| 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 |
– |
|
