| 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 |
< |
initial configurations generated by Packmol are further equilibrated |
| 245 |
< |
with the $x$ and $y$ dimensions fixed, only allowing length scale |
| 246 |
< |
change in $z$ dimension. This is to ensure that the equilibration of |
| 247 |
< |
liquid phase does not affect the metal crystal structure in $x$ and |
| 248 |
< |
$y$ dimensions. Further equilibration are run under NVT and then NVE ensembles. |
| 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 |
| 261 |
+ |
length scale change in $z$ dimension. This is to ensure that the |
| 262 |
+ |
equilibration of liquid phase does not affect the metal crystal |
| 263 |
+ |
structure in $x$ and $y$ dimensions. Further equilibration are run |
| 264 |
+ |
under NVT and then NVE ensembles. |
| 265 |
+ |
|
| 266 |
|
After the systems reach equilibrium, NIVS is implemented to impose a |
| 267 |
|
periodic unphysical thermal flux between the metal and the liquid |
| 268 |
< |
phase. Most of our simulations have this flux from the metal to the |
| 268 |
> |
phase. Most of our simulations are under an average temperature of |
| 269 |
> |
$\sim$200K. Therefore, this flux usually comes from the metal to the |
| 270 |
|
liquid so that the liquid has a higher temperature and would not |
| 271 |
|
freeze due to excessively low temperature. This induced temperature |
| 272 |
|
gradient is stablized and the simulation cell is devided evenly into |
| 284 |
|
\label{derivativeG2} |
| 285 |
|
\end{equation} |
| 286 |
|
|
| 270 |
– |
|
| 287 |
|
\subsection{Force Field Parameters} |
| 288 |
+ |
Our simulations include various components. Therefore, force field |
| 289 |
+ |
parameter descriptions are needed for interactions both between the |
| 290 |
+ |
same type of particles and between particles of different species. |
| 291 |
|
|
| 292 |
|
The Au-Au interactions in metal lattice slab is described by the |
| 293 |
|
quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC |
| 295 |
|
reparametrized for accurate surface energies compared to the |
| 296 |
|
Sutton-Chen potentials\cite{Chen90}. |
| 297 |
|
|
| 298 |
< |
Straight chain {\it n}-hexane and aromatic toluene are respectively |
| 299 |
< |
used as solvents. For hexane, both United-Atom\cite{TraPPE-UA.alkanes} |
| 300 |
< |
and All-Atom\cite{OPLSAA} force fields are used for comparison; for |
| 282 |
< |
toluene, United-Atom\cite{TraPPE-UA.alkylbenzenes} force fields are |
| 283 |
< |
used with rigid body constraints applied. (maybe needs more details |
| 284 |
< |
about rigid body) |
| 285 |
< |
|
| 286 |
< |
Buatnethiol molecules are used as capping agent for some of our |
| 287 |
< |
simulations. United-Atom\cite{TraPPE-UA.thiols} and All-Atom models |
| 288 |
< |
are respectively used corresponding to the force field type of |
| 289 |
< |
solvent. |
| 298 |
> |
Figure [REF] demonstrates how we name our pseudo-atoms of the |
| 299 |
> |
molecules in our simulations. |
| 300 |
> |
[FIGURE FOR MOLECULE NOMENCLATURE] |
| 301 |
|
|
| 302 |
< |
To describe the interactions between metal Au and non-metal capping |
| 303 |
< |
agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive |
| 304 |
< |
other interactions which are not parametrized in their work. (can add |
| 305 |
< |
hautman and klein's paper here and more discussion; need to put |
| 306 |
< |
aromatic-metal interaction approximation here) |
| 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 |
| 305 |
> |
parameters\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} are used |
| 306 |
> |
for our UA solvent molecules. In these models, pseudo-atoms are |
| 307 |
> |
located at the carbon centers for alkyl groups. By eliminating |
| 308 |
> |
explicit hydrogen atoms, these models are simple and computationally |
| 309 |
> |
efficient, while maintains good accuracy. However, the TraPPE-UA for |
| 310 |
> |
alkanes is known to predict a lower boiling point than experimental |
| 311 |
> |
values. Considering that after an unphysical thermal flux is applied |
| 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. [MORE DISCUSSION] |
| 316 |
> |
For UA-toluene model, rigid body constraints are applied, so that the |
| 317 |
> |
benzene ring and the methyl-CRar bond are kept rigid. This would save |
| 318 |
> |
computational time.[MORE DETAILS] |
| 319 |
|
|
| 320 |
< |
[TABULATED FORCE FIELD PARAMETERS NEEDED] |
| 320 |
> |
Besides the TraPPE-UA models, AA models for both organic solvents are |
| 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 |
< |
\section{Results} |
| 327 |
< |
\subsection{Toluene Solvent} |
| 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 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 |
< |
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. |
| 340 |
> |
|
| 341 |
> |
To describe the interactions between metal Au and non-metal capping |
| 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 |
> |
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 |
> |
\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 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 |
> |
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 |
| 351 |
< |
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 |
|
|
| 364 |
– |
It is also noted that the overall simulation temperature is another |
| 365 |
– |
factor that affects the interfacial thermal conductance. One |
| 366 |
– |
possibility of this effect may be rooted in the decrease in density of |
| 367 |
– |
the liquid phase. We observed that when the average temperature |
| 368 |
– |
increases from 200K to 250K, the bulk hexane density becomes lower |
| 369 |
– |
than experimental value, as the system is equilibrated under NPT |
| 370 |
– |
ensemble. This leads to lower contact between solvent and capping |
| 371 |
– |
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, |
| 381 |
< |
possibly because fully coverage prevents other means of capping agent |
| 382 |
< |
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} |
| 713 |
|
|
