211 |
|
\label{gradT} |
212 |
|
\end{figure} |
213 |
|
|
214 |
+ |
[MAY INCLUDE POWER SPECTRUM PROTOCOL] |
215 |
+ |
|
216 |
|
\section{Computational Details} |
217 |
< |
\subsection{System Geometry} |
217 |
> |
\subsection{Simulation Protocol} |
218 |
|
In our simulations, Au is used to construct a metal slab with bare |
219 |
|
(111) surface perpendicular to the $z$-axis. Different slab thickness |
220 |
|
(layer numbers of Au) are simulated. This metal slab is first |
242 |
|
interactions do not disrupt the simulations. Two solvents are |
243 |
|
investigated, one which has little vibrational overlap with the |
244 |
|
alkanethiol and plane-like shape (toluene), and one which has similar |
245 |
< |
vibrational frequencies and chain-like shape ({\it n}-hexane). The |
246 |
< |
spacing filled by solvent molecules, i.e. the gap between periodically |
247 |
< |
repeated Au-butanethiol surfaces should be carefully chosen so that it |
248 |
< |
would not be too short to affect the liquid phase structure, nor too |
249 |
< |
long, leading to over cooling (freezing) or heating (boiling) when a |
250 |
< |
thermal flux is applied. In our simulations, this spacing is usually |
251 |
< |
$35 \sim 60$\AA. |
245 |
> |
vibrational frequencies and chain-like shape ({\it n}-hexane). [MAY |
246 |
> |
EXPLAIN WHY WE CHOOSE THEM] |
247 |
> |
|
248 |
> |
The spacing filled by solvent molecules, i.e. the gap between |
249 |
> |
periodically repeated Au-butanethiol surfaces should be carefully |
250 |
> |
chosen. A very long length scale for the thermal gradient axis ($z$) |
251 |
> |
may cause excessively hot or cold temperatures in the middle of the |
252 |
> |
solvent region and lead to undesired phenomena such as solvent boiling |
253 |
> |
or freezing when a thermal flux is applied. Conversely, too few |
254 |
> |
solvent molecules would change the normal behavior of the liquid |
255 |
> |
phase. Therefore, our $N_{solvent}$ values were chosen to ensure that |
256 |
> |
these extreme cases did not happen to our simulations. And the |
257 |
> |
corresponding spacing is usually $35 \sim 60$\AA. |
258 |
|
|
259 |
|
The initial configurations generated by Packmol are further |
260 |
|
equilibrated with the $x$ and $y$ dimensions fixed, only allowing |
295 |
|
reparametrized for accurate surface energies compared to the |
296 |
|
Sutton-Chen potentials\cite{Chen90}. |
297 |
|
|
298 |
+ |
Figure [REF] demonstrates how we name our pseudo-atoms of the |
299 |
+ |
molecules in our simulations. |
300 |
+ |
[FIGURE FOR MOLECULE NOMENCLATURE] |
301 |
+ |
|
302 |
|
For both solvent molecules, straight chain {\it n}-hexane and aromatic |
303 |
|
toluene, United-Atom (UA) and All-Atom (AA) models are used |
304 |
|
respectively. The TraPPE-UA |
312 |
|
to a system, the temperature of ``hot'' area in the liquid phase would be |
313 |
|
significantly higher than the average, to prevent over heating and |
314 |
|
boiling of the liquid phase, the average temperature in our |
315 |
< |
simulations should be much lower than the liquid boiling point. [NEED MORE DISCUSSION] |
315 |
> |
simulations should be much lower than the liquid boiling point. [MORE DISCUSSION] |
316 |
|
For UA-toluene model, rigid body constraints are applied, so that the |
317 |
< |
benzene ring and the methyl-C(aromatic) bond are kept rigid. This |
318 |
< |
would save computational time.[MORE DETAILS NEEDED] |
317 |
> |
benzene ring and the methyl-CRar bond are kept rigid. This would save |
318 |
> |
computational time.[MORE DETAILS] |
319 |
|
|
320 |
|
Besides the TraPPE-UA models, AA models for both organic solvents are |
321 |
< |
included in our studies as well. For hexane, the OPLS |
322 |
< |
all-atom\cite{OPLSAA} force field is used. [MORE DETAILS] |
321 |
> |
included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA} |
322 |
> |
force field is used. [MORE DETAILS] |
323 |
|
For toluene, the United Force Field developed by Rapp\'{e} {\it et |
324 |
|
al.}\cite{doi:10.1021/ja00051a040} is adopted.[MORE DETAILS] |
325 |
|
|
326 |
|
The capping agent in our simulations, the butanethiol molecules can |
327 |
|
either use UA or AA model. The TraPPE-UA force fields includes |
328 |
< |
parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used in |
329 |
< |
our simulations corresponding to our TraPPE-UA models for solvent. |
330 |
< |
and All-Atom models [NEED CITATIONS] |
331 |
< |
However, the model choice (UA or AA) of capping agent can be different |
332 |
< |
from the solvent. Regardless of model choice, the force field |
333 |
< |
parameters for interactions between capping agent and solvent can be |
334 |
< |
derived using Lorentz-Berthelot Mixing Rule. |
328 |
> |
parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used for |
329 |
> |
UA butanethiol model in our simulations. The OPLS-AA also provides |
330 |
> |
parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111) |
331 |
> |
surfaces do not have the hydrogen atom bonded to sulfur. To adapt this |
332 |
> |
change and derive suitable parameters for butanethiol adsorbed on |
333 |
> |
Au(111) surfaces, we adopt the S parameters from [CITATION CF VLUGT] |
334 |
> |
and modify parameters for its neighbor C atom for charge balance in |
335 |
> |
the molecule. Note that the model choice (UA or AA) of capping agent |
336 |
> |
can be different from the solvent. Regardless of model choice, the |
337 |
> |
force field parameters for interactions between capping agent and |
338 |
> |
solvent can be derived using Lorentz-Berthelot Mixing Rule: |
339 |
|
|
340 |
+ |
|
341 |
|
To describe the interactions between metal Au and non-metal capping |
342 |
< |
agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive |
343 |
< |
other interactions which are not yet finely parametrized. [can add |
344 |
< |
hautman and klein's paper here and more discussion; need to put |
345 |
< |
aromatic-metal interaction approximation here]\cite{doi:10.1021/jp034405s} |
342 |
> |
agent and solvent particles, we refer to an adsorption study of alkyl |
343 |
> |
thiols on gold surfaces by Vlugt {\it et |
344 |
> |
al.}\cite{vlugt:cpc2007154} They fitted an effective Lennard-Jones |
345 |
> |
form of potential parameters for the interaction between Au and |
346 |
> |
pseudo-atoms CH$_x$ and S based on a well-established and widely-used |
347 |
> |
effective potential of Hautman and Klein[CITATION] for the Au(111) |
348 |
> |
surface. As our simulations require the gold lattice slab to be |
349 |
> |
non-rigid so that it could accommodate kinetic energy for thermal |
350 |
> |
transport study purpose, the pair-wise form of potentials is |
351 |
> |
preferred. |
352 |
|
|
353 |
< |
[TABULATED FORCE FIELD PARAMETERS NEEDED] |
353 |
> |
Besides, the potentials developed from {\it ab initio} calculations by |
354 |
> |
Leng {\it et al.}\cite{doi:10.1021/jp034405s} are adopted for the |
355 |
> |
interactions between Au and aromatic C/H atoms in toluene.[MORE DETAILS] |
356 |
|
|
357 |
+ |
However, the Lennard-Jones parameters between Au and other types of |
358 |
+ |
particles in our simulations are not yet well-established. For these |
359 |
+ |
interactions, we attempt to derive their parameters using the Mixing |
360 |
+ |
Rule. To do this, the ``Metal-non-Metal'' (MnM) interaction parameters |
361 |
+ |
for Au is first extracted from the Au-CH$_x$ parameters by applying |
362 |
+ |
the Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM'' |
363 |
+ |
parameters in our simulations. |
364 |
|
|
365 |
< |
[SURFACE RECONSTRUCTION PREVENTS SIMULATION TEMP TO GO HIGHER] |
365 |
> |
\begin{table*} |
366 |
> |
\begin{minipage}{\linewidth} |
367 |
> |
\begin{center} |
368 |
> |
\caption{Lennard-Jones parameters for Au-non-Metal |
369 |
> |
interactions in our simulations.} |
370 |
> |
|
371 |
> |
\begin{tabular}{ccc} |
372 |
> |
\hline\hline |
373 |
> |
Non-metal & $\sigma$/\AA & $\epsilon$/kcal/mol \\ |
374 |
> |
\hline |
375 |
> |
S & 2.40 & 8.465 \\ |
376 |
> |
CH3 & 3.54 & 0.2146 \\ |
377 |
> |
CH2 & 3.54 & 0.1749 \\ |
378 |
> |
CT3 & 3.365 & 0.1373 \\ |
379 |
> |
CT2 & 3.365 & 0.1373 \\ |
380 |
> |
CTT & 3.365 & 0.1373 \\ |
381 |
> |
HC & 2.865 & 0.09256 \\ |
382 |
> |
CHar & 3.4625 & 0.1680 \\ |
383 |
> |
CRar & 3.555 & 0.1604 \\ |
384 |
> |
CA & 3.173 & 0.0640 \\ |
385 |
> |
HA & 2.746 & 0.0414 \\ |
386 |
> |
\hline\hline |
387 |
> |
\end{tabular} |
388 |
> |
\label{MnM} |
389 |
> |
\end{center} |
390 |
> |
\end{minipage} |
391 |
> |
\end{table*} |
392 |
|
|
393 |
|
|
394 |
< |
\section{Results} |
395 |
< |
[REARRANGEMENT NEEDED] |
396 |
< |
\subsection{Toluene Solvent} |
394 |
> |
\section{Results and Discussions} |
395 |
> |
[MAY HAVE A BRIEF SUMMARY] |
396 |
> |
\subsection{How Simulation Parameters Affects $G$} |
397 |
> |
[MAY NOT PUT AT FIRST] |
398 |
> |
We have varied our protocol or other parameters of the simulations in |
399 |
> |
order to investigate how these factors would affect the measurement of |
400 |
> |
$G$'s. It turned out that while some of these parameters would not |
401 |
> |
affect the results substantially, some other changes to the |
402 |
> |
simulations would have a significant impact on the measurement |
403 |
> |
results. |
404 |
|
|
405 |
< |
The results (Table \ref{AuThiolToluene}) show a |
406 |
< |
significant conductance enhancement compared to the gold/water |
407 |
< |
interface without capping agent and agree with available experimental |
408 |
< |
data. This indicates that the metal-metal potential, though not |
409 |
< |
predicting an accurate bulk metal thermal conductivity, does not |
410 |
< |
greatly interfere with the simulation of the thermal conductance |
411 |
< |
behavior across a non-metal interface. The solvent model is not |
412 |
< |
particularly volatile, so the simulation cell does not expand |
413 |
< |
significantly under higher temperature. We did not observe a |
414 |
< |
significant conductance decrease when the temperature was increased to |
415 |
< |
300K. The results show that the two definitions used for $G$ yield |
416 |
< |
comparable values, though $G^\prime$ tends to be smaller. |
405 |
> |
In some of our simulations, we allowed $L_x$ and $L_y$ to change |
406 |
> |
during equilibrating the liquid phase. Due to the stiffness of the Au |
407 |
> |
slab, $L_x$ and $L_y$ would not change noticeably after |
408 |
> |
equilibration. Although $L_z$ could fluctuate $\sim$1\% after a system |
409 |
> |
is fully equilibrated in the NPT ensemble, this fluctuation, as well |
410 |
> |
as those comparably smaller to $L_x$ and $L_y$, would not be magnified |
411 |
> |
on the calculated $G$'s, as shown in Table \ref{AuThiolHexaneUA}. This |
412 |
> |
insensivity to $L_i$ fluctuations allows reliable measurement of $G$'s |
413 |
> |
without the necessity of extremely cautious equilibration process. |
414 |
> |
|
415 |
> |
As stated in our computational details, the spacing filled with |
416 |
> |
solvent molecules can be chosen within a range. This allows some |
417 |
> |
change of solvent molecule numbers for the same Au-butanethiol |
418 |
> |
surfaces. We did this study on our Au-butanethiol/hexane |
419 |
> |
simulations. Nevertheless, the results obtained from systems of |
420 |
> |
different $N_{hexane}$ did not indicate that the measurement of $G$ is |
421 |
> |
susceptible to this parameter. For computational efficiency concern, |
422 |
> |
smaller system size would be preferable, given that the liquid phase |
423 |
> |
structure is not affected. |
424 |
> |
|
425 |
> |
Our NIVS algorithm allows change of unphysical thermal flux both in |
426 |
> |
direction and in quantity. This feature extends our investigation of |
427 |
> |
interfacial thermal conductance. However, the magnitude of this |
428 |
> |
thermal flux is not arbitary if one aims to obtain a stable and |
429 |
> |
reliable thermal gradient. A temperature profile would be |
430 |
> |
substantially affected by noise when $|J_z|$ has a much too low |
431 |
> |
magnitude; while an excessively large $|J_z|$ that overwhelms the |
432 |
> |
conductance capacity of the interface would prevent a thermal gradient |
433 |
> |
to reach a stablized steady state. NIVS has the advantage of allowing |
434 |
> |
$J$ to vary in a wide range such that the optimal flux range for $G$ |
435 |
> |
measurement can generally be simulated by the algorithm. Within the |
436 |
> |
optimal range, we were able to study how $G$ would change according to |
437 |
> |
the thermal flux across the interface. For our simulations, we denote |
438 |
> |
$J_z$ to be positive when the physical thermal flux is from the liquid |
439 |
> |
to metal, and negative vice versa. The $G$'s measured under different |
440 |
> |
$J_z$ is listed in Table \ref{AuThiolHexaneUA} and [REF]. These |
441 |
> |
results do not suggest that $G$ is dependent on $J_z$ within this flux |
442 |
> |
range. The linear response of flux to thermal gradient simplifies our |
443 |
> |
investigations in that we can rely on $G$ measurement with only a |
444 |
> |
couple $J_z$'s and do not need to test a large series of fluxes. |
445 |
|
|
446 |
+ |
%ADD MORE TO TABLE |
447 |
|
\begin{table*} |
448 |
|
\begin{minipage}{\linewidth} |
449 |
|
\begin{center} |
450 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
451 |
+ |
$G^\prime$) values for the Au/butanethiol/hexane interface |
452 |
+ |
with united-atom model and different capping agent coverage |
453 |
+ |
and solvent molecule numbers at different temperatures using a |
454 |
+ |
range of energy fluxes.} |
455 |
+ |
|
456 |
+ |
\begin{tabular}{cccccc} |
457 |
+ |
\hline\hline |
458 |
+ |
Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\ |
459 |
+ |
coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) & |
460 |
+ |
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
461 |
+ |
\hline |
462 |
+ |
0.0 & 200 & 200 & 0.96 & 43.3 & 42.7 \\ |
463 |
+ |
& & & 1.91 & 45.7 & 42.9 \\ |
464 |
+ |
& & 166 & 0.96 & 43.1 & 53.4 \\ |
465 |
+ |
88.9 & 200 & 166 & 1.94 & 172 & 108 \\ |
466 |
+ |
100.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\ |
467 |
+ |
& & 166 & 0.98 & 79.0 & 62.9 \\ |
468 |
+ |
& & & 1.44 & 76.2 & 64.8 \\ |
469 |
+ |
& 200 & 200 & 1.92 & 129 & 87.3 \\ |
470 |
+ |
& & & 1.93 & 131 & 77.5 \\ |
471 |
+ |
& & 166 & 0.97 & 115 & 69.3 \\ |
472 |
+ |
& & & 1.94 & 125 & 87.1 \\ |
473 |
+ |
\hline\hline |
474 |
+ |
\end{tabular} |
475 |
+ |
\label{AuThiolHexaneUA} |
476 |
+ |
\end{center} |
477 |
+ |
\end{minipage} |
478 |
+ |
\end{table*} |
479 |
+ |
|
480 |
+ |
Furthermore, we also attempted to increase system average temperatures |
481 |
+ |
to above 200K. These simulations are first equilibrated in the NPT |
482 |
+ |
ensemble under normal pressure. As stated above, the TraPPE-UA model |
483 |
+ |
for hexane tends to predict a lower boiling point. In our simulations, |
484 |
+ |
hexane had diffculty to remain in liquid phase when NPT equilibration |
485 |
+ |
temperature is higher than 250K. Additionally, the equilibrated liquid |
486 |
+ |
hexane density under 250K becomes lower than experimental value. This |
487 |
+ |
expanded liquid phase leads to lower contact between hexane and |
488 |
+ |
butanethiol as well.[MAY NEED FIGURE] And this reduced contact would |
489 |
+ |
probably be accountable for a lower interfacial thermal conductance, |
490 |
+ |
as shown in Table \ref{AuThiolHexaneUA}. |
491 |
+ |
|
492 |
+ |
A similar study for TraPPE-UA toluene agrees with the above result as |
493 |
+ |
well. Having a higher boiling point, toluene tends to remain liquid in |
494 |
+ |
our simulations even equilibrated under 300K in NPT |
495 |
+ |
ensembles. Furthermore, the expansion of the toluene liquid phase is |
496 |
+ |
not as significant as that of the hexane. This prevents severe |
497 |
+ |
decrease of liquid-capping agent contact and the results (Table |
498 |
+ |
\ref{AuThiolToluene}) show only a slightly decreased interface |
499 |
+ |
conductance. Therefore, solvent-capping agent contact should play an |
500 |
+ |
important role in the thermal transport process across the interface |
501 |
+ |
in that higher degree of contact could yield increased conductance. |
502 |
+ |
|
503 |
+ |
[ADD SIGNS AND ERROR ESTIMATE TO TABLE] |
504 |
+ |
\begin{table*} |
505 |
+ |
\begin{minipage}{\linewidth} |
506 |
+ |
\begin{center} |
507 |
+ |
\caption{Computed interfacial thermal conductivity ($G$ and |
508 |
|
$G^\prime$) values for the Au/butanethiol/toluene interface at |
509 |
|
different temperatures using a range of energy fluxes.} |
510 |
|
|
525 |
|
\end{minipage} |
526 |
|
\end{table*} |
527 |
|
|
528 |
< |
\subsection{Hexane Solvent} |
528 |
> |
Besides lower interfacial thermal conductance, surfaces in relatively |
529 |
> |
high temperatures are susceptible to reconstructions, when |
530 |
> |
butanethiols have a full coverage on the Au(111) surface. These |
531 |
> |
reconstructions include surface Au atoms migrated outward to the S |
532 |
> |
atom layer, and butanethiol molecules embedded into the original |
533 |
> |
surface Au layer. The driving force for this behavior is the strong |
534 |
> |
Au-S interactions in our simulations. And these reconstructions lead |
535 |
> |
to higher ratio of Au-S attraction and thus is energetically |
536 |
> |
favorable. Furthermore, this phenomenon agrees with experimental |
537 |
> |
results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt |
538 |
> |
{\it et al.} had kept their Au(111) slab rigid so that their |
539 |
> |
simulations can reach 300K without surface reconstructions. Without |
540 |
> |
this practice, simulating 100\% thiol covered interfaces under higher |
541 |
> |
temperatures could hardly avoid surface reconstructions. However, our |
542 |
> |
measurement is based on assuming homogeneity on $x$ and $y$ dimensions |
543 |
> |
so that measurement of $T$ at particular $z$ would be an effective |
544 |
> |
average of the particles of the same type. Since surface |
545 |
> |
reconstructions could eliminate the original $x$ and $y$ dimensional |
546 |
> |
homogeneity, measurement of $G$ is more difficult to conduct under |
547 |
> |
higher temperatures. Therefore, most of our measurements are |
548 |
> |
undertaken at $<T>\sim$200K. |
549 |
|
|
550 |
< |
Using the united-atom model, different coverages of capping agent, |
551 |
< |
temperatures of simulations and numbers of solvent molecules were all |
552 |
< |
investigated and Table \ref{AuThiolHexaneUA} shows the results of |
553 |
< |
these computations. The number of hexane molecules in our simulations |
554 |
< |
does not affect the calculations significantly. However, a very long |
555 |
< |
length scale for the thermal gradient axis ($z$) may cause excessively |
556 |
< |
hot or cold temperatures in the middle of the solvent region and lead |
557 |
< |
to undesired phenomena such as solvent boiling or freezing, while too |
558 |
< |
few solvent molecules would change the normal behavior of the liquid |
559 |
< |
phase. Our $N_{hexane}$ values were chosen to ensure that these |
389 |
< |
extreme cases did not happen to our simulations. |
550 |
> |
However, when the surface is not completely covered by butanethiols, |
551 |
> |
the simulated system is more resistent to the reconstruction |
552 |
> |
above. Our Au-butanethiol/toluene system did not see this phenomena |
553 |
> |
even at $<T>\sim$300K. The Au(111) surfaces have a 90\% coverage of |
554 |
> |
butanethiols and have empty three-fold sites. These empty sites could |
555 |
> |
help prevent surface reconstruction in that they provide other means |
556 |
> |
of capping agent relaxation. It is observed that butanethiols can |
557 |
> |
migrate to their neighbor empty sites during a simulation. Therefore, |
558 |
> |
we were able to obtain $G$'s for these interfaces even at a relatively |
559 |
> |
high temperature without being affected by surface reconstructions. |
560 |
|
|
561 |
< |
Table \ref{AuThiolHexaneUA} enables direct comparison between |
562 |
< |
different coverages of capping agent, when other system parameters are |
563 |
< |
held constant. With high coverage of butanethiol on the gold surface, |
561 |
> |
\subsection{Influence of Capping Agent Coverage on $G$} |
562 |
> |
To investigate the influence of butanethiol coverage on interfacial |
563 |
> |
thermal conductance, a series of different coverage Au-butanethiol |
564 |
> |
surfaces is prepared and solvated with various organic |
565 |
> |
molecules. These systems are then equilibrated and their interfacial |
566 |
> |
thermal conductivity are measured with our NIVS algorithm. Table |
567 |
> |
\ref{tlnUhxnUhxnD} lists these results for direct comparison between |
568 |
> |
different coverages of butanethiol. |
569 |
> |
|
570 |
> |
With high coverage of butanethiol on the gold surface, |
571 |
|
the interfacial thermal conductance is enhanced |
572 |
|
significantly. Interestingly, a slightly lower butanethiol coverage |
573 |
|
leads to a moderately higher conductivity. This is probably due to |
574 |
|
more solvent/capping agent contact when butanethiol molecules are |
575 |
|
not densely packed, which enhances the interactions between the two |
576 |
|
phases and lowers the thermal transfer barrier of this interface. |
577 |
< |
% [COMPARE TO AU/WATER IN PAPER] |
577 |
> |
[COMPARE TO AU/WATER IN PAPER] |
578 |
|
|
402 |
– |
It is also noted that the overall simulation temperature is another |
403 |
– |
factor that affects the interfacial thermal conductance. One |
404 |
– |
possibility of this effect may be rooted in the decrease in density of |
405 |
– |
the liquid phase. We observed that when the average temperature |
406 |
– |
increases from 200K to 250K, the bulk hexane density becomes lower |
407 |
– |
than experimental value, as the system is equilibrated under NPT |
408 |
– |
ensemble. This leads to lower contact between solvent and capping |
409 |
– |
agent, and thus lower conductivity. |
579 |
|
|
580 |
< |
Conductivity values are more difficult to obtain under higher |
581 |
< |
temperatures. This is because the Au surface tends to undergo |
582 |
< |
reconstructions in relatively high temperatures. Surface Au atoms can |
583 |
< |
migrate outward to reach higher Au-S contact; and capping agent |
584 |
< |
molecules can be embedded into the surface Au layer due to the same |
585 |
< |
driving force. This phenomenon agrees with experimental |
586 |
< |
results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. A surface |
587 |
< |
fully covered in capping agent is more susceptible to reconstruction, |
419 |
< |
possibly because fully coverage prevents other means of capping agent |
420 |
< |
relaxation, such as migration to an empty neighbor three-fold site. |
580 |
> |
significant conductance enhancement compared to the gold/water |
581 |
> |
interface without capping agent and agree with available experimental |
582 |
> |
data. This indicates that the metal-metal potential, though not |
583 |
> |
predicting an accurate bulk metal thermal conductivity, does not |
584 |
> |
greatly interfere with the simulation of the thermal conductance |
585 |
> |
behavior across a non-metal interface. |
586 |
> |
The results show that the two definitions used for $G$ yield |
587 |
> |
comparable values, though $G^\prime$ tends to be smaller. |
588 |
|
|
589 |
< |
%MAY ADD MORE DATA TO TABLE |
589 |
> |
|
590 |
|
\begin{table*} |
591 |
|
\begin{minipage}{\linewidth} |
592 |
|
\begin{center} |
615 |
|
& & & 1.94 & 125 & 87.1 \\ |
616 |
|
\hline\hline |
617 |
|
\end{tabular} |
618 |
< |
\label{AuThiolHexaneUA} |
618 |
> |
\label{tlnUhxnUhxnD} |
619 |
|
\end{center} |
620 |
|
\end{minipage} |
621 |
|
\end{table*} |
622 |
|
|
623 |
+ |
\subsection{Influence of Chosen Molecule Model on $G$} |
624 |
+ |
[MAY COMBINE W MECHANISM STUDY] |
625 |
+ |
|
626 |
|
For the all-atom model, the liquid hexane phase was not stable under NPT |
627 |
|
conditions. Therefore, the simulation length scale parameters are |
628 |
|
adopted from previous equilibration results of the united-atom model |
665 |
|
\end{minipage} |
666 |
|
\end{table*} |
667 |
|
|
668 |
+ |
|
669 |
+ |
\subsection{Mechanism of Interfacial Thermal Conductance Enhancement |
670 |
+ |
by Capping Agent} |
671 |
+ |
[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL] |
672 |
+ |
|
673 |
+ |
|
674 |
|
%subsubsection{Vibrational spectrum study on conductance mechanism} |
675 |
|
To investigate the mechanism of this interfacial thermal conductance, |
676 |
|
the vibrational spectra of various gold systems were obtained and are |
696 |
|
all-atom model (lower panel).} |
697 |
|
\label{vibration} |
698 |
|
\end{figure} |
699 |
< |
% 600dpi, letter size. too large? |
699 |
> |
% MAY NEED TO CONVERT TO JPEG |
700 |
|
|
701 |
+ |
\section{Conclusions} |
702 |
|
|
703 |
+ |
|
704 |
+ |
[NECESSITY TO STUDY THERMAL CONDUCTANCE IN NANOCRYSTAL STRUCTURE]\cite{vlugt:cpc2007154} |
705 |
+ |
|
706 |
|
\section{Acknowledgments} |
707 |
|
Support for this project was provided by the National Science |
708 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
709 |
|
the Center for Research Computing (CRC) at the University of Notre |
710 |
< |
Dame. \newpage |
710 |
> |
Dame. \newpage |
711 |
|
|
712 |
|
\bibliography{interfacial} |
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|
|