| 193 |
|
One way is to assume the temperature is discrete on the two sides of |
| 194 |
|
the interface. $G$ can be calculated using the applied thermal flux |
| 195 |
|
$J$ and the maximum temperature difference measured along the thermal |
| 196 |
< |
gradient max($\Delta T$), which occurs at the Gibbs deviding surface, |
| 197 |
< |
as: |
| 196 |
> |
gradient max($\Delta T$), which occurs at the Gibbs deviding surface |
| 197 |
> |
(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} |
| 205 |
+ |
\caption{Interfacial conductance can be calculated by applying an |
| 206 |
+ |
(unphysical) kinetic energy flux between two slabs, one located |
| 207 |
+ |
within the metal and another on the edge of the periodic box. The |
| 208 |
+ |
system responds by forming a thermal response or a gradient. In |
| 209 |
+ |
bulk liquids, this gradient typically has a single slope, but in |
| 210 |
+ |
interfacial systems, there are distinct thermal conductivity |
| 211 |
+ |
domains. The interfacial conductance, $G$ is found by measuring the |
| 212 |
+ |
temperature gap at the Gibbs dividing surface, or by using second |
| 213 |
+ |
derivatives of the thermal profile.} |
| 214 |
+ |
\label{demoPic} |
| 215 |
+ |
\end{figure} |
| 216 |
+ |
|
| 217 |
|
The other approach is to assume a continuous temperature profile along |
| 218 |
|
the thermal gradient axis (e.g. $z$) and define $G$ at the point where |
| 219 |
|
the magnitude of thermal conductivity $\lambda$ change reach its |
| 240 |
|
surfaces, the metal slab is solvated with simple organic solvents, as |
| 241 |
|
illustrated in Figure \ref{demoPic}. |
| 242 |
|
|
| 229 |
– |
\begin{figure} |
| 230 |
– |
\includegraphics[width=\linewidth]{method} |
| 231 |
– |
\caption{Interfacial conductance can be calculated by applying an |
| 232 |
– |
(unphysical) kinetic energy flux between two slabs, one located |
| 233 |
– |
within the metal and another on the edge of the periodic box. The |
| 234 |
– |
system responds by forming a thermal response or a gradient. In |
| 235 |
– |
bulk liquids, this gradient typically has a single slope, but in |
| 236 |
– |
interfacial systems, there are distinct thermal conductivity |
| 237 |
– |
domains. The interfacial conductance, $G$ is found by measuring the |
| 238 |
– |
temperature gap at the Gibbs dividing surface, or by using second |
| 239 |
– |
derivatives of the thermal profile.} |
| 240 |
– |
\label{demoPic} |
| 241 |
– |
\end{figure} |
| 242 |
– |
|
| 243 |
|
With the simulation cell described above, we are able to equilibrate |
| 244 |
|
the system and impose an unphysical thermal flux between the liquid |
| 245 |
|
and the metal phase using the NIVS algorithm. By periodically applying |
| 251 |
|
|
| 252 |
|
\begin{figure} |
| 253 |
|
\includegraphics[width=\linewidth]{gradT} |
| 254 |
< |
\caption{The 1st and 2nd derivatives of temperature profile can be |
| 255 |
< |
obtained with finite difference approximation.} |
| 254 |
> |
\caption{A sample of Au-butanethiol/hexane interfacial system and the |
| 255 |
> |
temperature profile after a kinetic energy flux is imposed to |
| 256 |
> |
it. The 1st and 2nd derivatives of the temperature profile can be |
| 257 |
> |
obtained with finite difference approximation (lower panel).} |
| 258 |
|
\label{gradT} |
| 259 |
|
\end{figure} |
| 260 |
|
|
| 296 |
|
solvent molecules would change the normal behavior of the liquid |
| 297 |
|
phase. Therefore, our $N_{solvent}$ values were chosen to ensure that |
| 298 |
|
these extreme cases did not happen to our simulations. And the |
| 299 |
< |
corresponding spacing is usually $35 \sim 60$\AA. |
| 299 |
> |
corresponding spacing is usually $35 \sim 75$\AA. |
| 300 |
|
|
| 301 |
|
The initial configurations generated by Packmol are further |
| 302 |
|
equilibrated with the $x$ and $y$ dimensions fixed, only allowing |
| 388 |
|
adopted. Without the rigid body constraints, bonding interactions were |
| 389 |
|
included. For the aromatic ring, improper torsions (inversions) were |
| 390 |
|
added as an extra potential for maintaining the planar shape. |
| 391 |
< |
[MORE CITATIONS?] |
| 391 |
> |
[MORE CITATION?] |
| 392 |
|
|
| 393 |
|
The capping agent in our simulations, the butanethiol molecules can |
| 394 |
|
either use UA or AA model. The TraPPE-UA force fields includes |
| 533 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
| 534 |
|
$G^\prime$) values for the 100\% covered Au-butanethiol/hexane |
| 535 |
|
interfaces with UA model and different hexane molecule numbers |
| 536 |
< |
at different temperatures using a range of energy fluxes.} |
| 536 |
> |
at different temperatures using a range of energy |
| 537 |
> |
fluxes. Error estimates indicated in parenthesis.} |
| 538 |
|
|
| 539 |
|
\begin{tabular}{ccccccc} |
| 540 |
|
\hline\hline |
| 543 |
|
(K) & & $L_x$ \& $L_y$? & (g/cm$^3$) & (GW/m$^2$) & |
| 544 |
|
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 545 |
|
\hline |
| 546 |
< |
200 & 266 & No & 0.672 & -0.96 & 102() & 80.0() \\ |
| 546 |
> |
200 & 266 & No & 0.672 & -0.96 & 102(3) & 80.0(0.8) \\ |
| 547 |
|
& 200 & Yes & 0.694 & 1.92 & 129(11) & 87.3(0.3) \\ |
| 548 |
|
& & Yes & 0.672 & 1.93 & 131(16) & 78(13) \\ |
| 549 |
< |
& & No & 0.688 & 0.96 & 125() & 90.2() \\ |
| 549 |
> |
& & No & 0.688 & 0.96 & 125(16) & 90.2(15) \\ |
| 550 |
|
& & & & 1.91 & 139(10) & 101(10) \\ |
| 551 |
|
& & & & 2.83 & 141(6) & 89.9(9.8) \\ |
| 552 |
|
& 166 & Yes & 0.679 & 0.97 & 115(19) & 69(18) \\ |
| 592 |
|
important role in the thermal transport process across the interface |
| 593 |
|
in that higher degree of contact could yield increased conductance. |
| 594 |
|
|
| 592 |
– |
[ADD ERROR ESTIMATE TO TABLE] |
| 595 |
|
\begin{table*} |
| 596 |
|
\begin{minipage}{\linewidth} |
| 597 |
|
\begin{center} |
| 598 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
| 599 |
|
$G^\prime$) values for a 90\% coverage Au-butanethiol/toluene |
| 600 |
|
interface at different temperatures using a range of energy |
| 601 |
< |
fluxes.} |
| 601 |
> |
fluxes. Error estimates indicated in parenthesis.} |
| 602 |
|
|
| 603 |
|
\begin{tabular}{ccccc} |
| 604 |
|
\hline\hline |
| 605 |
|
$\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\ |
| 606 |
|
(K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 607 |
|
\hline |
| 608 |
< |
200 & 0.933 & -1.86 & 180() & 135() \\ |
| 609 |
< |
& & 2.15 & 204() & 113() \\ |
| 610 |
< |
& & -3.93 & 175() & 114() \\ |
| 608 |
> |
200 & 0.933 & 2.15 & 204(12) & 113(12) \\ |
| 609 |
> |
& & -1.86 & 180(3) & 135(21) \\ |
| 610 |
> |
& & -3.93 & 176(5) & 113(12) \\ |
| 611 |
|
\hline |
| 612 |
< |
300 & 0.855 & -1.91 & 143() & 125() \\ |
| 613 |
< |
& & -4.19 & 134() & 113() \\ |
| 612 |
> |
300 & 0.855 & -1.91 & 143(5) & 125(2) \\ |
| 613 |
> |
& & -4.19 & 135(9) & 113(12) \\ |
| 614 |
|
\hline\hline |
| 615 |
|
\end{tabular} |
| 616 |
|
\label{AuThiolToluene} |
| 853 |
|
power spectrum via a Fourier transform. |
| 854 |
|
|
| 855 |
|
[MAY RELATE TO HASE'S] |
| 856 |
< |
The gold surfaces covered by |
| 857 |
< |
butanethiol molecules, compared to bare gold surfaces, exhibit an |
| 858 |
< |
additional peak observed at a frequency of $\sim$170cm$^{-1}$, which |
| 859 |
< |
is attributed to the vibration of the S-Au bonding. This vibration |
| 860 |
< |
enables efficient thermal transport from surface Au atoms to the |
| 861 |
< |
capping agents. Simultaneously, as shown in the lower panel of |
| 862 |
< |
Fig. \ref{vibration}, the large overlap of the vibration spectra of |
| 863 |
< |
butanethiol and hexane in the all-atom model, including the C-H |
| 864 |
< |
vibration, also suggests high thermal exchange efficiency. The |
| 865 |
< |
combination of these two effects produces the drastic interfacial |
| 866 |
< |
thermal conductance enhancement in the all-atom model. |
| 856 |
> |
The gold surfaces covered by butanethiol molecules, compared to bare |
| 857 |
> |
gold surfaces, exhibit an additional peak observed at the frequency of |
| 858 |
> |
$\sim$170cm$^{-1}$, which is attributed to the S-Au bonding |
| 859 |
> |
vibration. This vibration enables efficient thermal transport from |
| 860 |
> |
surface Au layer to the capping agents. |
| 861 |
> |
[MAY PUT IN OTHER SECTION] Simultaneously, as shown in |
| 862 |
> |
the lower panel of Fig. \ref{vibration}, the large overlap of the |
| 863 |
> |
vibration spectra of butanethiol and hexane in the All-Atom model, |
| 864 |
> |
including the C-H vibration, also suggests high thermal exchange |
| 865 |
> |
efficiency. The combination of these two effects produces the drastic |
| 866 |
> |
interfacial thermal conductance enhancement in the All-Atom model. |
| 867 |
|
|
| 868 |
< |
[REDO. MAY NEED TO CONVERT TO JPEG] |
| 868 |
> |
[NEED SEPARATE FIGURE. MAY NEED TO CONVERT TO JPEG] |
| 869 |
|
\begin{figure} |
| 870 |
|
\includegraphics[width=\linewidth]{vibration} |
| 871 |
|
\caption{Vibrational spectra obtained for gold in different |
| 872 |
< |
environments (upper panel) and for Au/thiol/hexane simulation in |
| 871 |
< |
all-atom model (lower panel).} |
| 872 |
> |
environments.} |
| 873 |
|
\label{vibration} |
| 874 |
|
\end{figure} |
| 875 |
|
|
