| 375 |
|
Another series of our simulation is the calculation of interfacial |
| 376 |
|
thermal conductivity of a Au/H$_2$O system. Respective calculations of |
| 377 |
|
liquid water (Extended Simple Point Charge model) and crystal gold |
| 378 |
< |
(Quantum Sutton-Chen potential) thermal conductivity were performed |
| 379 |
< |
and compared with current results to ensure the validity of |
| 380 |
< |
NIVS-RNEMD. After that, a mixture system was simulated. |
| 378 |
> |
thermal conductivity were performed and compared with current results |
| 379 |
> |
to ensure the validity of NIVS-RNEMD. After that, a mixture system was |
| 380 |
> |
simulated. |
| 381 |
|
|
| 382 |
|
For thermal conductivity calculation of bulk water, a simulation box |
| 383 |
|
consisting of 1000 molecules were first equilibrated under ambient |
| 389 |
|
process was similar to Lennard-Jones fluid system. |
| 390 |
|
|
| 391 |
|
Thermal conductivity calculation of bulk crystal gold used a similar |
| 392 |
< |
protocol. The face-centered cubic crystal simulation box consists of |
| 392 |
> |
protocol. Two types of force field parameters, Embedded Atom Method |
| 393 |
> |
(EAM) and Quantum Sutten-Chen (QSC) force field were used |
| 394 |
> |
respectively. The face-centered cubic crystal simulation box consists of |
| 395 |
|
2880 Au atoms. The lattice was first allowed volume change to relax |
| 396 |
|
under ambient temperature and pressure. Equilibrations in canonical and |
| 397 |
|
microcanonical ensemble were followed in order. With the simulation |
| 570 |
|
\end{table*} |
| 571 |
|
|
| 572 |
|
\subsubsection{Crystal Gold} |
| 573 |
< |
Our results of gold thermal conductivity using QSC force field are |
| 574 |
< |
shown in Table \ref{AuThermal}. Although our calculation is smaller |
| 575 |
< |
than experimental value by an order of more than 100, this difference |
| 576 |
< |
is mainly attributed to the lack of electron interaction |
| 577 |
< |
representation in our force field parameters. Richardson {\it et |
| 578 |
< |
al.}\cite{ISI:A1992HX37800010} using similar force field parameters |
| 579 |
< |
in their metal thermal conductivity calculations. The EMD method they |
| 580 |
< |
employed in their simulations produced comparable results to |
| 581 |
< |
ours. Therefore, it is confident to conclude that NIVS-RNEMD is |
| 582 |
< |
applicable to metal force field system. |
| 573 |
> |
Our results of gold thermal conductivity using two force fields are |
| 574 |
> |
shown separately in Table \ref{qscThermal} and \ref{eamThermal}. In |
| 575 |
> |
these calculations,the end and middle slabs were excluded in thermal |
| 576 |
> |
gradient regession and only used as heat source and drain in the |
| 577 |
> |
systems. Our yielded values using EAM force field are slightly larger |
| 578 |
> |
than those using QSC force field. However, both series are |
| 579 |
> |
significantly smaller than experimental value by an order of more than |
| 580 |
> |
100. It has been verified that this difference is mainly attributed to |
| 581 |
> |
the lack of electron interaction representation in these force field |
| 582 |
> |
parameters. Richardson {\it et al.}\cite{ISI:A1992HX37800010} used EAM |
| 583 |
> |
force field parameters in their metal thermal conductivity |
| 584 |
> |
calculations. The Non-Equilibrium MD method they employed in their |
| 585 |
> |
simulations produced comparable results to ours. As Zhang {\it et |
| 586 |
> |
al.}\cite{ISI:000231042800044} stated, thermal conductivity values |
| 587 |
> |
are influenced mainly by force field. Therefore, it is confident to |
| 588 |
> |
conclude that NIVS-RNEMD is applicable to metal force field system. |
| 589 |
|
|
| 590 |
|
\begin{figure} |
| 591 |
|
\includegraphics[width=\linewidth]{AuGrad} |
| 592 |
< |
\caption{Temperature gradients for crystal gold thermal conductivity.} |
| 592 |
> |
\caption{Temperature gradients for thermal conductivity calculation of |
| 593 |
> |
crystal gold using QSC force field.} |
| 594 |
|
\label{AuGrad} |
| 595 |
|
\end{figure} |
| 596 |
|
|
| 599 |
|
\begin{center} |
| 600 |
|
|
| 601 |
|
\caption{Calculation results for thermal conductivity of crystal gold |
| 602 |
< |
at ${\langle T\rangle}$ = 300K at various thermal exchange rates. Errors of |
| 603 |
< |
calculations in parentheses. } |
| 602 |
> |
using QSC force field at ${\langle T\rangle}$ = 300K at various |
| 603 |
> |
thermal exchange rates. Errors of calculations in parentheses. } |
| 604 |
|
|
| 605 |
|
\begin{tabular}{cc} |
| 606 |
|
\hline |
| 611 |
|
5.14 & 1.15(0.01)\\ |
| 612 |
|
\hline |
| 613 |
|
\end{tabular} |
| 614 |
< |
\label{AuThermal} |
| 614 |
> |
\label{qscThermal} |
| 615 |
|
\end{center} |
| 616 |
|
\end{minipage} |
| 617 |
|
\end{table*} |
| 618 |
|
|
| 619 |
+ |
\begin{figure} |
| 620 |
+ |
\includegraphics[width=\linewidth]{eamGrad} |
| 621 |
+ |
\caption{Temperature gradients for thermal conductivity calculation of |
| 622 |
+ |
crystal gold using EAM force field.} |
| 623 |
+ |
\label{eamGrad} |
| 624 |
+ |
\end{figure} |
| 625 |
+ |
|
| 626 |
+ |
\begin{table*} |
| 627 |
+ |
\begin{minipage}{\linewidth} |
| 628 |
+ |
\begin{center} |
| 629 |
+ |
|
| 630 |
+ |
\caption{Calculation results for thermal conductivity of crystal gold |
| 631 |
+ |
using EAM force field at ${\langle T\rangle}$ = 300K at various |
| 632 |
+ |
thermal exchange rates. Errors of calculations in parentheses. } |
| 633 |
+ |
|
| 634 |
+ |
\begin{tabular}{cc} |
| 635 |
+ |
\hline |
| 636 |
+ |
$\langle dT/dz\rangle$(K/\AA) & $\lambda$(W/m/K)\\ |
| 637 |
+ |
\hline |
| 638 |
+ |
1.24 & 1.24(0.06)\\ |
| 639 |
+ |
2.06 & 1.37(0.04)\\ |
| 640 |
+ |
2.55 & 1.41(0.03)\\ |
| 641 |
+ |
\hline |
| 642 |
+ |
\end{tabular} |
| 643 |
+ |
\label{eamThermal} |
| 644 |
+ |
\end{center} |
| 645 |
+ |
\end{minipage} |
| 646 |
+ |
\end{table*} |
| 647 |
+ |
|
| 648 |
+ |
|
| 649 |
|
\subsection{Interfaciel Thermal Conductivity} |
| 650 |
|
After valid simulations of homogeneous water and gold systems using |
| 651 |
|
NIVS-RNEMD method, calculation of gold/water interfacial thermal |
| 652 |
|
conductivity was followed. It is found out that the interfacial |
| 653 |
|
conductance is low due to a hydrophobic surface in our system. Figure |
| 654 |
|
\ref{interfaceDensity} demonstrates this observance. Consequently, our |
| 655 |
< |
reported results (Table \ref{interfaceRes}) are of two orders of |
| 656 |
< |
magnitude smaller than our calculations on homogeneous systems. |
| 655 |
> |
approximation in $G$ calculation (Eq. \ref{interfaceCalc}) maintains |
| 656 |
> |
valid. Reported results (Table \ref{interfaceRes}) are of two orders of |
| 657 |
> |
magnitude smaller than our calculations on homogeneous systems, and |
| 658 |
> |
thus have larger relative errors than our calculation results on |
| 659 |
> |
homogeneous systems. |
| 660 |
|
|
| 661 |
|
\begin{figure} |
| 662 |
|
\includegraphics[width=\linewidth]{interfaceDensity} |
