| 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} |
| 451 |
> |
$G^\prime$) values for the 100\% covered Au-butanethiol/hexane |
| 452 |
> |
interfaces with UA model and different hexane molecule numbers |
| 453 |
> |
at different temperatures using a range of energy fluxes.} |
| 454 |
> |
|
| 455 |
> |
\begin{tabular}{cccccccc} |
| 456 |
|
\hline\hline |
| 457 |
< |
Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\ |
| 458 |
< |
coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) & |
| 457 |
> |
$\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ & |
| 458 |
> |
$G$ & $G^\prime$ \\ |
| 459 |
> |
(K) & $N_{hexane}$ & \multicolumn{3}{c}\AA & (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 \\ |
| 462 |
> |
200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 & |
| 463 |
> |
102() & 80.0() \\ |
| 464 |
> |
& 200 & 29.84 & 25.81 & 93.9 & 1.92 & |
| 465 |
> |
129() & 87.3() \\ |
| 466 |
> |
& & 29.84 & 25.81 & 95.3 & 1.93 & |
| 467 |
> |
131() & 77.5() \\ |
| 468 |
> |
& 166 & 29.84 & 25.81 & 85.7 & 0.97 & |
| 469 |
> |
115() & 69.3() \\ |
| 470 |
> |
& & & & & 1.94 & |
| 471 |
> |
125() & 87.1() \\ |
| 472 |
> |
250 & 200 & 29.84 & 25.87 & 106.8 & 0.96 & |
| 473 |
> |
81.8() & 67.0() \\ |
| 474 |
> |
& 166 & 29.87 & 25.84 & 94.8 & 0.98 & |
| 475 |
> |
79.0() & 62.9() \\ |
| 476 |
> |
& & 29.84 & 25.85 & 95.0 & 1.44 & |
| 477 |
> |
76.2() & 64.8() \\ |
| 478 |
|
\hline\hline |
| 479 |
|
\end{tabular} |
| 480 |
|
\label{AuThiolHexaneUA} |
| 505 |
|
important role in the thermal transport process across the interface |
| 506 |
|
in that higher degree of contact could yield increased conductance. |
| 507 |
|
|
| 508 |
< |
[ADD SIGNS AND ERROR ESTIMATE TO TABLE] |
| 508 |
> |
[ADD Lxyz AND ERROR ESTIMATE TO TABLE] |
| 509 |
|
\begin{table*} |
| 510 |
|
\begin{minipage}{\linewidth} |
| 511 |
|
\begin{center} |
| 512 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
| 513 |
< |
$G^\prime$) values for the Au/butanethiol/toluene interface at |
| 514 |
< |
different temperatures using a range of energy fluxes.} |
| 513 |
> |
$G^\prime$) values for a 90\% coverage Au-butanethiol/toluene |
| 514 |
> |
interface at different temperatures using a range of energy |
| 515 |
> |
fluxes.} |
| 516 |
|
|
| 517 |
|
\begin{tabular}{cccc} |
| 518 |
|
\hline\hline |
| 519 |
|
$\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\ |
| 520 |
|
(K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 521 |
|
\hline |
| 522 |
< |
200 & 1.86 & 180 & 135 \\ |
| 523 |
< |
& 2.15 & 204 & 113 \\ |
| 524 |
< |
& 3.93 & 175 & 114 \\ |
| 525 |
< |
300 & 1.91 & 143 & 125 \\ |
| 526 |
< |
& 4.19 & 134 & 113 \\ |
| 522 |
> |
200 & -1.86 & 180() & 135() \\ |
| 523 |
> |
& 2.15 & 204() & 113() \\ |
| 524 |
> |
& -3.93 & 175() & 114() \\ |
| 525 |
> |
300 & -1.91 & 143() & 125() \\ |
| 526 |
> |
& -4.19 & 134() & 113() \\ |
| 527 |
|
\hline\hline |
| 528 |
|
\end{tabular} |
| 529 |
|
\label{AuThiolToluene} |
| 571 |
|
molecules. These systems are then equilibrated and their interfacial |
| 572 |
|
thermal conductivity are measured with our NIVS algorithm. Table |
| 573 |
|
\ref{tlnUhxnUhxnD} lists these results for direct comparison between |
| 574 |
< |
different coverages of butanethiol. |
| 574 |
> |
different coverages of butanethiol. To study the isotope effect in |
| 575 |
> |
interfacial thermal conductance, deuterated UA-hexane is included as |
| 576 |
> |
well. |
| 577 |
|
|
| 578 |
< |
With high coverage of butanethiol on the gold surface, |
| 579 |
< |
the interfacial thermal conductance is enhanced |
| 580 |
< |
significantly. Interestingly, a slightly lower butanethiol coverage |
| 581 |
< |
leads to a moderately higher conductivity. This is probably due to |
| 582 |
< |
more solvent/capping agent contact when butanethiol molecules are |
| 583 |
< |
not densely packed, which enhances the interactions between the two |
| 584 |
< |
phases and lowers the thermal transfer barrier of this interface. |
| 577 |
< |
[COMPARE TO AU/WATER IN PAPER] |
| 578 |
> |
It turned out that with partial covered butanethiol on the Au(111) |
| 579 |
> |
surface, the derivative definition for $G$ (Eq. \ref{derivativeG}) has |
| 580 |
> |
difficulty to apply, due to the difficulty in locating the maximum of |
| 581 |
> |
change of $\lambda$. Instead, the discrete definition |
| 582 |
> |
(Eq. \ref{discreteG}) is easier to apply, as max($\Delta T$) can still |
| 583 |
> |
be well-defined. Therefore, $G$'s (not $G^\prime$) are used for this |
| 584 |
> |
section. |
| 585 |
|
|
| 586 |
+ |
From Table \ref{tlnUhxnUhxnD}, one can see the significance of the |
| 587 |
+ |
presence of capping agents. Even when a fraction of the Au(111) |
| 588 |
+ |
surface sites are covered with butanethiols, the conductivity would |
| 589 |
+ |
see an enhancement by at least a factor of 3. This indicates the |
| 590 |
+ |
important role cappping agent is playing for thermal transport |
| 591 |
+ |
phenomena on metal/organic solvent surfaces. |
| 592 |
|
|
| 593 |
< |
significant conductance enhancement compared to the gold/water |
| 594 |
< |
interface without capping agent and agree with available experimental |
| 595 |
< |
data. This indicates that the metal-metal potential, though not |
| 596 |
< |
predicting an accurate bulk metal thermal conductivity, does not |
| 597 |
< |
greatly interfere with the simulation of the thermal conductance |
| 598 |
< |
behavior across a non-metal interface. |
| 599 |
< |
The results show that the two definitions used for $G$ yield |
| 600 |
< |
comparable values, though $G^\prime$ tends to be smaller. |
| 593 |
> |
Interestingly, as one could observe from our results, the maximum |
| 594 |
> |
conductance enhancement (largest $G$) happens while the surfaces are |
| 595 |
> |
about 75\% covered with butanethiols. This again indicates that |
| 596 |
> |
solvent-capping agent contact has an important role of the thermal |
| 597 |
> |
transport process. Slightly lower butanethiol coverage allows small |
| 598 |
> |
gaps between butanethiols to form. And these gaps could be filled with |
| 599 |
> |
solvent molecules, which acts like ``heat conductors'' on the |
| 600 |
> |
surface. The higher degree of interaction between these solvent |
| 601 |
> |
molecules and capping agents increases the enhancement effect and thus |
| 602 |
> |
produces a higher $G$ than densely packed butanethiol arrays. However, |
| 603 |
> |
once this maximum conductance enhancement is reached, $G$ decreases |
| 604 |
> |
when butanethiol coverage continues to decrease. Each capping agent |
| 605 |
> |
molecule reaches its maximum capacity for thermal |
| 606 |
> |
conductance. Therefore, even higher solvent-capping agent contact |
| 607 |
> |
would not offset this effect. Eventually, when butanethiol coverage |
| 608 |
> |
continues to decrease, solvent-capping agent contact actually |
| 609 |
> |
decreases with the disappearing of butanethiol molecules. In this |
| 610 |
> |
case, $G$ decrease could not be offset but instead accelerated. |
| 611 |
|
|
| 612 |
+ |
A comparison of the results obtained from differenet organic solvents |
| 613 |
+ |
can also provide useful information of the interfacial thermal |
| 614 |
+ |
transport process. The deuterated hexane (UA) results do not appear to |
| 615 |
+ |
be much different from those of normal hexane (UA), given that |
| 616 |
+ |
butanethiol (UA) is non-deuterated for both solvents. These UA model |
| 617 |
+ |
studies, even though eliminating C-H vibration samplings, still have |
| 618 |
+ |
C-C vibrational frequencies different from each other. However, these |
| 619 |
+ |
differences in the IR range do not seem to produce an observable |
| 620 |
+ |
difference for the results of $G$. [MAY NEED FIGURE] |
| 621 |
|
|
| 622 |
+ |
Furthermore, results for rigid body toluene solvent, as well as other |
| 623 |
+ |
UA-hexane solvents, are reasonable within the general experimental |
| 624 |
+ |
ranges[CITATIONS]. This suggests that explicit hydrogen might not be a |
| 625 |
+ |
required factor for modeling thermal transport phenomena of systems |
| 626 |
+ |
such as Au-thiol/organic solvent. |
| 627 |
+ |
|
| 628 |
+ |
However, results for Au-butanethiol/toluene do not show an identical |
| 629 |
+ |
trend with those for Au-butanethiol/hexane in that $G$'s remain at |
| 630 |
+ |
approximately the same magnitue when butanethiol coverage differs from |
| 631 |
+ |
25\% to 75\%. This might be rooted in the molecule shape difference |
| 632 |
+ |
for plane-like toluene and chain-like {\it n}-hexane. Due to this |
| 633 |
+ |
difference, toluene molecules have more difficulty in occupying |
| 634 |
+ |
relatively small gaps among capping agents when their coverage is not |
| 635 |
+ |
too low. Therefore, the solvent-capping agent contact may keep |
| 636 |
+ |
increasing until the capping agent coverage reaches a relatively low |
| 637 |
+ |
level. This becomes an offset for decreasing butanethiol molecules on |
| 638 |
+ |
its effect to the process of interfacial thermal transport. Thus, one |
| 639 |
+ |
can see a plateau of $G$ vs. butanethiol coverage in our results. |
| 640 |
+ |
|
| 641 |
+ |
[NEED ERROR ESTIMATE, MAY ALSO PUT J HERE] |
| 642 |
|
\begin{table*} |
| 643 |
|
\begin{minipage}{\linewidth} |
| 644 |
|
\begin{center} |
| 645 |
< |
\caption{Computed interfacial thermal conductivity ($G$ and |
| 646 |
< |
$G^\prime$) values for the Au/butanethiol/hexane interface |
| 647 |
< |
with united-atom model and different capping agent coverage |
| 648 |
< |
and solvent molecule numbers at different temperatures using a |
| 597 |
< |
range of energy fluxes.} |
| 645 |
> |
\caption{Computed interfacial thermal conductivity ($G$ in |
| 646 |
> |
MW/m$^2$/K) values for the Au-butanethiol/solvent interface |
| 647 |
> |
with various UA models and different capping agent coverages |
| 648 |
> |
at $<T>\sim$200K using certain energy flux respectively.} |
| 649 |
|
|
| 650 |
< |
\begin{tabular}{cccccc} |
| 650 |
> |
\begin{tabular}{cccc} |
| 651 |
|
\hline\hline |
| 652 |
< |
Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\ |
| 653 |
< |
coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) & |
| 603 |
< |
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 652 |
> |
Thiol & & & \\ |
| 653 |
> |
coverage (\%) & hexane & hexane-D & toluene \\ |
| 654 |
|
\hline |
| 655 |
< |
0.0 & 200 & 200 & 0.96 & 43.3 & 42.7 \\ |
| 656 |
< |
& & & 1.91 & 45.7 & 42.9 \\ |
| 657 |
< |
& & 166 & 0.96 & 43.1 & 53.4 \\ |
| 658 |
< |
88.9 & 200 & 166 & 1.94 & 172 & 108 \\ |
| 659 |
< |
100.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\ |
| 660 |
< |
& & 166 & 0.98 & 79.0 & 62.9 \\ |
| 611 |
< |
& & & 1.44 & 76.2 & 64.8 \\ |
| 612 |
< |
& 200 & 200 & 1.92 & 129 & 87.3 \\ |
| 613 |
< |
& & & 1.93 & 131 & 77.5 \\ |
| 614 |
< |
& & 166 & 0.97 & 115 & 69.3 \\ |
| 615 |
< |
& & & 1.94 & 125 & 87.1 \\ |
| 655 |
> |
0.0 & 46.5 & 43.9 & 70.1 \\ |
| 656 |
> |
25.0 & 151 & 153 & 249 \\ |
| 657 |
> |
50.0 & 172 & 182 & 214 \\ |
| 658 |
> |
75.0 & 242 & 229 & 244 \\ |
| 659 |
> |
88.9 & 178 & - & - \\ |
| 660 |
> |
100.0 & 137 & 153 & 187 \\ |
| 661 |
|
\hline\hline |
| 662 |
|
\end{tabular} |
| 663 |
|
\label{tlnUhxnUhxnD} |
| 711 |
|
\end{table*} |
| 712 |
|
|
| 713 |
|
|
| 714 |
+ |
significant conductance enhancement compared to the gold/water |
| 715 |
+ |
interface without capping agent and agree with available experimental |
| 716 |
+ |
data. This indicates that the metal-metal potential, though not |
| 717 |
+ |
predicting an accurate bulk metal thermal conductivity, does not |
| 718 |
+ |
greatly interfere with the simulation of the thermal conductance |
| 719 |
+ |
behavior across a non-metal interface. |
| 720 |
+ |
|
| 721 |
+ |
% The results show that the two definitions used for $G$ yield |
| 722 |
+ |
% comparable values, though $G^\prime$ tends to be smaller. |
| 723 |
+ |
|
| 724 |
|
\subsection{Mechanism of Interfacial Thermal Conductance Enhancement |
| 725 |
|
by Capping Agent} |
| 726 |
|
[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL] |
