| 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 |
|
|
| 372 |
|
|
| 373 |
|
\begin{tabular}{ccc} |
| 374 |
|
\hline\hline |
| 375 |
< |
Non-metal & $\sigma$/\AA & $\epsilon$/kcal/mol \\ |
| 375 |
> |
Non-metal atom & $\sigma$ & $\epsilon$ \\ |
| 376 |
> |
(or pseudo-atom) & \AA & kcal/mol \\ |
| 377 |
|
\hline |
| 378 |
|
S & 2.40 & 8.465 \\ |
| 379 |
|
CH3 & 3.54 & 0.2146 \\ |
| 459 |
|
\hline\hline |
| 460 |
|
$\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ & |
| 461 |
|
$G$ & $G^\prime$ \\ |
| 462 |
< |
(K) & $N_{hexane}$ & \multicolumn{3}{c}\AA & (GW/m$^2$) & |
| 462 |
> |
(K) & $N_{hexane}$ & \multicolumn{3}{c}{(\AA)} & (GW/m$^2$) & |
| 463 |
|
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 464 |
|
\hline |
| 465 |
|
200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 & |
| 554 |
|
reconstructions could eliminate the original $x$ and $y$ dimensional |
| 555 |
|
homogeneity, measurement of $G$ is more difficult to conduct under |
| 556 |
|
higher temperatures. Therefore, most of our measurements are |
| 557 |
< |
undertaken at $<T>\sim$200K. |
| 557 |
> |
undertaken at $\langle T\rangle\sim$200K. |
| 558 |
|
|
| 559 |
|
However, when the surface is not completely covered by butanethiols, |
| 560 |
|
the simulated system is more resistent to the reconstruction |
| 619 |
|
butanethiol (UA) is non-deuterated for both solvents. These UA model |
| 620 |
|
studies, even though eliminating C-H vibration samplings, still have |
| 621 |
|
C-C vibrational frequencies different from each other. However, these |
| 622 |
< |
differences in the IR range do not seem to produce an observable |
| 622 |
> |
differences in the infrared range do not seem to produce an observable |
| 623 |
|
difference for the results of $G$. [MAY NEED FIGURE] |
| 624 |
|
|
| 625 |
|
Furthermore, results for rigid body toluene solvent, as well as other |
| 645 |
|
\begin{table*} |
| 646 |
|
\begin{minipage}{\linewidth} |
| 647 |
|
\begin{center} |
| 648 |
< |
\caption{Computed interfacial thermal conductivity ($G$ in |
| 649 |
< |
MW/m$^2$/K) values for the Au-butanethiol/solvent interface |
| 650 |
< |
with various UA models and different capping agent coverages |
| 651 |
< |
at $<T>\sim$200K using certain energy flux respectively.} |
| 648 |
> |
\caption{Computed interfacial thermal conductivity ($G$) values |
| 649 |
> |
for the Au-butanethiol/solvent interface with various UA |
| 650 |
> |
models and different capping agent coverages at $\langle |
| 651 |
> |
T\rangle\sim$200K using certain energy flux respectively.} |
| 652 |
|
|
| 653 |
|
\begin{tabular}{cccc} |
| 654 |
|
\hline\hline |
| 655 |
< |
Thiol & & & \\ |
| 656 |
< |
coverage (\%) & hexane & hexane-D & toluene \\ |
| 655 |
> |
Thiol & \multicolumn{3}{c}{$G$(MW/m$^2$/K)} \\ |
| 656 |
> |
coverage (\%) & hexane & hexane(D) & toluene \\ |
| 657 |
|
\hline |
| 658 |
< |
0.0 & 46.5 & 43.9 & 70.1 \\ |
| 659 |
< |
25.0 & 151 & 153 & 249 \\ |
| 660 |
< |
50.0 & 172 & 182 & 214 \\ |
| 661 |
< |
75.0 & 242 & 229 & 244 \\ |
| 662 |
< |
88.9 & 178 & - & - \\ |
| 663 |
< |
100.0 & 137 & 153 & 187 \\ |
| 658 |
> |
0.0 & 46.5() & 43.9() & 70.1() \\ |
| 659 |
> |
25.0 & 151() & 153() & 249() \\ |
| 660 |
> |
50.0 & 172() & 182() & 214() \\ |
| 661 |
> |
75.0 & 242() & 229() & 244() \\ |
| 662 |
> |
88.9 & 178() & - & - \\ |
| 663 |
> |
100.0 & 137() & 153() & 187() \\ |
| 664 |
|
\hline\hline |
| 665 |
|
\end{tabular} |
| 666 |
|
\label{tlnUhxnUhxnD} |
| 671 |
|
\subsection{Influence of Chosen Molecule Model on $G$} |
| 672 |
|
[MAY COMBINE W MECHANISM STUDY] |
| 673 |
|
|
| 674 |
< |
For the all-atom model, the liquid hexane phase was not stable under NPT |
| 675 |
< |
conditions. Therefore, the simulation length scale parameters are |
| 676 |
< |
adopted from previous equilibration results of the united-atom model |
| 677 |
< |
at 200K. Table \ref{AuThiolHexaneAA} shows the results of these |
| 678 |
< |
simulations. The conductivity values calculated with full capping |
| 679 |
< |
agent coverage are substantially larger than observed in the |
| 680 |
< |
united-atom model, and is even higher than predicted by |
| 678 |
< |
experiments. It is possible that our parameters for metal-non-metal |
| 679 |
< |
particle interactions lead to an overestimate of the interfacial |
| 680 |
< |
thermal conductivity, although the active C-H vibrations in the |
| 681 |
< |
all-atom model (which should not be appreciably populated at normal |
| 682 |
< |
temperatures) could also account for this high conductivity. The major |
| 683 |
< |
thermal transfer barrier of Au/butanethiol/hexane interface is between |
| 684 |
< |
the liquid phase and the capping agent, so extra degrees of freedom |
| 685 |
< |
such as the C-H vibrations could enhance heat exchange between these |
| 686 |
< |
two phases and result in a much higher conductivity. |
| 674 |
> |
In addition to UA solvent/capping agent models, AA models are included |
| 675 |
> |
in our simulations as well. Besides simulations of the same (UA or AA) |
| 676 |
> |
model for solvent and capping agent, different models can be applied |
| 677 |
> |
to different components. Furthermore, regardless of models chosen, |
| 678 |
> |
either the solvent or the capping agent can be deuterated, similar to |
| 679 |
> |
the previous section. Table \ref{modelTest} summarizes the results of |
| 680 |
> |
these studies. |
| 681 |
|
|
| 682 |
+ |
[MORE DATA; ERROR ESTIMATE] |
| 683 |
|
\begin{table*} |
| 684 |
|
\begin{minipage}{\linewidth} |
| 685 |
|
\begin{center} |
| 686 |
|
|
| 687 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
| 688 |
< |
$G^\prime$) values for the Au/butanethiol/hexane interface |
| 689 |
< |
with all-atom model and different capping agent coverage at |
| 690 |
< |
200K using a range of energy fluxes.} |
| 688 |
> |
$G^\prime$) values for interfaces using various models for |
| 689 |
> |
solvent and capping agent (or without capping agent) at |
| 690 |
> |
$\langle T\rangle\sim$200K.} |
| 691 |
|
|
| 692 |
< |
\begin{tabular}{cccc} |
| 692 |
> |
\begin{tabular}{ccccc} |
| 693 |
|
\hline\hline |
| 694 |
< |
Thiol & $J_z$ & $G$ & $G^\prime$ \\ |
| 695 |
< |
coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 694 |
> |
Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\ |
| 695 |
> |
(or bare surface) & model & (GW/m$^2$) & |
| 696 |
> |
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 697 |
|
\hline |
| 698 |
< |
0.0 & 0.95 & 28.5 & 27.2 \\ |
| 699 |
< |
& 1.88 & 30.3 & 28.9 \\ |
| 700 |
< |
100.0 & 2.87 & 551 & 294 \\ |
| 701 |
< |
& 3.81 & 494 & 193 \\ |
| 698 |
> |
UA & AA hexane & 1.94 & 135() & 129() \\ |
| 699 |
> |
& & 2.86 & 126() & 115() \\ |
| 700 |
> |
& AA toluene & 1.89 & 200() & 149() \\ |
| 701 |
> |
AA & UA hexane & 1.94 & 116() & 129() \\ |
| 702 |
> |
& AA hexane & 3.76 & 451() & 378() \\ |
| 703 |
> |
& & 4.71 & 432() & 334() \\ |
| 704 |
> |
& AA toluene & 3.79 & 487() & 290() \\ |
| 705 |
> |
AA(D) & UA hexane & 1.94 & 158() & 172() \\ |
| 706 |
> |
bare & AA hexane & 0.96 & 31.0() & 29.4() \\ |
| 707 |
|
\hline\hline |
| 708 |
|
\end{tabular} |
| 709 |
< |
\label{AuThiolHexaneAA} |
| 709 |
> |
\label{modelTest} |
| 710 |
|
\end{center} |
| 711 |
|
\end{minipage} |
| 712 |
|
\end{table*} |
| 713 |
|
|
| 714 |
+ |
To facilitate direct comparison, the same system with differnt models |
| 715 |
+ |
for different components uses the same length scale for their |
| 716 |
+ |
simulation cells. Without the presence of capping agent, using |
| 717 |
+ |
different models for hexane yields similar results for both $G$ and |
| 718 |
+ |
$G^\prime$, and these two definitions agree with eath other very |
| 719 |
+ |
well. This indicates very weak interaction between the metal and the |
| 720 |
+ |
solvent, and is a typical case for acoustic impedance mismatch between |
| 721 |
+ |
these two phases. |
| 722 |
|
|
| 723 |
< |
significant conductance enhancement compared to the gold/water |
| 724 |
< |
interface without capping agent and agree with available experimental |
| 725 |
< |
data. This indicates that the metal-metal potential, though not |
| 726 |
< |
predicting an accurate bulk metal thermal conductivity, does not |
| 727 |
< |
greatly interfere with the simulation of the thermal conductance |
| 728 |
< |
behavior across a non-metal interface. |
| 723 |
> |
As for Au(111) surfaces completely covered by butanethiols, the choice |
| 724 |
> |
of models for capping agent and solvent could impact the measurement |
| 725 |
> |
of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane |
| 726 |
> |
interfaces, using AA model for both butanethiol and hexane yields |
| 727 |
> |
substantially higher conductivity values than using UA model for at |
| 728 |
> |
least one component of the solvent and capping agent, which exceeds |
| 729 |
> |
the upper bond of experimental value range. This is probably due to |
| 730 |
> |
the classically treated C-H vibrations in the AA model, which should |
| 731 |
> |
not be appreciably populated at normal temperatures. In comparison, |
| 732 |
> |
once either the hexanes or the butanethiols are deuterated, one can |
| 733 |
> |
see a significantly lower $G$ and $G^\prime$. In either of these |
| 734 |
> |
cases, the C-H(D) vibrational overlap between the solvent and the |
| 735 |
> |
capping agent is removed. [MAY NEED FIGURE] Conclusively, the |
| 736 |
> |
improperly treated C-H vibration in the AA model produced |
| 737 |
> |
over-predicted results accordingly. Compared to the AA model, the UA |
| 738 |
> |
model yields more reasonable results with higher computational |
| 739 |
> |
efficiency. |
| 740 |
|
|
| 741 |
< |
% The results show that the two definitions used for $G$ yield |
| 742 |
< |
% comparable values, though $G^\prime$ tends to be smaller. |
| 741 |
> |
However, for Au-butanethiol/toluene interfaces, having the AA |
| 742 |
> |
butanethiol deuterated did not yield a significant change in the |
| 743 |
> |
measurement results. |
| 744 |
> |
. , so extra degrees of freedom |
| 745 |
> |
such as the C-H vibrations could enhance heat exchange between these |
| 746 |
> |
two phases and result in a much higher conductivity. |
| 747 |
|
|
| 748 |
+ |
|
| 749 |
+ |
Although the QSC model for Au is known to predict an overly low value |
| 750 |
+ |
for bulk metal gold conductivity[CITE NIVSRNEMD], our computational |
| 751 |
+ |
results for $G$ and $G^\prime$ do not seem to be affected by this |
| 752 |
+ |
drawback of the model for metal. Instead, the modeling of interfacial |
| 753 |
+ |
thermal transport behavior relies mainly on an accurate description of |
| 754 |
+ |
the interactions between components occupying the interfaces. |
| 755 |
+ |
|
| 756 |
|
\subsection{Mechanism of Interfacial Thermal Conductance Enhancement |
| 757 |
|
by Capping Agent} |
| 758 |
< |
[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL] |
| 758 |
> |
%OR\subsection{Vibrational spectrum study on conductance mechanism} |
| 759 |
|
|
| 760 |
+ |
[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S] |
| 761 |
|
|
| 729 |
– |
%subsubsection{Vibrational spectrum study on conductance mechanism} |
| 762 |
|
To investigate the mechanism of this interfacial thermal conductance, |
| 763 |
|
the vibrational spectra of various gold systems were obtained and are |
| 764 |
|
shown as in the upper panel of Fig. \ref{vibration}. To obtain these |
| 765 |
|
spectra, one first runs a simulation in the NVE ensemble and collects |
| 766 |
|
snapshots of configurations; these configurations are used to compute |
| 767 |
|
the velocity auto-correlation functions, which is used to construct a |
| 768 |
< |
power spectrum via a Fourier transform. The gold surfaces covered by |
| 737 |
< |
butanethiol molecules exhibit an additional peak observed at a |
| 738 |
< |
frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration |
| 739 |
< |
of the S-Au bond. This vibration enables efficient thermal transport |
| 740 |
< |
from surface Au atoms to the capping agents. Simultaneously, as shown |
| 741 |
< |
in the lower panel of Fig. \ref{vibration}, the large overlap of the |
| 742 |
< |
vibration spectra of butanethiol and hexane in the all-atom model, |
| 743 |
< |
including the C-H vibration, also suggests high thermal exchange |
| 744 |
< |
efficiency. The combination of these two effects produces the drastic |
| 745 |
< |
interfacial thermal conductance enhancement in the all-atom model. |
| 768 |
> |
power spectrum via a Fourier transform. |
| 769 |
|
|
| 770 |
+ |
The gold surfaces covered by |
| 771 |
+ |
butanethiol molecules, compared to bare gold surfaces, exhibit an |
| 772 |
+ |
additional peak observed at a frequency of $\sim$170cm$^{-1}$, which |
| 773 |
+ |
is attributed to the vibration of the S-Au bond. This vibration |
| 774 |
+ |
enables efficient thermal transport from surface Au atoms to the |
| 775 |
+ |
capping agents. Simultaneously, as shown in the lower panel of |
| 776 |
+ |
Fig. \ref{vibration}, the large overlap of the vibration spectra of |
| 777 |
+ |
butanethiol and hexane in the all-atom model, including the C-H |
| 778 |
+ |
vibration, also suggests high thermal exchange efficiency. The |
| 779 |
+ |
combination of these two effects produces the drastic interfacial |
| 780 |
+ |
thermal conductance enhancement in the all-atom model. |
| 781 |
+ |
|
| 782 |
+ |
[MAY NEED TO CONVERT TO JPEG] |
| 783 |
|
\begin{figure} |
| 784 |
|
\includegraphics[width=\linewidth]{vibration} |
| 785 |
|
\caption{Vibrational spectra obtained for gold in different |
| 787 |
|
all-atom model (lower panel).} |
| 788 |
|
\label{vibration} |
| 789 |
|
\end{figure} |
| 754 |
– |
% MAY NEED TO CONVERT TO JPEG |
| 790 |
|
|
| 791 |
+ |
[COMPARISON OF TWO G'S; AU SLAB WIDTHS; ETC] |
| 792 |
+ |
% The results show that the two definitions used for $G$ yield |
| 793 |
+ |
% comparable values, though $G^\prime$ tends to be smaller. |
| 794 |
+ |
|
| 795 |
|
\section{Conclusions} |
| 796 |
+ |
The NIVS algorithm we developed has been applied to simulations of |
| 797 |
+ |
Au-butanethiol surfaces with organic solvents. This algorithm allows |
| 798 |
+ |
effective unphysical thermal flux transferred between the metal and |
| 799 |
+ |
the liquid phase. With the flux applied, we were able to measure the |
| 800 |
+ |
corresponding thermal gradient and to obtain interfacial thermal |
| 801 |
+ |
conductivities. Our simulations have seen significant conductance |
| 802 |
+ |
enhancement with the presence of capping agent, compared to the bare |
| 803 |
+ |
gold/liquid interfaces. The acoustic impedance mismatch between the |
| 804 |
+ |
metal and the liquid phase is effectively eliminated by proper capping |
| 805 |
+ |
agent. Furthermore, the coverage precentage of the capping agent plays |
| 806 |
+ |
an important role in the interfacial thermal transport process. |
| 807 |
|
|
| 808 |
+ |
Our measurement results, particularly of the UA models, agree with |
| 809 |
+ |
available experimental data. This indicates that our force field |
| 810 |
+ |
parameters have a nice description of the interactions between the |
| 811 |
+ |
particles at the interfaces. AA models tend to overestimate the |
| 812 |
+ |
interfacial thermal conductance in that the classically treated C-H |
| 813 |
+ |
vibration would be overly sampled. Compared to the AA models, the UA |
| 814 |
+ |
models have higher computational efficiency with satisfactory |
| 815 |
+ |
accuracy, and thus are preferable in interfacial thermal transport |
| 816 |
+ |
modelings. |
| 817 |
|
|
| 818 |
< |
[NECESSITY TO STUDY THERMAL CONDUCTANCE IN NANOCRYSTAL STRUCTURE]\cite{vlugt:cpc2007154} |
| 818 |
> |
Vlugt {\it et al.} has investigated the surface thiol structures for |
| 819 |
> |
nanocrystal gold and pointed out that they differs from those of the |
| 820 |
> |
Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to |
| 821 |
> |
change of interfacial thermal transport behavior as well. To |
| 822 |
> |
investigate this problem, an effective means to introduce thermal flux |
| 823 |
> |
and measure the corresponding thermal gradient is desirable for |
| 824 |
> |
simulating structures with spherical symmetry. |
| 825 |
|
|
| 826 |
+ |
|
| 827 |
|
\section{Acknowledgments} |
| 828 |
|
Support for this project was provided by the National Science |
| 829 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
