| 104 |
|
this phenomena at the molecular level. Recently, Hase and coworkers |
| 105 |
|
employed Non-Equilibrium Molecular Dynamics (NEMD) simulations to |
| 106 |
|
study thermal transport from hot Au(111) substrate to a self-assembled |
| 107 |
< |
monolayer of alkylthiolate with relatively long chain (8-20 carbon |
| 107 |
> |
monolayer of alkylthiol with relatively long chain (8-20 carbon |
| 108 |
|
atoms)\cite{hase:2010,hase:2011}. However, ensemble averaged |
| 109 |
|
measurements for heat conductance of interfaces between the capping |
| 110 |
|
monolayer on Au and a solvent phase has yet to be studied. |
| 111 |
< |
The relatively low thermal flux through interfaces is |
| 111 |
> |
The comparatively low thermal flux through interfaces is |
| 112 |
|
difficult to measure with Equilibrium MD or forward NEMD simulation |
| 113 |
|
methods. Therefore, the Reverse NEMD (RNEMD) methods would have the |
| 114 |
|
advantage of having this difficult to measure flux known when studying |
| 375 |
|
(UA or AA) of capping agent can be different from the |
| 376 |
|
solvent. Regardless of model choice, the force field parameters for |
| 377 |
|
interactions between capping agent and solvent can be derived using |
| 378 |
< |
Lorentz-Berthelot Mixing Rule:[EQN'S] |
| 379 |
< |
|
| 378 |
> |
Lorentz-Berthelot Mixing Rule: |
| 379 |
> |
\begin{eqnarray} |
| 380 |
> |
\sigma_{IJ} & = & \frac{1}{2} \left(\sigma_{II} + \sigma_{JJ}\right) \\ |
| 381 |
> |
\epsilon_{IJ} & = & \sqrt{\epsilon_{II}\epsilon_{JJ}} |
| 382 |
> |
\end{eqnarray} |
| 383 |
|
|
| 384 |
|
To describe the interactions between metal Au and non-metal capping |
| 385 |
|
agent and solvent particles, we refer to an adsorption study of alkyl |
| 408 |
|
\begin{table*} |
| 409 |
|
\begin{minipage}{\linewidth} |
| 410 |
|
\begin{center} |
| 411 |
< |
\caption{Lennard-Jones parameters for Au-non-Metal |
| 412 |
< |
interactions in our simulations.} |
| 413 |
< |
|
| 414 |
< |
\begin{tabular}{ccc} |
| 411 |
> |
\caption{Non-bonded interaction paramters for non-metal |
| 412 |
> |
particles and metal-non-metal interactions in our |
| 413 |
> |
simulations.} |
| 414 |
> |
|
| 415 |
> |
\begin{tabular}{cccccc} |
| 416 |
|
\hline\hline |
| 417 |
< |
Non-metal atom & $\sigma$ & $\epsilon$ \\ |
| 418 |
< |
(or pseudo-atom) & \AA & kcal/mol \\ |
| 417 |
> |
Non-metal atom $I$ & $\sigma_{II}$ & $\epsilon_{II}$ & $q_I$ & |
| 418 |
> |
$\sigma_{AuI}$ & $\epsilon_{AuI}$ \\ |
| 419 |
> |
(or pseudo-atom) & \AA & kcal/mol & & \AA & kcal/mol \\ |
| 420 |
|
\hline |
| 421 |
< |
S & 2.40 & 8.465 \\ |
| 422 |
< |
CH3 & 3.54 & 0.2146 \\ |
| 423 |
< |
CH2 & 3.54 & 0.1749 \\ |
| 424 |
< |
CT3 & 3.365 & 0.1373 \\ |
| 425 |
< |
CT2 & 3.365 & 0.1373 \\ |
| 426 |
< |
CTT & 3.365 & 0.1373 \\ |
| 427 |
< |
HC & 2.865 & 0.09256 \\ |
| 428 |
< |
CHar & 3.4625 & 0.1680 \\ |
| 429 |
< |
CRar & 3.555 & 0.1604 \\ |
| 430 |
< |
CA & 3.173 & 0.0640 \\ |
| 431 |
< |
HA & 2.746 & 0.0414 \\ |
| 421 |
> |
CH3 & 3.75 & 0.1947 & - & 3.54 & 0.2146 \\ |
| 422 |
> |
CH2 & 3.95 & 0.0914 & - & 3.54 & 0.1749 \\ |
| 423 |
> |
CHar & 3.695 & 0.1003 & - & 3.4625 & 0.1680 \\ |
| 424 |
> |
CRar & 3.88 & 0.04173 & - & 3.555 & 0.1604 \\ |
| 425 |
> |
S & 4.45 & 0.25 & - & 2.40 & 8.465 \\ |
| 426 |
> |
CT3 & 3.50 & 0.066 & -0.18 & 3.365 & 0.1373 \\ |
| 427 |
> |
CT2 & 3.50 & 0.066 & -0.12 & 3.365 & 0.1373 \\ |
| 428 |
> |
CTT & 3.50 & 0.066 & -0.065 & 3.365 & 0.1373 \\ |
| 429 |
> |
HC & 2.50 & 0.030 & 0.06 & 2.865 & 0.09256 \\ |
| 430 |
> |
CA & 3.55 & 0.070 & -0.115 & 3.173 & 0.0640 \\ |
| 431 |
> |
HA & 2.42 & 0.030 & 0.115 & 2.746 & 0.0414 \\ |
| 432 |
|
\hline\hline |
| 433 |
|
\end{tabular} |
| 434 |
|
\label{MnM} |
| 498 |
|
interfaces with UA model and different hexane molecule numbers |
| 499 |
|
at different temperatures using a range of energy fluxes.} |
| 500 |
|
|
| 501 |
< |
\begin{tabular}{cccccccc} |
| 501 |
> |
\begin{tabular}{ccccccc} |
| 502 |
|
\hline\hline |
| 503 |
< |
$\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ & |
| 504 |
< |
$G$ & $G^\prime$ \\ |
| 505 |
< |
(K) & $N_{hexane}$ & \multicolumn{3}{c}{(\AA)} & (GW/m$^2$) & |
| 503 |
> |
$\langle T\rangle$ & $N_{hexane}$ & Fixed & $\rho_{hexane}$ & |
| 504 |
> |
$J_z$ & $G$ & $G^\prime$ \\ |
| 505 |
> |
(K) & & $L_x$ \& $L_y$? & (g/cm$^3$) & (GW/m$^2$) & |
| 506 |
|
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 507 |
|
\hline |
| 508 |
< |
200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 & |
| 509 |
< |
102() & 80.0() \\ |
| 510 |
< |
& 200 & 29.84 & 25.81 & 93.9 & 1.92 & |
| 511 |
< |
129() & 87.3() \\ |
| 512 |
< |
& & 29.84 & 25.81 & 95.3 & 1.93 & |
| 513 |
< |
131() & 77.5() \\ |
| 514 |
< |
& 166 & 29.84 & 25.81 & 85.7 & 0.97 & |
| 515 |
< |
115() & 69.3() \\ |
| 516 |
< |
& & & & & 1.94 & |
| 517 |
< |
125() & 87.1() \\ |
| 518 |
< |
250 & 200 & 29.84 & 25.87 & 106.8 & 0.96 & |
| 519 |
< |
81.8() & 67.0() \\ |
| 520 |
< |
& 166 & 29.87 & 25.84 & 94.8 & 0.98 & |
| 521 |
< |
79.0() & 62.9() \\ |
| 522 |
< |
& & 29.84 & 25.85 & 95.0 & 1.44 & |
| 523 |
< |
76.2() & 64.8() \\ |
| 508 |
> |
200 & 266 & No & 0.672 & -0.96 & 102() & 80.0() \\ |
| 509 |
> |
& 200 & Yes & 0.694 & 1.92 & 129() & 87.3() \\ |
| 510 |
> |
& & Yes & 0.672 & 1.93 & 131() & 77.5() \\ |
| 511 |
> |
& & No & 0.688 & 0.96 & 125() & 90.2() \\ |
| 512 |
> |
& & & & 1.91 & 139() & 101() \\ |
| 513 |
> |
& & & & 2.83 & 141() & 89.9() \\ |
| 514 |
> |
& 166 & Yes & 0.679 & 0.97 & 115() & 69.3() \\ |
| 515 |
> |
& & & & 1.94 & 125() & 87.1() \\ |
| 516 |
> |
& & No & 0.681 & 0.97 & 141() & 77.7() \\ |
| 517 |
> |
& & & & 1.92 & 138() & 98.9() \\ |
| 518 |
> |
\hline |
| 519 |
> |
250 & 200 & No & 0.560 & 0.96 & 74.8() & 61.8() \\ |
| 520 |
> |
& & & & -0.95 & 49.4() & 45.7() \\ |
| 521 |
> |
& 166 & Yes & 0.570 & 0.98 & 79.0() & 62.9() \\ |
| 522 |
> |
& & No & 0.569 & 0.97 & 80.3() & 67.1() \\ |
| 523 |
> |
& & & & 1.44 & 76.2() & 64.8() \\ |
| 524 |
> |
& & & & -0.95 & 56.4() & 54.4() \\ |
| 525 |
> |
& & & & -1.85 & 47.8() & 53.5() \\ |
| 526 |
|
\hline\hline |
| 527 |
|
\end{tabular} |
| 528 |
|
\label{AuThiolHexaneUA} |
| 553 |
|
important role in the thermal transport process across the interface |
| 554 |
|
in that higher degree of contact could yield increased conductance. |
| 555 |
|
|
| 556 |
< |
[ADD Lxyz AND ERROR ESTIMATE TO TABLE] |
| 556 |
> |
[ADD ERROR ESTIMATE TO TABLE] |
| 557 |
|
\begin{table*} |
| 558 |
|
\begin{minipage}{\linewidth} |
| 559 |
|
\begin{center} |
| 562 |
|
interface at different temperatures using a range of energy |
| 563 |
|
fluxes.} |
| 564 |
|
|
| 565 |
< |
\begin{tabular}{cccc} |
| 565 |
> |
\begin{tabular}{ccccc} |
| 566 |
|
\hline\hline |
| 567 |
< |
$\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\ |
| 568 |
< |
(K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 567 |
> |
$\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\ |
| 568 |
> |
(K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 569 |
|
\hline |
| 570 |
< |
200 & -1.86 & 180() & 135() \\ |
| 571 |
< |
& 2.15 & 204() & 113() \\ |
| 572 |
< |
& -3.93 & 175() & 114() \\ |
| 573 |
< |
300 & -1.91 & 143() & 125() \\ |
| 574 |
< |
& -4.19 & 134() & 113() \\ |
| 570 |
> |
200 & 0.933 & -1.86 & 180() & 135() \\ |
| 571 |
> |
& & 2.15 & 204() & 113() \\ |
| 572 |
> |
& & -3.93 & 175() & 114() \\ |
| 573 |
> |
\hline |
| 574 |
> |
300 & 0.855 & -1.91 & 143() & 125() \\ |
| 575 |
> |
& & -4.19 & 134() & 113() \\ |
| 576 |
|
\hline\hline |
| 577 |
|
\end{tabular} |
| 578 |
|
\label{AuThiolToluene} |
| 605 |
|
However, when the surface is not completely covered by butanethiols, |
| 606 |
|
the simulated system is more resistent to the reconstruction |
| 607 |
|
above. Our Au-butanethiol/toluene system did not see this phenomena |
| 608 |
< |
even at $\langle T\rangle\sim$300K. The Au(111) surfaces have a 90\% coverage of |
| 609 |
< |
butanethiols and have empty three-fold sites. These empty sites could |
| 610 |
< |
help prevent surface reconstruction in that they provide other means |
| 611 |
< |
of capping agent relaxation. It is observed that butanethiols can |
| 612 |
< |
migrate to their neighbor empty sites during a simulation. Therefore, |
| 613 |
< |
we were able to obtain $G$'s for these interfaces even at a relatively |
| 614 |
< |
high temperature without being affected by surface reconstructions. |
| 608 |
> |
even at $\langle T\rangle\sim$300K. The Au(111) surfaces have a 90\% |
| 609 |
> |
coverage of butanethiols and have empty three-fold sites. These empty |
| 610 |
> |
sites could help prevent surface reconstruction in that they provide |
| 611 |
> |
other means of capping agent relaxation. It is observed that |
| 612 |
> |
butanethiols can migrate to their neighbor empty sites during a |
| 613 |
> |
simulation. Therefore, we were able to obtain $G$'s for these |
| 614 |
> |
interfaces even at a relatively high temperature without being |
| 615 |
> |
affected by surface reconstructions. |
| 616 |
|
|
| 617 |
|
\subsection{Influence of Capping Agent Coverage on $G$} |
| 618 |
|
To investigate the influence of butanethiol coverage on interfacial |
| 688 |
|
its effect to the process of interfacial thermal transport. Thus, one |
| 689 |
|
can see a plateau of $G$ vs. butanethiol coverage in our results. |
| 690 |
|
|
| 691 |
< |
[NEED ERROR ESTIMATE, MAY ALSO PUT J HERE] |
| 692 |
< |
\begin{table*} |
| 693 |
< |
\begin{minipage}{\linewidth} |
| 694 |
< |
\begin{center} |
| 695 |
< |
\caption{Computed interfacial thermal conductivity ($G$) values |
| 696 |
< |
for the Au-butanethiol/solvent interface with various UA |
| 697 |
< |
models and different capping agent coverages at $\langle |
| 698 |
< |
T\rangle\sim$200K using certain energy flux respectively.} |
| 699 |
< |
|
| 691 |
< |
\begin{tabular}{cccc} |
| 692 |
< |
\hline\hline |
| 693 |
< |
Thiol & \multicolumn{3}{c}{$G$(MW/m$^2$/K)} \\ |
| 694 |
< |
coverage (\%) & hexane & hexane(D) & toluene \\ |
| 695 |
< |
\hline |
| 696 |
< |
0.0 & 46.5() & 43.9() & 70.1() \\ |
| 697 |
< |
25.0 & 151() & 153() & 249() \\ |
| 698 |
< |
50.0 & 172() & 182() & 214() \\ |
| 699 |
< |
75.0 & 242() & 229() & 244() \\ |
| 700 |
< |
88.9 & 178() & - & - \\ |
| 701 |
< |
100.0 & 137() & 153() & 187() \\ |
| 702 |
< |
\hline\hline |
| 703 |
< |
\end{tabular} |
| 704 |
< |
\label{tlnUhxnUhxnD} |
| 705 |
< |
\end{center} |
| 706 |
< |
\end{minipage} |
| 707 |
< |
\end{table*} |
| 691 |
> |
[NEED ERROR ESTIMATE] |
| 692 |
> |
\begin{figure} |
| 693 |
> |
\includegraphics[width=\linewidth]{coverage} |
| 694 |
> |
\caption{Comparison of interfacial thermal conductivity ($G$) values |
| 695 |
> |
for the Au-butanethiol/solvent interface with various UA models and |
| 696 |
> |
different capping agent coverages at $\langle T\rangle\sim$200K |
| 697 |
> |
using certain energy flux respectively.} |
| 698 |
> |
\label{coverage} |
| 699 |
> |
\end{figure} |
| 700 |
|
|
| 701 |
|
\subsection{Influence of Chosen Molecule Model on $G$} |
| 702 |
|
[MAY COMBINE W MECHANISM STUDY] |
| 717 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
| 718 |
|
$G^\prime$) values for interfaces using various models for |
| 719 |
|
solvent and capping agent (or without capping agent) at |
| 720 |
< |
$\langle T\rangle\sim$200K.} |
| 720 |
> |
$\langle T\rangle\sim$200K. (D stands for deuterated solvent |
| 721 |
> |
or capping agent molecules; ``Avg.'' denotes results that are |
| 722 |
> |
averages of several simulations.)} |
| 723 |
|
|
| 724 |
|
\begin{tabular}{ccccc} |
| 725 |
|
\hline\hline |
| 727 |
|
(or bare surface) & model & (GW/m$^2$) & |
| 728 |
|
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 729 |
|
\hline |
| 730 |
< |
UA & AA hexane & 1.94 & 135() & 129() \\ |
| 731 |
< |
& & 2.86 & 126() & 115() \\ |
| 732 |
< |
& AA toluene & 1.89 & 200() & 149() \\ |
| 733 |
< |
AA & UA hexane & 1.94 & 116() & 129() \\ |
| 734 |
< |
& AA hexane & 3.76 & 451() & 378() \\ |
| 735 |
< |
& & 4.71 & 432() & 334() \\ |
| 736 |
< |
& AA toluene & 3.79 & 487() & 290() \\ |
| 737 |
< |
AA(D) & UA hexane & 1.94 & 158() & 172() \\ |
| 738 |
< |
bare & AA hexane & 0.96 & 31.0() & 29.4() \\ |
| 730 |
> |
UA & UA hexane & Avg. & 131() & 86.5() \\ |
| 731 |
> |
& UA hexane(D) & 1.95 & 153() & 136() \\ |
| 732 |
> |
& AA hexane & 1.94 & 135() & 129() \\ |
| 733 |
> |
& & 2.86 & 126() & 115() \\ |
| 734 |
> |
& UA toluene & 1.96 & 187() & 151() \\ |
| 735 |
> |
& AA toluene & 1.89 & 200() & 149() \\ |
| 736 |
> |
\hline |
| 737 |
> |
AA & UA hexane & 1.94 & 116() & 129() \\ |
| 738 |
> |
& AA hexane & Avg. & 442() & 356() \\ |
| 739 |
> |
& AA hexane(D) & 1.93 & 222() & 234() \\ |
| 740 |
> |
& UA toluene & 1.98 & 125() & 96.5() \\ |
| 741 |
> |
& AA toluene & 3.79 & 487() & 290() \\ |
| 742 |
> |
\hline |
| 743 |
> |
AA(D) & UA hexane & 1.94 & 158() & 172() \\ |
| 744 |
> |
& AA hexane & 1.92 & 243() & 191() \\ |
| 745 |
> |
& AA toluene & 1.93 & 364() & 322() \\ |
| 746 |
> |
\hline |
| 747 |
> |
bare & UA hexane & Avg. & 46.5() & 49.4() \\ |
| 748 |
> |
& UA hexane(D) & 0.98 & 43.9() & 43.0() \\ |
| 749 |
> |
& AA hexane & 0.96 & 31.0() & 29.4() \\ |
| 750 |
> |
& UA toluene & 1.99 & 70.1() & 65.8() \\ |
| 751 |
|
\hline\hline |
| 752 |
|
\end{tabular} |
| 753 |
|
\label{modelTest} |
| 784 |
|
|
| 785 |
|
However, for Au-butanethiol/toluene interfaces, having the AA |
| 786 |
|
butanethiol deuterated did not yield a significant change in the |
| 787 |
< |
measurement results. |
| 788 |
< |
. , so extra degrees of freedom |
| 789 |
< |
such as the C-H vibrations could enhance heat exchange between these |
| 790 |
< |
two phases and result in a much higher conductivity. |
| 787 |
> |
measurement results. Compared to the C-H vibrational overlap between |
| 788 |
> |
hexane and butanethiol, both of which have alkyl chains, that overlap |
| 789 |
> |
between toluene and butanethiol is not so significant and thus does |
| 790 |
> |
not have as much contribution to the ``Intramolecular Vibration |
| 791 |
> |
Redistribution''[CITE HASE]. Conversely, extra degrees of freedom such |
| 792 |
> |
as the C-H vibrations could yield higher heat exchange rate between |
| 793 |
> |
these two phases and result in a much higher conductivity. |
| 794 |
|
|
| 786 |
– |
|
| 795 |
|
Although the QSC model for Au is known to predict an overly low value |
| 796 |
< |
for bulk metal gold conductivity[CITE NIVSRNEMD], our computational |
| 796 |
> |
for bulk metal gold conductivity\cite{kuang:164101}, our computational |
| 797 |
|
results for $G$ and $G^\prime$ do not seem to be affected by this |
| 798 |
< |
drawback of the model for metal. Instead, the modeling of interfacial |
| 799 |
< |
thermal transport behavior relies mainly on an accurate description of |
| 800 |
< |
the interactions between components occupying the interfaces. |
| 798 |
> |
drawback of the model for metal. Instead, our results suggest that the |
| 799 |
> |
modeling of interfacial thermal transport behavior relies mainly on |
| 800 |
> |
the accuracy of the interaction descriptions between components |
| 801 |
> |
occupying the interfaces. |
| 802 |
|
|
| 803 |
|
\subsection{Mechanism of Interfacial Thermal Conductance Enhancement |
| 804 |
|
by Capping Agent} |
| 814 |
|
the velocity auto-correlation functions, which is used to construct a |
| 815 |
|
power spectrum via a Fourier transform. |
| 816 |
|
|
| 817 |
+ |
[MAY RELATE TO HASE'S] |
| 818 |
|
The gold surfaces covered by |
| 819 |
|
butanethiol molecules, compared to bare gold surfaces, exhibit an |
| 820 |
|
additional peak observed at a frequency of $\sim$170cm$^{-1}$, which |
| 827 |
|
combination of these two effects produces the drastic interfacial |
| 828 |
|
thermal conductance enhancement in the all-atom model. |
| 829 |
|
|
| 830 |
< |
[MAY NEED TO CONVERT TO JPEG] |
| 830 |
> |
[REDO. MAY NEED TO CONVERT TO JPEG] |
| 831 |
|
\begin{figure} |
| 832 |
|
\includegraphics[width=\linewidth]{vibration} |
| 833 |
|
\caption{Vibrational spectra obtained for gold in different |
