218 |
|
scaling. More importantly, separating the momentum flux imposing from |
219 |
|
velocity scaling avoids the underlying cause that NIVS produced |
220 |
|
thermal anisotropy when applying a momentum flux. |
221 |
– |
%NEW METHOD DOESN'T CAUSE UNDESIRED CONCOMITENT MOMENTUM FLUX WHEN |
222 |
– |
%IMPOSING A THERMAL FLUX |
221 |
|
|
222 |
|
The advantages of the approach over the original momentum swapping |
223 |
|
approach lies in its nature to preserve a Gaussian |
387 |
|
so that $\delta\rightarrow 0$ in the ``no-slip'' boundary condition, |
388 |
|
and depicts how ``slippery'' an interface is. Figure \ref{slipLength} |
389 |
|
illustrates how this quantity is defined and computed for a |
390 |
< |
solid-liquid interface. |
390 |
> |
solid-liquid interface. [MAY INCLUDE A SNAPSHOT IN FIGURE] |
391 |
|
|
392 |
|
\begin{figure} |
393 |
|
\includegraphics[width=\linewidth]{defDelta} |
407 |
|
data. |
408 |
|
[MENTION IN RESULTS THAT ETA OBTAINED HERE DOES NOT NECESSARILY EQUAL |
409 |
|
TO BULK VALUES] |
412 |
– |
|
413 |
– |
\section{Results} |
414 |
– |
[L-J COMPARED TO RNEMD NIVS; WATER COMPARED TO RNEMD NIVS AND EMD; |
415 |
– |
SLIP BOUNDARY VS STICK BOUNDARY; ICE-WATER INTERFACES] |
410 |
|
|
411 |
< |
There are many factors contributing to the measured interfacial |
412 |
< |
conductance; some of these factors are physically motivated |
413 |
< |
(e.g. coverage of the surface by the capping agent coverage and |
414 |
< |
solvent identity), while some are governed by parameters of the |
415 |
< |
methodology (e.g. applied flux and the formulas used to obtain the |
416 |
< |
conductance). In this section we discuss the major physical and |
417 |
< |
calculational effects on the computed conductivity. |
411 |
> |
\section{Results and Discussions} |
412 |
> |
\subsection{Lennard-Jones fluid} |
413 |
> |
Our orthorhombic simulation cell of Lennard-Jones fluid has identical |
414 |
> |
parameters to our previous work\cite{kuang:164101} to facilitate |
415 |
> |
comparison. Thermal conductivitis and shear viscosities were computed |
416 |
> |
with the algorithm applied to the simulations. The results of thermal |
417 |
> |
conductivity are compared with our previous NIVS algorithm. However, |
418 |
> |
since the NIVS algorithm could produce temperature anisotropy for |
419 |
> |
shear viscocity computations, these results are instead compared to |
420 |
> |
the momentum swapping approaches. Table \ref{LJ} lists these |
421 |
> |
calculations with various fluxes in reduced units. |
422 |
|
|
423 |
< |
\subsection{Effects due to capping agent coverage} |
423 |
> |
\begin{table*} |
424 |
> |
\begin{minipage}{\linewidth} |
425 |
> |
\begin{center} |
426 |
> |
|
427 |
> |
\caption{Thermal conductivity ($\lambda^*$) and shear viscosity |
428 |
> |
($\eta^*$) (in reduced units) of a Lennard-Jones fluid at |
429 |
> |
${\langle T^* \rangle = 0.72}$ and ${\rho^* = 0.85}$ computed |
430 |
> |
at various momentum fluxes. The new method yields similar |
431 |
> |
results to previous RNEMD methods. All results are reported in |
432 |
> |
reduced unit. Uncertainties are indicated in parentheses.} |
433 |
> |
|
434 |
> |
\begin{tabular}{cccccc} |
435 |
> |
\hline\hline |
436 |
> |
\multicolumn{2}{c}{Momentum Exchange} & |
437 |
> |
\multicolumn{2}{c}{$\lambda^*$} & |
438 |
> |
\multicolumn{2}{c}{$\eta^*$} \\ |
439 |
> |
\hline |
440 |
> |
Swap Interval & Equivalent $J_z^*$ or $j_z^*(p_x)$ & |
441 |
> |
NIVS & This work & Swapping & This work \\ |
442 |
> |
\hline |
443 |
> |
0.116 & 0.16 & 7.30(0.10) & 6.25(0.23) & 3.57(0.06) & 3.53(0.16)\\ |
444 |
> |
0.232 & 0.09 & 6.95(0.09) & 8.02(0.56) & 3.64(0.05) & 3.43(0.17)\\ |
445 |
> |
0.463 & 0.047 & 7.19(0.07) & 6.48(0.15) & 3.52(0.16) & 3.51(0.08)\\ |
446 |
> |
0.926 & 0.024 & 7.19(0.28) & 7.02(0.13) & 3.72(0.05) & 3.79(0.11)\\ |
447 |
> |
1.158 & 0.019 & 7.98(0.33) & 7.37(0.23) & 3.42(0.06) & 3.53(0.06)\\ |
448 |
> |
\hline\hline |
449 |
> |
\end{tabular} |
450 |
> |
\label{LJ} |
451 |
> |
\end{center} |
452 |
> |
\end{minipage} |
453 |
> |
\end{table*} |
454 |
|
|
455 |
< |
A series of different initial conditions with a range of surface |
456 |
< |
coverages was prepared and solvated with various with both of the |
457 |
< |
solvent molecules. These systems were then equilibrated and their |
458 |
< |
interfacial thermal conductivity was measured with the NIVS |
459 |
< |
algorithm. Figure \ref{coverage} demonstrates the trend of conductance |
460 |
< |
with respect to surface coverage. |
455 |
> |
\subsubsection{Thermal conductivity} |
456 |
> |
Our thermal conductivity calculations with this method yields |
457 |
> |
comparable results to the previous NIVS algorithm. This indicates that |
458 |
> |
the thermal gradients rendered using this method are also close to |
459 |
> |
previous RNEMD methods. Simulations with moderately higher thermal |
460 |
> |
fluxes tend to yield more reliable thermal gradients and thus avoid |
461 |
> |
large errors, while overly high thermal fluxes could introduce side |
462 |
> |
effects such as non-linear temperature gradient response or |
463 |
> |
inadvertent phase transitions. |
464 |
|
|
465 |
+ |
Since the scaling operation is isotropic in this method, one does not |
466 |
+ |
need extra care to ensure temperature isotropy between the $x$, $y$ |
467 |
+ |
and $z$ axes, while thermal anisotropy might happen if the criteria |
468 |
+ |
function for choosing scaling coefficients does not perform as |
469 |
+ |
expected. Furthermore, this method avoids inadvertent concomitant |
470 |
+ |
momentum flux when only thermal flux is imposed, which could not be |
471 |
+ |
achieved with swapping or NIVS approaches. The thermal energy exchange |
472 |
+ |
in swapping ($\vec{p}_i$ in slab ``c'' with $\vec{p}_j$ in slab ``j'') |
473 |
+ |
or NIVS (total slab momentum conponemts $P^\alpha$ scaled to $\alpha |
474 |
+ |
P^\alpha$) would not obtain this result unless thermal flux vanishes |
475 |
+ |
(i.e. $\vec{p}_i=\vec{p}_j$ or $\alpha=1$ which are trivial to apply a |
476 |
+ |
thermal flux). In this sense, this method contributes to having |
477 |
+ |
minimal perturbation to a simulation while imposing thermal flux. |
478 |
+ |
|
479 |
+ |
\subsubsection{Shear viscosity} |
480 |
+ |
Table \ref{LJ} also compares our shear viscosity results with momentum |
481 |
+ |
swapping approach. Our calculations show that our method predicted |
482 |
+ |
similar values for shear viscosities to the momentum swapping |
483 |
+ |
approach, as well as the velocity gradient profiles. Moderately larger |
484 |
+ |
momentum fluxes are helpful to reduce the errors of measured velocity |
485 |
+ |
gradients and thus the final result. However, it is pointed out that |
486 |
+ |
the momentum swapping approach tends to produce nonthermal velocity |
487 |
+ |
distributions.\cite{Maginn:2010} |
488 |
+ |
|
489 |
+ |
To examine that temperature isotropy holds in simulations using our |
490 |
+ |
method, we measured the three one-dimensional temperatures in each of |
491 |
+ |
the slabs (Figure \ref{tempXyz}). Note that the $x$-dimensional |
492 |
+ |
temperatures were calculated after subtracting the effects from bulk |
493 |
+ |
velocities of the slabs. The one-dimensional temperature profiles |
494 |
+ |
showed no observable difference between the three dimensions. This |
495 |
+ |
ensures that isotropic scaling automatically preserves temperature |
496 |
+ |
isotropy and that our method is useful in shear viscosity |
497 |
+ |
computations. |
498 |
+ |
|
499 |
|
\begin{figure} |
500 |
< |
\includegraphics[width=\linewidth]{coverage} |
501 |
< |
\caption{The interfacial thermal conductivity ($G$) has a |
502 |
< |
non-monotonic dependence on the degree of surface capping. This |
438 |
< |
data is for the Au(111) / butanethiol / solvent interface with |
439 |
< |
various UA force fields at $\langle T\rangle \sim $200K.} |
440 |
< |
\label{coverage} |
500 |
> |
\includegraphics[width=\linewidth]{tempXyz} |
501 |
> |
\caption{.} |
502 |
> |
\label{tempXyz} |
503 |
|
\end{figure} |
504 |
|
|
505 |
< |
In partially covered surfaces, the derivative definition for |
506 |
< |
$G^\prime$ (Eq. \ref{derivativeG}) becomes difficult to apply, as the |
507 |
< |
location of maximum change of $\lambda$ becomes washed out. The |
508 |
< |
discrete definition (Eq. \ref{discreteG}) is easier to apply, as the |
509 |
< |
Gibbs dividing surface is still well-defined. Therefore, $G$ (not |
510 |
< |
$G^\prime$) was used in this section. |
505 |
> |
Furthermore, the velocity distribution profiles are tested by imposing |
506 |
> |
a large shear stress into the simulations. Figure \ref{vDist} |
507 |
> |
demonstrates how our method is able to maintain thermal velocity |
508 |
> |
distributions against the momentum swapping approach even under large |
509 |
> |
imposed fluxes. Previous swapping methods tend to deplete particles of |
510 |
> |
positive velocities in the negative velocity slab (``c'') and vice |
511 |
> |
versa in slab ``h'', where the distributions leave a notch. This |
512 |
> |
problematic profiles become significant when the imposed-flux becomes |
513 |
> |
larger and diffusions from neighboring slabs could not offset the |
514 |
> |
depletion. Simutaneously, abnormal peaks appear corresponding to |
515 |
> |
excessive velocity swapped from the other slab. This nonthermal |
516 |
> |
distributions limit applications of the swapping approach in shear |
517 |
> |
stress simulations. Our method avoids the above problematic |
518 |
> |
distributions by altering the means of applying momentum |
519 |
> |
fluxes. Comparatively, velocity distributions recorded from |
520 |
> |
simulations with our method is so close to the ideal thermal |
521 |
> |
prediction that no observable difference is shown in Figure |
522 |
> |
\ref{vDist}. Conclusively, our method avoids problems happened in |
523 |
> |
previous RNEMD methods and provides a useful means for shear viscosity |
524 |
> |
computations. |
525 |
|
|
526 |
< |
From Figure \ref{coverage}, one can see the significance of the |
527 |
< |
presence of capping agents. When even a small fraction of the Au(111) |
528 |
< |
surface sites are covered with butanethiols, the conductivity exhibits |
529 |
< |
an enhancement by at least a factor of 3. Capping agents are clearly |
530 |
< |
playing a major role in thermal transport at metal / organic solvent |
455 |
< |
surfaces. |
526 |
> |
\begin{figure} |
527 |
> |
\includegraphics[width=\linewidth]{velDist} |
528 |
> |
\caption{.} |
529 |
> |
\label{vDist} |
530 |
> |
\end{figure} |
531 |
|
|
532 |
< |
We note a non-monotonic behavior in the interfacial conductance as a |
533 |
< |
function of surface coverage. The maximum conductance (largest $G$) |
459 |
< |
happens when the surfaces are about 75\% covered with butanethiol |
460 |
< |
caps. The reason for this behavior is not entirely clear. One |
461 |
< |
explanation is that incomplete butanethiol coverage allows small gaps |
462 |
< |
between butanethiols to form. These gaps can be filled by transient |
463 |
< |
solvent molecules. These solvent molecules couple very strongly with |
464 |
< |
the hot capping agent molecules near the surface, and can then carry |
465 |
< |
away (diffusively) the excess thermal energy from the surface. |
532 |
> |
\subsection{Bulk SPC/E water} |
533 |
> |
[WATER COMPARED TO RNEMD NIVS AND EMD] |
534 |
|
|
535 |
< |
There appears to be a competition between the conduction of the |
536 |
< |
thermal energy away from the surface by the capping agents (enhanced |
469 |
< |
by greater coverage) and the coupling of the capping agents with the |
470 |
< |
solvent (enhanced by interdigitation at lower coverages). This |
471 |
< |
competition would lead to the non-monotonic coverage behavior observed |
472 |
< |
here. |
535 |
> |
\subsubsection{Thermal conductivity} |
536 |
> |
[VSIS DOES AS WELL AS NIVS] |
537 |
|
|
538 |
< |
Results for rigid body toluene solvent, as well as the UA hexane, are |
539 |
< |
within the ranges expected from prior experimental |
476 |
< |
work.\cite{Wilson:2002uq,cahill:793,PhysRevB.80.195406} This suggests |
477 |
< |
that explicit hydrogen atoms might not be required for modeling |
478 |
< |
thermal transport in these systems. C-H vibrational modes do not see |
479 |
< |
significant excited state population at low temperatures, and are not |
480 |
< |
likely to carry lower frequency excitations from the solid layer into |
481 |
< |
the bulk liquid. |
538 |
> |
\subsubsection{Shear viscosity} |
539 |
> |
[COMPARE W EMD] |
540 |
|
|
541 |
< |
The toluene solvent does not exhibit the same behavior as hexane in |
484 |
< |
that $G$ remains at approximately the same magnitude when the capping |
485 |
< |
coverage increases from 25\% to 75\%. Toluene, as a rigid planar |
486 |
< |
molecule, cannot occupy the relatively small gaps between the capping |
487 |
< |
agents as easily as the chain-like {\it n}-hexane. The effect of |
488 |
< |
solvent coupling to the capping agent is therefore weaker in toluene |
489 |
< |
except at the very lowest coverage levels. This effect counters the |
490 |
< |
coverage-dependent conduction of heat away from the metal surface, |
491 |
< |
leading to a much flatter $G$ vs. coverage trend than is observed in |
492 |
< |
{\it n}-hexane. |
541 |
> |
[MAY HAVE A FIRURE FOR DATA] |
542 |
|
|
543 |
< |
\subsection{Effects due to Solvent \& Solvent Models} |
544 |
< |
In addition to UA solvent and capping agent models, AA models have |
545 |
< |
also been included in our simulations. In most of this work, the same |
546 |
< |
(UA or AA) model for solvent and capping agent was used, but it is |
498 |
< |
also possible to utilize different models for different components. |
499 |
< |
We have also included isotopic substitutions (Hydrogen to Deuterium) |
500 |
< |
to decrease the explicit vibrational overlap between solvent and |
501 |
< |
capping agent. Table \ref{modelTest} summarizes the results of these |
502 |
< |
studies. |
543 |
> |
[MAY COMBINE JZPX AND JZKE TO RUN ONE JOB BUT GET ETA=F(T)] |
544 |
> |
[PUT RESULT AND FIGURE HERE IF IT WORKS] |
545 |
> |
\subsection{Interfacial frictions} |
546 |
> |
[SLIP BOUNDARY VS STICK BOUNDARY; ICE-WATER INTERFACES] |
547 |
|
|
548 |
+ |
qualitative agreement w interfacial thermal conductance |
549 |
+ |
|
550 |
+ |
[FUTURE WORK HERE OR IN CONCLUSIONS] |
551 |
+ |
|
552 |
+ |
|
553 |
|
\begin{table*} |
554 |
|
\begin{minipage}{\linewidth} |
555 |
|
\begin{center} |
572 |
|
& UA toluene & 187(16) & 151(11) \\ |
573 |
|
& AA toluene & 200(36) & 149(53) \\ |
574 |
|
\hline |
526 |
– |
AA & UA hexane & 116(9) & 129(8) \\ |
527 |
– |
& AA hexane & 442(14) & 356(31) \\ |
528 |
– |
& AA hexane(D) & 222(12) & 234(54) \\ |
529 |
– |
& UA toluene & 125(25) & 97(60) \\ |
530 |
– |
& AA toluene & 487(56) & 290(42) \\ |
531 |
– |
\hline |
532 |
– |
AA(D) & UA hexane & 158(25) & 172(4) \\ |
533 |
– |
& AA hexane & 243(29) & 191(11) \\ |
534 |
– |
& AA toluene & 364(36) & 322(67) \\ |
535 |
– |
\hline |
575 |
|
bare & UA hexane & 46.5(3.2) & 49.4(4.5) \\ |
576 |
|
& UA hexane(D) & 43.9(4.6) & 43.0(2.0) \\ |
577 |
|
& AA hexane & 31.0(1.4) & 29.4(1.3) \\ |
583 |
|
\end{minipage} |
584 |
|
\end{table*} |
585 |
|
|
547 |
– |
To facilitate direct comparison between force fields, systems with the |
548 |
– |
same capping agent and solvent were prepared with the same length |
549 |
– |
scales for the simulation cells. |
550 |
– |
|
586 |
|
On bare metal / solvent surfaces, different force field models for |
587 |
|
hexane yield similar results for both $G$ and $G^\prime$, and these |
588 |
|
two definitions agree with each other very well. This is primarily an |
599 |
|
to the AA model, the UA model yields more reasonable conductivity |
600 |
|
values with much higher computational efficiency. |
601 |
|
|
567 |
– |
\subsubsection{Are electronic excitations in the metal important?} |
568 |
– |
Because they lack electronic excitations, the QSC and related embedded |
569 |
– |
atom method (EAM) models for gold are known to predict unreasonably |
570 |
– |
low values for bulk conductivity |
571 |
– |
($\lambda$).\cite{kuang:164101,ISI:000207079300006,Clancy:1992} If the |
572 |
– |
conductance between the phases ($G$) is governed primarily by phonon |
573 |
– |
excitation (and not electronic degrees of freedom), one would expect a |
574 |
– |
classical model to capture most of the interfacial thermal |
575 |
– |
conductance. Our results for $G$ and $G^\prime$ indicate that this is |
576 |
– |
indeed the case, and suggest that the modeling of interfacial thermal |
577 |
– |
transport depends primarily on the description of the interactions |
578 |
– |
between the various components at the interface. When the metal is |
579 |
– |
chemically capped, the primary barrier to thermal conductivity appears |
580 |
– |
to be the interface between the capping agent and the surrounding |
581 |
– |
solvent, so the excitations in the metal have little impact on the |
582 |
– |
value of $G$. |
583 |
– |
|
584 |
– |
\subsection{Effects due to methodology and simulation parameters} |
585 |
– |
|
586 |
– |
We have varied the parameters of the simulations in order to |
587 |
– |
investigate how these factors would affect the computation of $G$. Of |
588 |
– |
particular interest are: 1) the length scale for the applied thermal |
589 |
– |
gradient (modified by increasing the amount of solvent in the system), |
590 |
– |
2) the sign and magnitude of the applied thermal flux, 3) the average |
591 |
– |
temperature of the simulation (which alters the solvent density during |
592 |
– |
equilibration), and 4) the definition of the interfacial conductance |
593 |
– |
(Eqs. (\ref{discreteG}) or (\ref{derivativeG})) used in the |
594 |
– |
calculation. |
595 |
– |
|
596 |
– |
Systems of different lengths were prepared by altering the number of |
597 |
– |
solvent molecules and extending the length of the box along the $z$ |
598 |
– |
axis to accomodate the extra solvent. Equilibration at the same |
599 |
– |
temperature and pressure conditions led to nearly identical surface |
600 |
– |
areas ($L_x$ and $L_y$) available to the metal and capping agent, |
601 |
– |
while the extra solvent served mainly to lengthen the axis that was |
602 |
– |
used to apply the thermal flux. For a given value of the applied |
603 |
– |
flux, the different $z$ length scale has only a weak effect on the |
604 |
– |
computed conductivities. |
605 |
– |
|
606 |
– |
\subsubsection{Effects of applied flux} |
607 |
– |
The NIVS algorithm allows changes in both the sign and magnitude of |
608 |
– |
the applied flux. It is possible to reverse the direction of heat |
609 |
– |
flow simply by changing the sign of the flux, and thermal gradients |
610 |
– |
which would be difficult to obtain experimentally ($5$ K/\AA) can be |
611 |
– |
easily simulated. However, the magnitude of the applied flux is not |
612 |
– |
arbitrary if one aims to obtain a stable and reliable thermal gradient. |
613 |
– |
A temperature gradient can be lost in the noise if $|J_z|$ is too |
614 |
– |
small, and excessive $|J_z|$ values can cause phase transitions if the |
615 |
– |
extremes of the simulation cell become widely separated in |
616 |
– |
temperature. Also, if $|J_z|$ is too large for the bulk conductivity |
617 |
– |
of the materials, the thermal gradient will never reach a stable |
618 |
– |
state. |
619 |
– |
|
620 |
– |
Within a reasonable range of $J_z$ values, we were able to study how |
621 |
– |
$G$ changes as a function of this flux. In what follows, we use |
622 |
– |
positive $J_z$ values to denote the case where energy is being |
623 |
– |
transferred by the method from the metal phase and into the liquid. |
624 |
– |
The resulting gradient therefore has a higher temperature in the |
625 |
– |
liquid phase. Negative flux values reverse this transfer, and result |
626 |
– |
in higher temperature metal phases. The conductance measured under |
627 |
– |
different applied $J_z$ values is listed in Tables 2 and 3 in the |
628 |
– |
supporting information. These results do not indicate that $G$ depends |
629 |
– |
strongly on $J_z$ within this flux range. The linear response of flux |
630 |
– |
to thermal gradient simplifies our investigations in that we can rely |
631 |
– |
on $G$ measurement with only a small number $J_z$ values. |
632 |
– |
|
633 |
– |
The sign of $J_z$ is a different matter, however, as this can alter |
634 |
– |
the temperature on the two sides of the interface. The average |
635 |
– |
temperature values reported are for the entire system, and not for the |
636 |
– |
liquid phase, so at a given $\langle T \rangle$, the system with |
637 |
– |
positive $J_z$ has a warmer liquid phase. This means that if the |
638 |
– |
liquid carries thermal energy via diffusive transport, {\it positive} |
639 |
– |
$J_z$ values will result in increased molecular motion on the liquid |
640 |
– |
side of the interface, and this will increase the measured |
641 |
– |
conductivity. |
642 |
– |
|
602 |
|
\subsubsection{Effects due to average temperature} |
603 |
|
|
604 |
|
We also studied the effect of average system temperature on the |
624 |
|
of one side of the interface (notably the density) change rapidly as a |
625 |
|
function of temperature. |
626 |
|
|
668 |
– |
Besides the lower interfacial thermal conductance, surfaces at |
669 |
– |
relatively high temperatures are susceptible to reconstructions, |
670 |
– |
particularly when butanethiols fully cover the Au(111) surface. These |
671 |
– |
reconstructions include surface Au atoms which migrate outward to the |
672 |
– |
S atom layer, and butanethiol molecules which embed into the surface |
673 |
– |
Au layer. The driving force for this behavior is the strong Au-S |
674 |
– |
interactions which are modeled here with a deep Lennard-Jones |
675 |
– |
potential. This phenomenon agrees with reconstructions that have been |
676 |
– |
experimentally |
677 |
– |
observed.\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt |
678 |
– |
{\it et al.} kept their Au(111) slab rigid so that their simulations |
679 |
– |
could reach 300K without surface |
680 |
– |
reconstructions.\cite{vlugt:cpc2007154} Since surface reconstructions |
681 |
– |
blur the interface, the measurement of $G$ becomes more difficult to |
682 |
– |
conduct at higher temperatures. For this reason, most of our |
683 |
– |
measurements are undertaken at $\langle T\rangle\sim$200K where |
684 |
– |
reconstruction is minimized. |
685 |
– |
|
686 |
– |
However, when the surface is not completely covered by butanethiols, |
687 |
– |
the simulated system appears to be more resistent to the |
688 |
– |
reconstruction. Our Au / butanethiol / toluene system had the Au(111) |
689 |
– |
surfaces 90\% covered by butanethiols, but did not see this above |
690 |
– |
phenomena even at $\langle T\rangle\sim$300K. That said, we did |
691 |
– |
observe butanethiols migrating to neighboring three-fold sites during |
692 |
– |
a simulation. Since the interface persisted in these simulations, we |
693 |
– |
were able to obtain $G$'s for these interfaces even at a relatively |
694 |
– |
high temperature without being affected by surface reconstructions. |
695 |
– |
|
696 |
– |
\section{Discussion} |
697 |
– |
[COMBINE W. RESULTS] |
698 |
– |
The primary result of this work is that the capping agent acts as an |
699 |
– |
efficient thermal coupler between solid and solvent phases. One of |
700 |
– |
the ways the capping agent can carry out this role is to down-shift |
701 |
– |
between the phonon vibrations in the solid (which carry the heat from |
702 |
– |
the gold) and the molecular vibrations in the liquid (which carry some |
703 |
– |
of the heat in the solvent). |
704 |
– |
|
705 |
– |
To investigate the mechanism of interfacial thermal conductance, the |
706 |
– |
vibrational power spectrum was computed. Power spectra were taken for |
707 |
– |
individual components in different simulations. To obtain these |
708 |
– |
spectra, simulations were run after equilibration in the |
709 |
– |
microcanonical (NVE) ensemble and without a thermal |
710 |
– |
gradient. Snapshots of configurations were collected at a frequency |
711 |
– |
that is higher than that of the fastest vibrations occurring in the |
712 |
– |
simulations. With these configurations, the velocity auto-correlation |
713 |
– |
functions can be computed: |
714 |
– |
\begin{equation} |
715 |
– |
C_A (t) = \langle\vec{v}_A (t)\cdot\vec{v}_A (0)\rangle |
716 |
– |
\label{vCorr} |
717 |
– |
\end{equation} |
718 |
– |
The power spectrum is constructed via a Fourier transform of the |
719 |
– |
symmetrized velocity autocorrelation function, |
720 |
– |
\begin{equation} |
721 |
– |
\hat{f}(\omega) = |
722 |
– |
\int_{-\infty}^{\infty} C_A (t) e^{-2\pi it\omega}\,dt |
723 |
– |
\label{fourier} |
724 |
– |
\end{equation} |
725 |
– |
|
726 |
– |
\subsection{The role of specific vibrations} |
727 |
– |
The vibrational spectra for gold slabs in different environments are |
728 |
– |
shown as in Figure \ref{specAu}. Regardless of the presence of |
729 |
– |
solvent, the gold surfaces which are covered by butanethiol molecules |
730 |
– |
exhibit an additional peak observed at a frequency of |
731 |
– |
$\sim$165cm$^{-1}$. We attribute this peak to the S-Au bonding |
732 |
– |
vibration. This vibration enables efficient thermal coupling of the |
733 |
– |
surface Au layer to the capping agents. Therefore, in our simulations, |
734 |
– |
the Au / S interfaces do not appear to be the primary barrier to |
735 |
– |
thermal transport when compared with the butanethiol / solvent |
736 |
– |
interfaces. This supports the results of Luo {\it et |
737 |
– |
al.}\cite{Luo20101}, who reported $G$ for Au-SAM junctions roughly |
738 |
– |
twice as large as what we have computed for the thiol-liquid |
739 |
– |
interfaces. |
740 |
– |
|
741 |
– |
\begin{figure} |
742 |
– |
\includegraphics[width=\linewidth]{vibration} |
743 |
– |
\caption{The vibrational power spectrum for thiol-capped gold has an |
744 |
– |
additional vibrational peak at $\sim $165cm$^{-1}$. Bare gold |
745 |
– |
surfaces (both with and without a solvent over-layer) are missing |
746 |
– |
this peak. A similar peak at $\sim $165cm$^{-1}$ also appears in |
747 |
– |
the vibrational power spectrum for the butanethiol capping agents.} |
748 |
– |
\label{specAu} |
749 |
– |
\end{figure} |
750 |
– |
|
751 |
– |
Also in this figure, we show the vibrational power spectrum for the |
752 |
– |
bound butanethiol molecules, which also exhibits the same |
753 |
– |
$\sim$165cm$^{-1}$ peak. |
754 |
– |
|
755 |
– |
\subsection{Overlap of power spectra} |
756 |
– |
A comparison of the results obtained from the two different organic |
757 |
– |
solvents can also provide useful information of the interfacial |
758 |
– |
thermal transport process. In particular, the vibrational overlap |
759 |
– |
between the butanethiol and the organic solvents suggests a highly |
760 |
– |
efficient thermal exchange between these components. Very high |
761 |
– |
thermal conductivity was observed when AA models were used and C-H |
762 |
– |
vibrations were treated classically. The presence of extra degrees of |
763 |
– |
freedom in the AA force field yields higher heat exchange rates |
764 |
– |
between the two phases and results in a much higher conductivity than |
765 |
– |
in the UA force field. The all-atom classical models include high |
766 |
– |
frequency modes which should be unpopulated at our relatively low |
767 |
– |
temperatures. This artifact is likely the cause of the high thermal |
768 |
– |
conductance in all-atom MD simulations. |
769 |
– |
|
770 |
– |
The similarity in the vibrational modes available to solvent and |
771 |
– |
capping agent can be reduced by deuterating one of the two components |
772 |
– |
(Fig. \ref{aahxntln}). Once either the hexanes or the butanethiols |
773 |
– |
are deuterated, one can observe a significantly lower $G$ and |
774 |
– |
$G^\prime$ values (Table \ref{modelTest}). |
775 |
– |
|
776 |
– |
\begin{figure} |
777 |
– |
\includegraphics[width=\linewidth]{aahxntln} |
778 |
– |
\caption{Spectra obtained for all-atom (AA) Au / butanethiol / solvent |
779 |
– |
systems. When butanethiol is deuterated (lower left), its |
780 |
– |
vibrational overlap with hexane decreases significantly. Since |
781 |
– |
aromatic molecules and the butanethiol are vibrationally dissimilar, |
782 |
– |
the change is not as dramatic when toluene is the solvent (right).} |
783 |
– |
\label{aahxntln} |
784 |
– |
\end{figure} |
785 |
– |
|
786 |
– |
For the Au / butanethiol / toluene interfaces, having the AA |
787 |
– |
butanethiol deuterated did not yield a significant change in the |
788 |
– |
measured conductance. Compared to the C-H vibrational overlap between |
789 |
– |
hexane and butanethiol, both of which have alkyl chains, the overlap |
790 |
– |
between toluene and butanethiol is not as significant and thus does |
791 |
– |
not contribute as much to the heat exchange process. |
792 |
– |
|
793 |
– |
Previous observations of Zhang {\it et al.}\cite{hase:2010} indicate |
794 |
– |
that the {\it intra}molecular heat transport due to alkylthiols is |
795 |
– |
highly efficient. Combining our observations with those of Zhang {\it |
796 |
– |
et al.}, it appears that butanethiol acts as a channel to expedite |
797 |
– |
heat flow from the gold surface and into the alkyl chain. The |
798 |
– |
vibrational coupling between the metal and the liquid phase can |
799 |
– |
therefore be enhanced with the presence of suitable capping agents. |
800 |
– |
|
801 |
– |
Deuterated models in the UA force field did not decouple the thermal |
802 |
– |
transport as well as in the AA force field. The UA models, even |
803 |
– |
though they have eliminated the high frequency C-H vibrational |
804 |
– |
overlap, still have significant overlap in the lower-frequency |
805 |
– |
portions of the infrared spectra (Figure \ref{uahxnua}). Deuterating |
806 |
– |
the UA models did not decouple the low frequency region enough to |
807 |
– |
produce an observable difference for the results of $G$ (Table |
808 |
– |
\ref{modelTest}). |
809 |
– |
|
810 |
– |
\begin{figure} |
811 |
– |
\includegraphics[width=\linewidth]{uahxnua} |
812 |
– |
\caption{Vibrational power spectra for UA models for the butanethiol |
813 |
– |
and hexane solvent (upper panel) show the high degree of overlap |
814 |
– |
between these two molecules, particularly at lower frequencies. |
815 |
– |
Deuterating a UA model for the solvent (lower panel) does not |
816 |
– |
decouple the two spectra to the same degree as in the AA force |
817 |
– |
field (see Fig \ref{aahxntln}).} |
818 |
– |
\label{uahxnua} |
819 |
– |
\end{figure} |
820 |
– |
|
627 |
|
\section{Conclusions} |
628 |
+ |
[VSIS WORKS! COMBINES NICE FEATURES OF PREVIOUS RNEMD METHODS AND |
629 |
+ |
IMPROVEMENTS TO THEIR PROBLEMS!] |
630 |
+ |
|
631 |
|
The NIVS algorithm has been applied to simulations of |
632 |
|
butanethiol-capped Au(111) surfaces in the presence of organic |
633 |
|
solvents. This algorithm allows the application of unphysical thermal |
655 |
|
accuracy, and thus are preferable in modeling interfacial thermal |
656 |
|
transport. |
657 |
|
|
849 |
– |
Of the two definitions for $G$, the discrete form |
850 |
– |
(Eq. \ref{discreteG}) was easier to use and gives out relatively |
851 |
– |
consistent results, while the derivative form (Eq. \ref{derivativeG}) |
852 |
– |
is not as versatile. Although $G^\prime$ gives out comparable results |
853 |
– |
and follows similar trend with $G$ when measuring close to fully |
854 |
– |
covered or bare surfaces, the spatial resolution of $T$ profile |
855 |
– |
required for the use of a derivative form is limited by the number of |
856 |
– |
bins and the sampling required to obtain thermal gradient information. |
857 |
– |
|
858 |
– |
Vlugt {\it et al.} have investigated the surface thiol structures for |
859 |
– |
nanocrystalline gold and pointed out that they differ from those of |
860 |
– |
the Au(111) surface.\cite{landman:1998,vlugt:cpc2007154} This |
861 |
– |
difference could also cause differences in the interfacial thermal |
862 |
– |
transport behavior. To investigate this problem, one would need an |
863 |
– |
effective method for applying thermal gradients in non-planar |
864 |
– |
(i.e. spherical) geometries. |
865 |
– |
|
658 |
|
\section{Acknowledgments} |
659 |
|
Support for this project was provided by the National Science |
660 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
667 |
|
|
668 |
|
\end{doublespace} |
669 |
|
\end{document} |
878 |
– |
|