| 329 |
|
after an MD step with a variable frequency. We have tested the method |
| 330 |
|
in a variety of different systems, including homogeneous fluids |
| 331 |
|
(Lennard-Jones and SPC/E water), crystalline solids ({\sc |
| 332 |
< |
eam}~\cite{PhysRevB.33.7983} and quantum Sutton-Chen ({\sc |
| 332 |
> |
eam})~\cite{PhysRevB.33.7983} and quantum Sutton-Chen ({\sc |
| 333 |
|
q-sc})~\cite{PhysRevB.59.3527} models for Gold), and heterogeneous |
| 334 |
< |
interfaces (QSC gold - SPC/E water). The last of these systems would |
| 334 |
> |
interfaces ({\sc q-sc} gold - SPC/E water). The last of these systems would |
| 335 |
|
have been difficult to study using previous RNEMD methods, but using |
| 336 |
|
velocity scaling moves, we can even obtain estimates of the |
| 337 |
|
interfacial thermal conductivities ($G$). |
| 602 |
|
data collection under RNEMD. |
| 603 |
|
|
| 604 |
|
As shown in Figure \ref{spceGrad}, temperature gradients were |
| 605 |
< |
established similar to the previous work. However, the average |
| 606 |
< |
temperature of our system is 300K, while that in Bedrov {\it et al.} |
| 607 |
< |
is 318K, which would be attributed for part of the difference between |
| 608 |
< |
the final calculation results (Table \ref{spceThermal}). [WHY DIDN'T |
| 609 |
< |
WE DO 318 K?] Both methods yield values in reasonable agreement with |
| 610 |
< |
experiment [DONE AT WHAT TEMPERATURE?] |
| 605 |
> |
established similar to the previous work. Our simulation results under |
| 606 |
> |
318K are in well agreement with those from Bedrov {\it et al.} (Table |
| 607 |
> |
\ref{spceThermal}). And both methods yield values in reasonable |
| 608 |
> |
agreement with experimental value. A larger difference between |
| 609 |
> |
simulation result and experiment is found under 300K. This could |
| 610 |
> |
result from the force field that is used in simulation. |
| 611 |
|
|
| 612 |
|
\begin{figure} |
| 613 |
|
\includegraphics[width=\linewidth]{spceGrad} |
| 624 |
|
imposed thermal gradients. Uncertainties are indicated in |
| 625 |
|
parentheses.} |
| 626 |
|
|
| 627 |
< |
\begin{tabular}{|c|ccc|} |
| 627 |
> |
\begin{tabular}{|c|c|ccc|} |
| 628 |
|
\hline |
| 629 |
< |
\multirow{2}{*}{$\langle dT/dz\rangle$(K/\AA)} & \multicolumn{3}{|c|}{$\lambda |
| 630 |
< |
(\mathrm{W m}^{-1} \mathrm{K}^{-1})$} \\ |
| 631 |
< |
& This work (300K) & Previous simulations (318K)\cite{Bedrov:2000} & |
| 629 |
> |
\multirow{2}{*}{$\langle T\rangle$(K)} & |
| 630 |
> |
\multirow{2}{*}{$\langle dT/dz\rangle$(K/\AA)} & |
| 631 |
> |
\multicolumn{3}{|c|}{$\lambda (\mathrm{W m}^{-1} |
| 632 |
> |
\mathrm{K}^{-1})$} \\ |
| 633 |
> |
& & This work & Previous simulations\cite{Bedrov:2000} & |
| 634 |
|
Experiment\cite{WagnerKruse}\\ |
| 635 |
|
\hline |
| 636 |
< |
0.38 & 0.816(0.044) & & 0.64\\ |
| 637 |
< |
0.81 & 0.770(0.008) & 0.784 & \\ |
| 638 |
< |
1.54 & 0.813(0.007) & 0.730 & \\ |
| 636 |
> |
\multirow{3}{*}{300} & 0.38 & 0.816(0.044) & & |
| 637 |
> |
\multirow{3}{*}{0.61}\\ |
| 638 |
> |
& 0.81 & 0.770(0.008) & & \\ |
| 639 |
> |
& 1.54 & 0.813(0.007) & & \\ |
| 640 |
|
\hline |
| 641 |
+ |
\multirow{2}{*}{318} & 0.75 & 0.750(0.032) & 0.784 & |
| 642 |
+ |
\multirow{2}{*}{0.64}\\ |
| 643 |
+ |
& 1.59 & 0.778(0.019) & 0.730 & \\ |
| 644 |
+ |
\hline |
| 645 |
|
\end{tabular} |
| 646 |
|
\label{spceThermal} |
| 647 |
|
\end{center} |
| 707 |
|
slightly larger thermal conductivities than {\sc q-sc}. However, both |
| 708 |
|
values are smaller than experimental value by a factor of more than |
| 709 |
|
200. This behavior has been observed previously by Richardson and |
| 710 |
< |
Clancy, and has been attributed to the lack of electronic effects in |
| 711 |
< |
these force fields.\cite{Clancy:1992} The non-equilibrium MD method |
| 710 |
> |
Clancy, and has been attributed to the lack of electronic contribution |
| 711 |
> |
in these force fields.\cite{Clancy:1992} The non-equilibrium MD method |
| 712 |
|
employed in their simulations gave an thermal conductance estimation |
| 713 |
< |
of [FORCE FIELD] gold as [RESULT IN REF], which is comparable to ours. It |
| 714 |
< |
should be noted that the density of the metal being simulated also |
| 715 |
< |
greatly affects the thermal conductivity. With an expanded lattice, |
| 716 |
< |
lower thermal conductance is expected (and observed). We also observed |
| 717 |
< |
a decrease in thermal conductance at higher temperatures, a trend that |
| 718 |
< |
agrees with experimental measurements [PAGE |
| 719 |
< |
NUMBERS?].\cite{AshcroftMermin} |
| 713 |
> |
of {\sc eam} gold as 1.74$\mathrm{W m}^{-1}\mathrm{K}^{-1}$. As stated |
| 714 |
> |
in their work, this was a rough estimation in the temperature range |
| 715 |
> |
300K-800K. Therefore, our results could be more accurate. It should be |
| 716 |
> |
noted that the density of the metal being simulated also affects the |
| 717 |
> |
thermal conductivity significantly. With an expanded lattice, lower |
| 718 |
> |
thermal conductance is expected (and observed). We also observed a |
| 719 |
> |
decrease in thermal conductance at higher temperatures, a trend that |
| 720 |
> |
agrees with experimental measurements [PAGE NUMBERS?].\cite{AshcroftMermin} |
| 721 |
|
|
| 722 |
|
\begin{table*} |
| 723 |
|
\begin{minipage}{\linewidth} |
