et
362    al.}\cite{doi:10.1021/ja00051a040} is adopted.[MORE DETAILS]
363  
364   The capping agent in our simulations, the butanethiol molecules can
365   either use UA or AA model. The TraPPE-UA force fields includes
366 < parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used in
367 < our simulations corresponding to our TraPPE-UA models for solvent.
368 < and All-Atom models [NEED CITATIONS]
369 < However, the model choice (UA or AA) of capping agent can be different
370 < from the solvent. Regardless of model choice, the force field
371 < parameters for interactions between capping agent and solvent can be
372 < derived using Lorentz-Berthelot Mixing Rule.
366 > parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used for
367 > UA butanethiol model in our simulations. The OPLS-AA also provides
368 > parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111)
369 > surfaces do not have the hydrogen atom bonded to sulfur. To adapt this
370 > change and derive suitable parameters for butanethiol adsorbed on
371 > Au(111) surfaces, we adopt the S parameters from [CITATION CF VLUGT]
372 > and modify parameters for its neighbor C atom for charge balance in
373 > the molecule. Note that the model choice (UA or AA) of capping agent
374 > can be different from the solvent. Regardless of model choice, the
375 > force field parameters for interactions between capping agent and
376 > solvent can be derived using Lorentz-Berthelot Mixing Rule:
377  
378 +
379   To describe the interactions between metal Au and non-metal capping
380 < agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive
381 < other interactions which are not yet finely parametrized. [can add
382 < hautman and klein's paper here and more discussion; need to put
383 < aromatic-metal interaction approximation here]\cite{doi:10.1021/jp034405s}
380 > agent and solvent particles, we refer to an adsorption study of alkyl
381 > thiols on gold surfaces by Vlugt {\it et
382 >  al.}\cite{vlugt:cpc2007154} They fitted an effective Lennard-Jones
383 > form of potential parameters for the interaction between Au and
384 > pseudo-atoms CH$_x$ and S based on a well-established and widely-used
385 > effective potential of Hautman and Klein[CITATION] for the Au(111)
386 > surface. As our simulations require the gold lattice slab to be
387 > non-rigid so that it could accommodate kinetic energy for thermal
388 > transport study purpose, the pair-wise form of potentials is
389 > preferred.
390  
391 < [TABULATED FORCE FIELD PARAMETERS NEEDED]
391 > Besides, the potentials developed from {\it ab initio} calculations by
392 > Leng {\it et al.}\cite{doi:10.1021/jp034405s} are adopted for the
393 > interactions between Au and aromatic C/H atoms in toluene.[MORE DETAILS]
394  
395 <
396 < [SURFACE RECONSTRUCTION PREVENTS SIMULATION TEMP TO GO HIGHER]
397 <
398 <
399 < \section{Results}
400 < [REARRANGEMENT NEEDED]
401 < \subsection{Toluene Solvent}
339 <
340 < The results (Table \ref{AuThiolToluene}) show a
341 < significant conductance enhancement compared to the gold/water
342 < interface without capping agent and agree with available experimental
343 < data. This indicates that the metal-metal potential, though not
344 < predicting an accurate bulk metal thermal conductivity, does not
345 < greatly interfere with the simulation of the thermal conductance
346 < behavior across a non-metal interface. The solvent model is not
347 < particularly volatile, so the simulation cell does not expand
348 < significantly under higher temperature. We did not observe a
349 < significant conductance decrease when the temperature was increased to
350 < 300K. The results show that the two definitions used for $G$ yield
351 < comparable values, though $G^\prime$ tends to be smaller.
395 > However, the Lennard-Jones parameters between Au and other types of
396 > particles in our simulations are not yet well-established. For these
397 > interactions, we attempt to derive their parameters using the Mixing
398 > Rule. To do this, the ``Metal-non-Metal'' (MnM) interaction parameters
399 > for Au is first extracted from the Au-CH$_x$ parameters by applying
400 > the Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM''
401 > parameters in our simulations.
402  
403   \begin{table*}
404    \begin{minipage}{\linewidth}
405      \begin{center}
406 <      \caption{Computed interfacial thermal conductivity ($G$ and
407 <        $G^\prime$) values for the Au/butanethiol/toluene interface at
358 <        different temperatures using a range of energy fluxes.}
406 >      \caption{Lennard-Jones parameters for Au-non-Metal
407 >        interactions in our simulations.}
408        
409 <      \begin{tabular}{cccc}
409 >      \begin{tabular}{ccc}
410          \hline\hline
411 <        $\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\
412 <        (K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
411 >        Non-metal atom   & $\sigma$ & $\epsilon$ \\
412 >        (or pseudo-atom) & \AA      & kcal/mol  \\
413          \hline
414 <        200 & 1.86 & 180 & 135 \\
415 <            & 2.15 & 204 & 113 \\
416 <            & 3.93 & 175 & 114 \\
417 <        300 & 1.91 & 143 & 125 \\
418 <            & 4.19 & 134 & 113 \\
414 >        S    & 2.40   & 8.465   \\
415 >        CH3  & 3.54   & 0.2146  \\
416 >        CH2  & 3.54   & 0.1749  \\
417 >        CT3  & 3.365  & 0.1373  \\
418 >        CT2  & 3.365  & 0.1373  \\
419 >        CTT  & 3.365  & 0.1373  \\
420 >        HC   & 2.865  & 0.09256 \\
421 >        CHar & 3.4625 & 0.1680  \\
422 >        CRar & 3.555  & 0.1604  \\
423 >        CA   & 3.173  & 0.0640  \\
424 >        HA   & 2.746  & 0.0414  \\
425          \hline\hline
426        \end{tabular}
427 <      \label{AuThiolToluene}
427 >      \label{MnM}
428      \end{center}
429    \end{minipage}
430   \end{table*}
431  
377 – \subsection{Hexane Solvent}
432  
433 < Using the united-atom model, different coverages of capping agent,
434 < temperatures of simulations and numbers of solvent molecules were all
435 < investigated and Table \ref{AuThiolHexaneUA} shows the results of
436 < these computations. The number of hexane molecules in our simulations
437 < does not affect the calculations significantly. However, a very long
438 < length scale for the thermal gradient axis ($z$) may cause excessively
439 < hot or cold temperatures in the middle of the solvent region and lead
440 < to undesired phenomena such as solvent boiling or freezing, while too
441 < few solvent molecules would change the normal behavior of the liquid
442 < phase. Our $N_{hexane}$ values were chosen to ensure that these
389 < extreme cases did not happen to our simulations.
433 > \section{Results and Discussions}
434 > [MAY HAVE A BRIEF SUMMARY]
435 > \subsection{How Simulation Parameters Affects $G$}
436 > [MAY NOT PUT AT FIRST]
437 > We have varied our protocol or other parameters of the simulations in
438 > order to investigate how these factors would affect the measurement of
439 > $G$'s. It turned out that while some of these parameters would not
440 > affect the results substantially, some other changes to the
441 > simulations would have a significant impact on the measurement
442 > results.
443  
444 < Table \ref{AuThiolHexaneUA} enables direct comparison between
445 < different coverages of capping agent, when other system parameters are
446 < held constant. With high coverage of butanethiol on the gold surface,
447 < the interfacial thermal conductance is enhanced
448 < significantly. Interestingly, a slightly lower butanethiol coverage
449 < leads to a moderately higher conductivity. This is probably due to
450 < more solvent/capping agent contact when butanethiol molecules are
451 < not densely packed, which enhances the interactions between the two
452 < phases and lowers the thermal transfer barrier of this interface.
400 < % [COMPARE TO AU/WATER IN PAPER]
444 > In some of our simulations, we allowed $L_x$ and $L_y$ to change
445 > during equilibrating the liquid phase. Due to the stiffness of the Au
446 > slab, $L_x$ and $L_y$ would not change noticeably after
447 > equilibration. Although $L_z$ could fluctuate $\sim$1\% after a system
448 > is fully equilibrated in the NPT ensemble, this fluctuation, as well
449 > as those comparably smaller to $L_x$ and $L_y$, would not be magnified
450 > on the calculated $G$'s, as shown in Table \ref{AuThiolHexaneUA}. This
451 > insensivity to $L_i$ fluctuations allows reliable measurement of $G$'s
452 > without the necessity of extremely cautious equilibration process.
453  
454 < It is also noted that the overall simulation temperature is another
455 < factor that affects the interfacial thermal conductance. One
456 < possibility of this effect may be rooted in the decrease in density of
457 < the liquid phase. We observed that when the average temperature
458 < increases from 200K to 250K, the bulk hexane density becomes lower
459 < than experimental value, as the system is equilibrated under NPT
460 < ensemble. This leads to lower contact between solvent and capping
461 < agent, and thus lower conductivity.
454 > As stated in our computational details, the spacing filled with
455 > solvent molecules can be chosen within a range. This allows some
456 > change of solvent molecule numbers for the same Au-butanethiol
457 > surfaces. We did this study on our Au-butanethiol/hexane
458 > simulations. Nevertheless, the results obtained from systems of
459 > different $N_{hexane}$ did not indicate that the measurement of $G$ is
460 > susceptible to this parameter. For computational efficiency concern,
461 > smaller system size would be preferable, given that the liquid phase
462 > structure is not affected.
463  
464 < Conductivity values are more difficult to obtain under higher
465 < temperatures. This is because the Au surface tends to undergo
466 < reconstructions in relatively high temperatures. Surface Au atoms can
467 < migrate outward to reach higher Au-S contact; and capping agent
468 < molecules can be embedded into the surface Au layer due to the same
469 < driving force. This phenomenon agrees with experimental
470 < results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. A surface
471 < fully covered in capping agent is more susceptible to reconstruction,
472 < possibly because fully coverage prevents other means of capping agent
473 < relaxation, such as migration to an empty neighbor three-fold site.
464 > Our NIVS algorithm allows change of unphysical thermal flux both in
465 > direction and in quantity. This feature extends our investigation of
466 > interfacial thermal conductance. However, the magnitude of this
467 > thermal flux is not arbitary if one aims to obtain a stable and
468 > reliable thermal gradient. A temperature profile would be
469 > substantially affected by noise when $|J_z|$ has a much too low
470 > magnitude; while an excessively large $|J_z|$ that overwhelms the
471 > conductance capacity of the interface would prevent a thermal gradient
472 > to reach a stablized steady state. NIVS has the advantage of allowing
473 > $J$ to vary in a wide range such that the optimal flux range for $G$
474 > measurement can generally be simulated by the algorithm. Within the
475 > optimal range, we were able to study how $G$ would change according to
476 > the thermal flux across the interface. For our simulations, we denote
477 > $J_z$ to be positive when the physical thermal flux is from the liquid
478 > to metal, and negative vice versa. The $G$'s measured under different
479 > $J_z$ is listed in Table \ref{AuThiolHexaneUA} and [REF]. These
480 > results do not suggest that $G$ is dependent on $J_z$ within this flux
481 > range. The linear response of flux to thermal gradient simplifies our
482 > investigations in that we can rely on $G$ measurement with only a
483 > couple $J_z$'s and do not need to test a large series of fluxes.
484  
485 < %MAY ADD MORE DATA TO TABLE
485 > %ADD MORE TO TABLE
486   \begin{table*}
487    \begin{minipage}{\linewidth}
488      \begin{center}
489        \caption{Computed interfacial thermal conductivity ($G$ and
490 <        $G^\prime$) values for the Au/butanethiol/hexane interface
491 <        with united-atom model and different capping agent coverage
492 <        and solvent molecule numbers at different temperatures using a
430 <        range of energy fluxes.}
490 >        $G^\prime$) values for the 100\% covered Au-butanethiol/hexane
491 >        interfaces with UA model and different hexane molecule numbers
492 >        at different temperatures using a range of energy fluxes.}
493        
494 <      \begin{tabular}{cccccc}
494 >      \begin{tabular}{cccccccc}
495          \hline\hline
496 <        Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\
497 <        coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) &
496 >        $\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ &
497 >        $G$ & $G^\prime$ \\
498 >        (K) & $N_{hexane}$ & \multicolumn{3}{c}{(\AA)} & (GW/m$^2$) &
499          \multicolumn{2}{c}{(MW/m$^2$/K)} \\
500          \hline
501 <        0.0   & 200 & 200 & 0.96 & 43.3 & 42.7 \\
502 <              &     &     & 1.91 & 45.7 & 42.9 \\
503 <              &     & 166 & 0.96 & 43.1 & 53.4 \\
504 <        88.9  & 200 & 166 & 1.94 & 172  & 108  \\
505 <        100.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\
506 <              &     & 166 & 0.98 & 79.0 & 62.9 \\
507 <              &     &     & 1.44 & 76.2 & 64.8 \\
508 <              & 200 & 200 & 1.92 & 129  & 87.3 \\
509 <              &     &     & 1.93 & 131  & 77.5 \\
510 <              &     & 166 & 0.97 & 115  & 69.3 \\
511 <              &     &     & 1.94 & 125  & 87.1 \\
501 >        200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 &
502 >        102()  & 80.0() \\
503 >            & 200 & 29.84 & 25.81 &  93.9 &  1.92 &
504 >        129()  & 87.3() \\
505 >            &     & 29.84 & 25.81 &  95.3 &  1.93 &
506 >        131()  & 77.5() \\
507 >            & 166 & 29.84 & 25.81 &  85.7 &  0.97 &
508 >        115()  & 69.3() \\
509 >            &     &       &       &       &  1.94 &
510 >        125()  & 87.1() \\
511 >        250 & 200 & 29.84 & 25.87 & 106.8 &  0.96 &
512 >        81.8() & 67.0() \\
513 >            & 166 & 29.87 & 25.84 &  94.8 &  0.98 &
514 >        79.0() & 62.9() \\
515 >            &     & 29.84 & 25.85 &  95.0 &  1.44 &
516 >        76.2() & 64.8() \\
517          \hline\hline
518        \end{tabular}
519        \label{AuThiolHexaneUA}
# Line 453 | Line 521 | For the all-atom model, the liquid hexane phase was no
521    \end{minipage}
522   \end{table*}
523  
524 < For the all-atom model, the liquid hexane phase was not stable under NPT
525 < conditions. Therefore, the simulation length scale parameters are
526 < adopted from previous equilibration results of the united-atom model
527 < at 200K. Table \ref{AuThiolHexaneAA} shows the results of these
528 < simulations. The conductivity values calculated with full capping
529 < agent coverage are substantially larger than observed in the
530 < united-atom model, and is even higher than predicted by
531 < experiments. It is possible that our parameters for metal-non-metal
532 < particle interactions lead to an overestimate of the interfacial
533 < thermal conductivity, although the active C-H vibrations in the
534 < all-atom model (which should not be appreciably populated at normal
467 < temperatures) could also account for this high conductivity. The major
468 < thermal transfer barrier of Au/butanethiol/hexane interface is between
469 < the liquid phase and the capping agent, so extra degrees of freedom
470 < such as the C-H vibrations could enhance heat exchange between these
471 < two phases and result in a much higher conductivity.
524 > Furthermore, we also attempted to increase system average temperatures
525 > to above 200K. These simulations are first equilibrated in the NPT
526 > ensemble under normal pressure. As stated above, the TraPPE-UA model
527 > for hexane tends to predict a lower boiling point. In our simulations,
528 > hexane had diffculty to remain in liquid phase when NPT equilibration
529 > temperature is higher than 250K. Additionally, the equilibrated liquid
530 > hexane density under 250K becomes lower than experimental value. This
531 > expanded liquid phase leads to lower contact between hexane and
532 > butanethiol as well.[MAY NEED FIGURE] And this reduced contact would
533 > probably be accountable for a lower interfacial thermal conductance,
534 > as shown in Table \ref{AuThiolHexaneUA}.
535  
536 + A similar study for TraPPE-UA toluene agrees with the above result as
537 + well. Having a higher boiling point, toluene tends to remain liquid in
538 + our simulations even equilibrated under 300K in NPT
539 + ensembles. Furthermore, the expansion of the toluene liquid phase is
540 + not as significant as that of the hexane. This prevents severe
541 + decrease of liquid-capping agent contact and the results (Table
542 + \ref{AuThiolToluene}) show only a slightly decreased interface
543 + conductance. Therefore, solvent-capping agent contact should play an
544 + important role in the thermal transport process across the interface
545 + in that higher degree of contact could yield increased conductance.
546 +
547 + [ADD Lxyz AND ERROR ESTIMATE TO TABLE]
548   \begin{table*}
549    \begin{minipage}{\linewidth}
550      \begin{center}
476 –      
551        \caption{Computed interfacial thermal conductivity ($G$ and
552 <        $G^\prime$) values for the Au/butanethiol/hexane interface
553 <        with all-atom model and different capping agent coverage at
554 <        200K using a range of energy fluxes.}
552 >        $G^\prime$) values for a 90\% coverage Au-butanethiol/toluene
553 >        interface at different temperatures using a range of energy
554 >        fluxes.}
555        
556        \begin{tabular}{cccc}
557          \hline\hline
558 <        Thiol & $J_z$ & $G$ & $G^\prime$ \\
559 <        coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
558 >        $\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\
559 >        (K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
560          \hline
561 <        0.0   & 0.95 & 28.5 & 27.2 \\
562 <              & 1.88 & 30.3 & 28.9 \\
563 <        100.0 & 2.87 & 551  & 294  \\
564 <              & 3.81 & 494  & 193  \\
561 >        200 & -1.86 & 180() & 135() \\
562 >            &  2.15 & 204() & 113() \\
563 >            & -3.93 & 175() & 114() \\
564 >        300 & -1.91 & 143() & 125() \\
565 >            & -4.19 & 134() & 113() \\
566          \hline\hline
567        \end{tabular}
568 <      \label{AuThiolHexaneAA}
568 >      \label{AuThiolToluene}
569      \end{center}
570    \end{minipage}
571   \end{table*}
572  
573 < %subsubsection{Vibrational spectrum study on conductance mechanism}
573 > Besides lower interfacial thermal conductance, surfaces in relatively
574 > high temperatures are susceptible to reconstructions, when
575 > butanethiols have a full coverage on the Au(111) surface. These
576 > reconstructions include surface Au atoms migrated outward to the S
577 > atom layer, and butanethiol molecules embedded into the original
578 > surface Au layer. The driving force for this behavior is the strong
579 > Au-S interactions in our simulations. And these reconstructions lead
580 > to higher ratio of Au-S attraction and thus is energetically
581 > favorable. Furthermore, this phenomenon agrees with experimental
582 > results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt
583 > {\it et al.} had kept their Au(111) slab rigid so that their
584 > simulations can reach 300K without surface reconstructions. Without
585 > this practice, simulating 100\% thiol covered interfaces under higher
586 > temperatures could hardly avoid surface reconstructions. However, our
587 > measurement is based on assuming homogeneity on $x$ and $y$ dimensions
588 > so that measurement of $T$ at particular $z$ would be an effective
589 > average of the particles of the same type. Since surface
590 > reconstructions could eliminate the original $x$ and $y$ dimensional
591 > homogeneity, measurement of $G$ is more difficult to conduct under
592 > higher temperatures. Therefore, most of our measurements are
593 > undertaken at $\langle T\rangle\sim$200K.
594 >
595 > However, when the surface is not completely covered by butanethiols,
596 > the simulated system is more resistent to the reconstruction
597 > above. Our Au-butanethiol/toluene system did not see this phenomena
598 > even at $\langle T\rangle\sim$300K. The Au(111) surfaces have a 90\% coverage of
599 > butanethiols and have empty three-fold sites. These empty sites could
600 > help prevent surface reconstruction in that they provide other means
601 > of capping agent relaxation. It is observed that butanethiols can
602 > migrate to their neighbor empty sites during a simulation. Therefore,
603 > we were able to obtain $G$'s for these interfaces even at a relatively
604 > high temperature without being affected by surface reconstructions.
605 >
606 > \subsection{Influence of Capping Agent Coverage on $G$}
607 > To investigate the influence of butanethiol coverage on interfacial
608 > thermal conductance, a series of different coverage Au-butanethiol
609 > surfaces is prepared and solvated with various organic
610 > molecules. These systems are then equilibrated and their interfacial
611 > thermal conductivity are measured with our NIVS algorithm. Table
612 > \ref{tlnUhxnUhxnD} lists these results for direct comparison between
613 > different coverages of butanethiol. To study the isotope effect in
614 > interfacial thermal conductance, deuterated UA-hexane is included as
615 > well.
616 >
617 > It turned out that with partial covered butanethiol on the Au(111)
618 > surface, the derivative definition for $G$ (Eq. \ref{derivativeG}) has
619 > difficulty to apply, due to the difficulty in locating the maximum of
620 > change of $\lambda$. Instead, the discrete definition
621 > (Eq. \ref{discreteG}) is easier to apply, as max($\Delta T$) can still
622 > be well-defined. Therefore, $G$'s (not $G^\prime$) are used for this
623 > section.
624 >
625 > From Table \ref{tlnUhxnUhxnD}, one can see the significance of the
626 > presence of capping agents. Even when a fraction of the Au(111)
627 > surface sites are covered with butanethiols, the conductivity would
628 > see an enhancement by at least a factor of 3. This indicates the
629 > important role cappping agent is playing for thermal transport
630 > phenomena on metal/organic solvent surfaces.
631 >
632 > Interestingly, as one could observe from our results, the maximum
633 > conductance enhancement (largest $G$) happens while the surfaces are
634 > about 75\% covered with butanethiols. This again indicates that
635 > solvent-capping agent contact has an important role of the thermal
636 > transport process. Slightly lower butanethiol coverage allows small
637 > gaps between butanethiols to form. And these gaps could be filled with
638 > solvent molecules, which acts like ``heat conductors'' on the
639 > surface. The higher degree of interaction between these solvent
640 > molecules and capping agents increases the enhancement effect and thus
641 > produces a higher $G$ than densely packed butanethiol arrays. However,
642 > once this maximum conductance enhancement is reached, $G$ decreases
643 > when butanethiol coverage continues to decrease. Each capping agent
644 > molecule reaches its maximum capacity for thermal
645 > conductance. Therefore, even higher solvent-capping agent contact
646 > would not offset this effect. Eventually, when butanethiol coverage
647 > continues to decrease, solvent-capping agent contact actually
648 > decreases with the disappearing of butanethiol molecules. In this
649 > case, $G$ decrease could not be offset but instead accelerated.
650 >
651 > A comparison of the results obtained from differenet organic solvents
652 > can also provide useful information of the interfacial thermal
653 > transport process. The deuterated hexane (UA) results do not appear to
654 > be much different from those of normal hexane (UA), given that
655 > butanethiol (UA) is non-deuterated for both solvents. These UA model
656 > studies, even though eliminating C-H vibration samplings, still have
657 > C-C vibrational frequencies different from each other. However, these
658 > differences in the infrared range do not seem to produce an observable
659 > difference for the results of $G$. [MAY NEED FIGURE]
660 >
661 > Furthermore, results for rigid body toluene solvent, as well as other
662 > UA-hexane solvents, are reasonable within the general experimental
663 > ranges[CITATIONS]. This suggests that explicit hydrogen might not be a
664 > required factor for modeling thermal transport phenomena of systems
665 > such as Au-thiol/organic solvent.
666 >
667 > However, results for Au-butanethiol/toluene do not show an identical
668 > trend with those for Au-butanethiol/hexane in that $G$'s remain at
669 > approximately the same magnitue when butanethiol coverage differs from
670 > 25\% to 75\%. This might be rooted in the molecule shape difference
671 > for plane-like toluene and chain-like {\it n}-hexane. Due to this
672 > difference, toluene molecules have more difficulty in occupying
673 > relatively small gaps among capping agents when their coverage is not
674 > too low. Therefore, the solvent-capping agent contact may keep
675 > increasing until the capping agent coverage reaches a relatively low
676 > level. This becomes an offset for decreasing butanethiol molecules on
677 > its effect to the process of interfacial thermal transport. Thus, one
678 > can see a plateau of $G$ vs. butanethiol coverage in our results.
679 >
680 > [NEED ERROR ESTIMATE, MAY ALSO PUT J HERE]
681 > \begin{table*}
682 >  \begin{minipage}{\linewidth}
683 >    \begin{center}
684 >      \caption{Computed interfacial thermal conductivity ($G$) values
685 >        for the Au-butanethiol/solvent interface with various UA
686 >        models and different capping agent coverages at $\langle
687 >        T\rangle\sim$200K using certain energy flux respectively.}
688 >      
689 >      \begin{tabular}{cccc}
690 >        \hline\hline
691 >        Thiol & \multicolumn{3}{c}{$G$(MW/m$^2$/K)} \\
692 >        coverage (\%) & hexane & hexane(D) & toluene \\
693 >        \hline
694 >        0.0   & 46.5() & 43.9() & 70.1() \\
695 >        25.0  & 151()  & 153()  & 249()  \\
696 >        50.0  & 172()  & 182()  & 214()  \\
697 >        75.0  & 242()  & 229()  & 244()  \\
698 >        88.9  & 178()  & -      & -      \\
699 >        100.0 & 137()  & 153()  & 187()  \\
700 >        \hline\hline
701 >      \end{tabular}
702 >      \label{tlnUhxnUhxnD}
703 >    \end{center}
704 >  \end{minipage}
705 > \end{table*}
706 >
707 > \subsection{Influence of Chosen Molecule Model on $G$}
708 > [MAY COMBINE W MECHANISM STUDY]
709 >
710 > In addition to UA solvent/capping agent models, AA models are included
711 > in our simulations as well. Besides simulations of the same (UA or AA)
712 > model for solvent and capping agent, different models can be applied
713 > to different components. Furthermore, regardless of models chosen,
714 > either the solvent or the capping agent can be deuterated, similar to
715 > the previous section. Table \ref{modelTest} summarizes the results of
716 > these studies.
717 >
718 > [MORE DATA; ERROR ESTIMATE]
719 > \begin{table*}
720 >  \begin{minipage}{\linewidth}
721 >    \begin{center}
722 >      
723 >      \caption{Computed interfacial thermal conductivity ($G$ and
724 >        $G^\prime$) values for interfaces using various models for
725 >        solvent and capping agent (or without capping agent) at
726 >        $\langle T\rangle\sim$200K.}
727 >      
728 >      \begin{tabular}{ccccc}
729 >        \hline\hline
730 >        Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\
731 >        (or bare surface) & model & (GW/m$^2$) &
732 >        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
733 >        \hline
734 >        UA    & AA hexane  & 1.94 & 135()  & 129()  \\
735 >              &            & 2.86 & 126()  & 115()  \\
736 >              & AA toluene & 1.89 & 200()  & 149()  \\
737 >        AA    & UA hexane  & 1.94 & 116()  & 129()  \\
738 >              & AA hexane  & 3.76 & 451()  & 378()  \\
739 >              &            & 4.71 & 432()  & 334()  \\
740 >              & AA toluene & 3.79 & 487()  & 290()  \\
741 >        AA(D) & UA hexane  & 1.94 & 158()  & 172()  \\
742 >        bare  & AA hexane  & 0.96 & 31.0() & 29.4() \\
743 >        \hline\hline
744 >      \end{tabular}
745 >      \label{modelTest}
746 >    \end{center}
747 >  \end{minipage}
748 > \end{table*}
749 >
750 > To facilitate direct comparison, the same system with differnt models
751 > for different components uses the same length scale for their
752 > simulation cells. Without the presence of capping agent, using
753 > different models for hexane yields similar results for both $G$ and
754 > $G^\prime$, and these two definitions agree with eath other very
755 > well. This indicates very weak interaction between the metal and the
756 > solvent, and is a typical case for acoustic impedance mismatch between
757 > these two phases.
758 >
759 > As for Au(111) surfaces completely covered by butanethiols, the choice
760 > of models for capping agent and solvent could impact the measurement
761 > of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane
762 > interfaces, using AA model for both butanethiol and hexane yields
763 > substantially higher conductivity values than using UA model for at
764 > least one component of the solvent and capping agent, which exceeds
765 > the upper bond of experimental value range. This is probably due to
766 > the classically treated C-H vibrations in the AA model, which should
767 > not be appreciably populated at normal temperatures. In comparison,
768 > once either the hexanes or the butanethiols are deuterated, one can
769 > see a significantly lower $G$ and $G^\prime$. In either of these
770 > cases, the C-H(D) vibrational overlap between the solvent and the
771 > capping agent is removed. [MAY NEED FIGURE] Conclusively, the
772 > improperly treated C-H vibration in the AA model produced
773 > over-predicted results accordingly. Compared to the AA model, the UA
774 > model yields more reasonable results with higher computational
775 > efficiency.
776 >
777 > However, for Au-butanethiol/toluene interfaces, having the AA
778 > butanethiol deuterated did not yield a significant change in the
779 > measurement results.
780 > . , so extra degrees of freedom
781 > such as the C-H vibrations could enhance heat exchange between these
782 > two phases and result in a much higher conductivity.
783 >
784 >
785 > Although the QSC model for Au is known to predict an overly low value
786 > for bulk metal gold conductivity[CITE NIVSRNEMD], our computational
787 > results for $G$ and $G^\prime$ do not seem to be affected by this
788 > drawback of the model for metal. Instead, the modeling of interfacial
789 > thermal transport behavior relies mainly on an accurate description of
790 > the interactions between components occupying the interfaces.
791 >
792 > \subsection{Mechanism of Interfacial Thermal Conductance Enhancement
793 >  by Capping Agent}
794 > %OR\subsection{Vibrational spectrum study on conductance mechanism}
795 >
796 > [MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S]
797 >
798   To investigate the mechanism of this interfacial thermal conductance,
799   the vibrational spectra of various gold systems were obtained and are
800   shown as in the upper panel of Fig. \ref{vibration}. To obtain these
801   spectra, one first runs a simulation in the NVE ensemble and collects
802   snapshots of configurations; these configurations are used to compute
803   the velocity auto-correlation functions, which is used to construct a
804 < power spectrum via a Fourier transform. The gold surfaces covered by
506 < butanethiol molecules exhibit an additional peak observed at a
507 < frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration
508 < of the S-Au bond. This vibration enables efficient thermal transport
509 < from surface Au atoms to the capping agents. Simultaneously, as shown
510 < in the lower panel of Fig. \ref{vibration}, the large overlap of the
511 < vibration spectra of butanethiol and hexane in the all-atom model,
512 < including the C-H vibration, also suggests high thermal exchange
513 < efficiency. The combination of these two effects produces the drastic
514 < interfacial thermal conductance enhancement in the all-atom model.
804 > power spectrum via a Fourier transform.
805  
806 + The gold surfaces covered by
807 + butanethiol molecules, compared to bare gold surfaces, exhibit an
808 + additional peak observed at a frequency of $\sim$170cm$^{-1}$, which
809 + is attributed to the vibration of the S-Au bond. This vibration
810 + enables efficient thermal transport from surface Au atoms to the
811 + capping agents. Simultaneously, as shown in the lower panel of
812 + Fig. \ref{vibration}, the large overlap of the vibration spectra of
813 + butanethiol and hexane in the all-atom model, including the C-H
814 + vibration, also suggests high thermal exchange efficiency. The
815 + combination of these two effects produces the drastic interfacial
816 + thermal conductance enhancement in the all-atom model.
817 +
818 + [MAY NEED TO CONVERT TO JPEG]
819   \begin{figure}
820   \includegraphics[width=\linewidth]{vibration}
821   \caption{Vibrational spectra obtained for gold in different
# Line 520 | Line 823 | interfacial thermal conductance enhancement in the all
823    all-atom model (lower panel).}
824   \label{vibration}
825   \end{figure}
523 – % 600dpi, letter size. too large?
826  
827 + [COMPARISON OF TWO G'S; AU SLAB WIDTHS; ETC]
828 + % The results show that the two definitions used for $G$ yield
829 + % comparable values, though $G^\prime$ tends to be smaller.
830  
831 + \section{Conclusions}
832 + The NIVS algorithm we developed has been applied to simulations of
833 + Au-butanethiol surfaces with organic solvents. This algorithm allows
834 + effective unphysical thermal flux transferred between the metal and
835 + the liquid phase. With the flux applied, we were able to measure the
836 + corresponding thermal gradient and to obtain interfacial thermal
837 + conductivities. Our simulations have seen significant conductance
838 + enhancement with the presence of capping agent, compared to the bare
839 + gold/liquid interfaces. The acoustic impedance mismatch between the
840 + metal and the liquid phase is effectively eliminated by proper capping
841 + agent. Furthermore, the coverage precentage of the capping agent plays
842 + an important role in the interfacial thermal transport process.
843 +
844 + Our measurement results, particularly of the UA models, agree with
845 + available experimental data. This indicates that our force field
846 + parameters have a nice description of the interactions between the
847 + particles at the interfaces. AA models tend to overestimate the
848 + interfacial thermal conductance in that the classically treated C-H
849 + vibration would be overly sampled. Compared to the AA models, the UA
850 + models have higher computational efficiency with satisfactory
851 + accuracy, and thus are preferable in interfacial thermal transport
852 + modelings.
853 +
854 + Vlugt {\it et al.} has investigated the surface thiol structures for
855 + nanocrystal gold and pointed out that they differs from those of the
856 + Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to
857 + change of interfacial thermal transport behavior as well. To
858 + investigate this problem, an effective means to introduce thermal flux
859 + and measure the corresponding thermal gradient is desirable for
860 + simulating structures with spherical symmetry.
861 +
862 +
863   \section{Acknowledgments}
864   Support for this project was provided by the National Science
865   Foundation under grant CHE-0848243. Computational time was provided by
866   the Center for Research Computing (CRC) at the University of Notre
867 < Dame.  \newpage
867 > Dame. \newpage
868  
869   \bibliography{interfacial}
870  

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