| 75 |
|
from liquid copper to monatomic liquids to molecular fluids |
| 76 |
|
(e.g. ionic liquids).\cite{ISI:000246190100032} |
| 77 |
|
|
| 78 |
+ |
\begin{figure} |
| 79 |
+ |
\includegraphics[width=\linewidth]{thermalDemo} |
| 80 |
+ |
\caption{Demostration of thermal gradient estalished by RNEMD method.} |
| 81 |
+ |
\label{thermalDemo} |
| 82 |
+ |
\end{figure} |
| 83 |
+ |
|
| 84 |
|
RNEMD is preferable in many ways to the forward NEMD methods because |
| 85 |
|
it imposes what is typically difficult to measure (a flux or stress) |
| 86 |
|
and it is typically much easier to compute momentum gradients or |
| 362 |
|
m^{1/2} k_B^{-1}\varepsilon^{-1/2}}$. |
| 363 |
|
|
| 364 |
|
Another series of our simulation is to calculate the interfacial |
| 365 |
< |
thermal conductivity of a Au/H${_2}$O system. Respective calculations of |
| 365 |
> |
thermal conductivity of a Au/H$_2$O system. Respective calculations of |
| 366 |
|
water (SPC/E) and gold (QSC) thermal conductivity were performed and |
| 367 |
|
compared with current results to ensure the validity of |
| 368 |
< |
NIVS-RNEMD. After that, the mixture system was simulated. |
| 368 |
> |
NIVS-RNEMD. After that, a mixture system was simulated. |
| 369 |
> |
|
| 370 |
> |
For thermal conductivity calculation of bulk water, a simulation box |
| 371 |
> |
consisting of 1000 molecules were first equilibrated under ambient |
| 372 |
> |
pressure and temperature conditions (NPT), followed by equilibration |
| 373 |
> |
in fixed volume (NVT). The system was then equilibrated in |
| 374 |
> |
microcanonical ensemble (NVE). Also in NVE ensemble, establishing |
| 375 |
> |
stable thermal gradient was followed. The simulation box was under |
| 376 |
> |
periodic boundary condition and devided into 10 slabs. Data collection |
| 377 |
> |
process was similar to Lennard-Jones fluid system. Thermal |
| 378 |
> |
conductivity calculation of bulk crystal gold used a similar |
| 379 |
> |
protocol. And the face centered cubic crystal simulation box consists |
| 380 |
> |
of 2880 Au atoms. |
| 381 |
> |
|
| 382 |
> |
After simulations of bulk water and crystal gold, a mixture system was |
| 383 |
> |
constructed, consisting of 1188 Au atoms and 1862 H$_2$O |
| 384 |
> |
molecules. Spohr potential was adopted in depicting the interaction |
| 385 |
> |
between metal atom and water molecule.\cite{ISI:000167766600035} A |
| 386 |
> |
similar protocol of equilibration was followed. A thermal gradient was |
| 387 |
> |
built. It was found out that compared to homogeneous systems, the two |
| 388 |
> |
phases could have large temperature difference under a relatively low |
| 389 |
> |
thermal flux. Therefore, under our low flux condition, it is assumed |
| 390 |
> |
that the metal and water phases have respectively homogeneous |
| 391 |
> |
temperature. In calculating the interfacial thermal conductivity $G$, |
| 392 |
> |
this assumptioin was applied and thus our formula becomes: |
| 393 |
> |
|
| 394 |
> |
\begin{equation} |
| 395 |
> |
G = \frac{E_{total}}{2 t L_x L_y \left( \langle T_{gold}\rangle - |
| 396 |
> |
\langle T_{water}\rangle \right)} |
| 397 |
> |
\label{interfaceCalc} |
| 398 |
> |
\end{equation} |
| 399 |
> |
where ${E_{total}}$ is the imposed unphysical kinetic energy transfer |
| 400 |
> |
and ${\langle T_{gold}\rangle}$ and ${\langle T_{water}\rangle}$ are the |
| 401 |
> |
average observed temperature of gold and water phases respectively. |
| 402 |
|
|
| 403 |
|
\section{Results And Discussion} |
| 404 |
|
\subsection{Shear Viscosity} |
| 471 |
|
attractive than swapping RNEMD in shear viscosity calculation. |
| 472 |
|
|
| 473 |
|
\subsection{Thermal Conductivity} |
| 474 |
< |
|
| 474 |
> |
\subsubsection{Lennard-Jones Fluid} |
| 475 |
|
Our thermal conductivity calculations also show that scaling method results |
| 476 |
|
agree with swapping method. Table \ref{thermal} lists our simulation |
| 477 |
|
results with similar manner we used in shear viscosity |
| 540 |
|
\label{histScale} |
| 541 |
|
\end{figure} |
| 542 |
|
|
| 543 |
< |
\subsection{Interfaciel Thermal Conductivity} |
| 543 |
> |
\subsubsection{SPC/E Water} |
| 544 |
> |
Our results of SPC/E water thermal conductivity are comparable to |
| 545 |
> |
Bedrov {\it et al.}\cite{ISI:000090151400044}, which employed the |
| 546 |
> |
previous swapping RNEMD method for their calculation. Our simulations |
| 547 |
> |
were able to produce a similar temperature gradient to their |
| 548 |
> |
system. However, the average temperature of our system is 300K, while |
| 549 |
> |
theirs is 318K, which would be attributed for part of the difference |
| 550 |
> |
between the two series of results. Both methods yields values in |
| 551 |
> |
agreement with experiment. And this shows the applicability of our |
| 552 |
> |
method to multi-atom molecular system. |
| 553 |
|
|
| 554 |
|
\begin{figure} |
| 555 |
|
\includegraphics[width=\linewidth]{spceGrad} |
| 568 |
|
\begin{tabular}{cccc} |
| 569 |
|
\hline |
| 570 |
|
$\langle dT/dz\rangle$(K/\AA) & & $\lambda$(W/m/K) & \\ |
| 571 |
< |
& This work & Previous simulations$^a$ & Experiment$^b$\\ |
| 571 |
> |
& This work & Previous simulations\cite{ISI:000090151400044} & |
| 572 |
> |
Experiment$^a$\\ |
| 573 |
|
\hline |
| 574 |
< |
0.3 & 0.82() & 0.784 & 0.64\\ |
| 575 |
< |
0.8 & 0.770() & 0.730\\ |
| 576 |
< |
1.5 & 0.813() & \\ |
| 574 |
> |
0.38 & 0.816(0.044) & & 0.64\\ |
| 575 |
> |
0.81 & 0.770(0.008) & 0.784\\ |
| 576 |
> |
1.54 & 0.813(0.007) & 0.730\\ |
| 577 |
|
\hline |
| 578 |
|
\end{tabular} |
| 579 |
|
\label{spceThermal} |
| 581 |
|
\end{minipage} |
| 582 |
|
\end{table*} |
| 583 |
|
|
| 584 |
+ |
\subsubsection{Crystal Gold} |
| 585 |
+ |
Our results of gold thermal conductivity used QSC force field are |
| 586 |
+ |
shown in Table \ref{AuThermal}. Although our calculation is smaller |
| 587 |
+ |
than experimental value by an order of more than 100, this difference |
| 588 |
+ |
is mainly attributed to the lack of electron interaction |
| 589 |
+ |
representation in our force field parameters. Richardson {\it et |
| 590 |
+ |
al.}\cite{ISI:A1992HX37800010} used similar force field parameters |
| 591 |
+ |
in their metal thermal conductivity calculations. The EMD method they |
| 592 |
+ |
employed in their simulations produced comparable results to |
| 593 |
+ |
ours. Therefore, it is confident to conclude that NIVS-RNEMD is |
| 594 |
+ |
applicable to metal force field system. |
| 595 |
|
|
| 596 |
|
\begin{figure} |
| 597 |
|
\includegraphics[width=\linewidth]{AuGrad} |
| 610 |
|
\begin{tabular}{ccc} |
| 611 |
|
\hline |
| 612 |
|
$\langle dT/dz\rangle$(K/\AA) & $\lambda$(W/m/K)\\ |
| 613 |
< |
& This work & Previous simulations$^a$ \\ |
| 613 |
> |
& This work & Previous simulations\cite{ISI:A1992HX37800010} \\ |
| 614 |
|
\hline |
| 615 |
< |
1.4 & 1.10() & \\ |
| 616 |
< |
2.8 & 1.08() & \\ |
| 617 |
< |
5.1 & 1.15() & \\ |
| 615 |
> |
1.44 & 1.10(0.01) & \\ |
| 616 |
> |
2.86 & 1.08(0.02) & \\ |
| 617 |
> |
5.14 & 1.15(0.01) & \\ |
| 618 |
|
\hline |
| 619 |
|
\end{tabular} |
| 620 |
|
\label{AuThermal} |
| 622 |
|
\end{minipage} |
| 623 |
|
\end{table*} |
| 624 |
|
|
| 625 |
+ |
\subsection{Interfaciel Thermal Conductivity} |
| 626 |
+ |
After valid simulations of homogeneous water and gold systems using |
| 627 |
+ |
NIVS-RNEMD method, calculation of gold/water interfacial thermal |
| 628 |
+ |
conductivity was followed. It is found out that the interfacial |
| 629 |
+ |
conductance is low due to a hydrophobic surface in our system. Figure |
| 630 |
+ |
\ref{interfaceDensity} demonstrates this observance. Consequently, our |
| 631 |
+ |
reported results (Table \ref{interfaceRes}) are of two orders of |
| 632 |
+ |
magnitude smaller than our calculations on homogeneous systems. |
| 633 |
|
|
| 634 |
+ |
\begin{figure} |
| 635 |
+ |
\includegraphics[width=\linewidth]{interfaceDensity} |
| 636 |
+ |
\caption{Density profile for interfacial thermal conductivity |
| 637 |
+ |
simulation box.} |
| 638 |
+ |
\label{interfaceDensity} |
| 639 |
+ |
\end{figure} |
| 640 |
+ |
|
| 641 |
+ |
\begin{figure} |
| 642 |
+ |
\includegraphics[width=\linewidth]{interfaceGrad} |
| 643 |
+ |
\caption{Temperature profiles for interfacial thermal conductivity |
| 644 |
+ |
simulation box.} |
| 645 |
+ |
\label{interfaceGrad} |
| 646 |
+ |
\end{figure} |
| 647 |
+ |
|
| 648 |
+ |
\begin{table*} |
| 649 |
+ |
\begin{minipage}{\linewidth} |
| 650 |
+ |
\begin{center} |
| 651 |
+ |
|
| 652 |
+ |
\caption{Calculation results for interfacial thermal conductivity |
| 653 |
+ |
at ${\langle T\rangle \sim}$ 300K at various thermal exchange |
| 654 |
+ |
rates. Errors of calculations in parentheses. } |
| 655 |
+ |
|
| 656 |
+ |
\begin{tabular}{cccc} |
| 657 |
+ |
\hline |
| 658 |
+ |
$J_z$(MW/m$^2$) & $T_{gold}$ & $T_{water}$ & $G$(MW/m$^2$/K)\\ |
| 659 |
+ |
\hline |
| 660 |
+ |
98.0 & 355.2 & 295.8 & 1.65(0.21) \\ |
| 661 |
+ |
78.8 & 343.8 & 298.0 & 1.72(0.32) \\ |
| 662 |
+ |
73.6 & 344.3 & 298.0 & 1.59(0.24) \\ |
| 663 |
+ |
49.2 & 330.1 & 300.4 & 1.65(0.35) \\ |
| 664 |
+ |
\hline |
| 665 |
+ |
\end{tabular} |
| 666 |
+ |
\label{interfaceRes} |
| 667 |
+ |
\end{center} |
| 668 |
+ |
\end{minipage} |
| 669 |
+ |
\end{table*} |
| 670 |
+ |
|
| 671 |
+ |
\section{Conclusions} |
| 672 |
+ |
NIVS-RNEMD simulation method is developed and tested on various |
| 673 |
+ |
systems. Simulation results demonstrate its validity of thermal |
| 674 |
+ |
conductivity calculations. NIVS-RNEMD improves non-Boltzmann-Maxwell |
| 675 |
+ |
distributions existing in previous RNEMD methods, and extends its |
| 676 |
+ |
applicability to interfacial systems. NIVS-RNEMD has also limited |
| 677 |
+ |
application on shear viscosity calculations, but under high momentum |
| 678 |
+ |
flux, it could cause temperature difference among different |
| 679 |
+ |
dimensions. Modification is necessary to extend the applicability of |
| 680 |
+ |
NIVS-RNEMD in shear viscosity calculations. |
| 681 |
+ |
|
| 682 |
|
\section{Acknowledgments} |
| 683 |
|
Support for this project was provided by the National Science |
| 684 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
