| 190 |
|
temperature of the two separated phases. |
| 191 |
|
|
| 192 |
|
When the interfacial conductance is {\it not} small, there are two |
| 193 |
< |
ways to define $G$. One way is to assume the temperature is discrete |
| 194 |
< |
on the two sides of the interface. $G$ can be calculated using the |
| 195 |
< |
applied thermal flux $J$ and the maximum temperature difference |
| 196 |
< |
measured along the thermal gradient max($\Delta T$), which occurs at |
| 197 |
< |
the Gibbs deviding surface (Figure \ref{demoPic}): \begin{equation} |
| 198 |
< |
G=\frac{J}{\Delta T} \label{discreteG} \end{equation} |
| 193 |
> |
ways to define $G$. One common way is to assume the temperature is |
| 194 |
> |
discrete on the two sides of the interface. $G$ can be calculated |
| 195 |
> |
using the applied thermal flux $J$ and the maximum temperature |
| 196 |
> |
difference measured along the thermal gradient max($\Delta T$), which |
| 197 |
> |
occurs at the Gibbs deviding surface (Figure \ref{demoPic}): |
| 198 |
> |
\begin{equation} |
| 199 |
> |
G=\frac{J}{\Delta T} |
| 200 |
> |
\label{discreteG} |
| 201 |
> |
\end{equation} |
| 202 |
|
|
| 203 |
|
\begin{figure} |
| 204 |
|
\includegraphics[width=\linewidth]{method} |
| 299 |
|
solvent molecules would change the normal behavior of the liquid |
| 300 |
|
phase. Therefore, our $N_{solvent}$ values were chosen to ensure that |
| 301 |
|
these extreme cases did not happen to our simulations. The spacing |
| 302 |
< |
between periodic images of the gold interfaces is $35 \sim 75$\AA. |
| 302 |
> |
between periodic images of the gold interfaces is $45 \sim 75$\AA. |
| 303 |
|
|
| 304 |
|
The initial configurations generated are further equilibrated with the |
| 305 |
|
$x$ and $y$ dimensions fixed, only allowing the $z$-length scale to |
| 350 |
|
these simulations. The chemically-distinct sites (a-e) are expanded |
| 351 |
|
in terms of constituent atoms for both United Atom (UA) and All Atom |
| 352 |
|
(AA) force fields. Most parameters are from |
| 353 |
< |
Refs. \protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} (UA) and |
| 351 |
< |
\protect\cite{OPLSAA} (AA). Cross-interactions with the Au atoms are given |
| 352 |
< |
in Table \ref{MnM}.} |
| 353 |
> |
Refs. \protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes,TraPPE-UA.thiols} (UA) and \protect\cite{OPLSAA} (AA). Cross-interactions with the Au atoms are given in Table \ref{MnM}.} |
| 354 |
|
\label{demoMol} |
| 355 |
|
\end{figure} |
| 356 |
|
|
| 387 |
|
this solvent model. |
| 388 |
|
|
| 389 |
|
Besides the TraPPE-UA models, AA models for both organic solvents are |
| 390 |
< |
included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA} |
| 391 |
< |
force field is used, and additional explicit hydrogen sites were |
| 390 |
> |
included in our studies as well. The OPLS-AA\cite{OPLSAA} force fields |
| 391 |
> |
were used. For hexane, additional explicit hydrogen sites were |
| 392 |
|
included. Besides bonding and non-bonded site-site interactions, |
| 393 |
|
partial charges and the electrostatic interactions were added to each |
| 394 |
< |
CT and HC site. For toluene, the United Force Field developed by |
| 395 |
< |
Rapp\'{e} {\it et al.}\cite{doi:10.1021/ja00051a040} was adopted, and |
| 396 |
< |
a flexible model for the toluene molecule was utilized which included |
| 396 |
< |
bond, bend, torsion, and inversion potentials to enforce ring |
| 397 |
< |
planarity. |
| 394 |
> |
CT and HC site. For toluene, a flexible model for the toluene molecule |
| 395 |
> |
was utilized which included bond, bend, torsion, and inversion |
| 396 |
> |
potentials to enforce ring planarity. |
| 397 |
|
|
| 398 |
|
The butanethiol capping agent in our simulations, were also modeled |
| 399 |
|
with both UA and AA model. The TraPPE-UA force field includes |
| 729 |
|
would not offset this effect. Eventually, when butanethiol coverage |
| 730 |
|
continues to decrease, solvent-capping agent contact actually |
| 731 |
|
decreases with the disappearing of butanethiol molecules. In this |
| 732 |
< |
case, $G$ decrease could not be offset but instead accelerated. [NEED |
| 732 |
> |
case, $G$ decrease could not be offset but instead accelerated. [MAY NEED |
| 733 |
|
SNAPSHOT SHOWING THE PHENOMENA / SLAB DENSITY ANALYSIS] |
| 734 |
|
|
| 735 |
|
A comparison of the results obtained from differenet organic solvents |
| 955 |
|
|
| 956 |
|
Vlugt {\it et al.} has investigated the surface thiol structures for |
| 957 |
|
nanocrystal gold and pointed out that they differs from those of the |
| 958 |
< |
Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to |
| 959 |
< |
change of interfacial thermal transport behavior as well. To |
| 960 |
< |
investigate this problem, an effective means to introduce thermal flux |
| 961 |
< |
and measure the corresponding thermal gradient is desirable for |
| 962 |
< |
simulating structures with spherical symmetry. |
| 958 |
> |
Au(111) surface\cite{landman:1998,vlugt:cpc2007154}. This difference |
| 959 |
> |
might lead to change of interfacial thermal transport behavior as |
| 960 |
> |
well. To investigate this problem, an effective means to introduce |
| 961 |
> |
thermal flux and measure the corresponding thermal gradient is |
| 962 |
> |
desirable for simulating structures with spherical symmetry. |
| 963 |
|
|
| 964 |
|
\section{Acknowledgments} |
| 965 |
|
Support for this project was provided by the National Science |
