| 137 |
|
|
| 138 |
|
\section{Methodology} |
| 139 |
|
\subsection{Imposd-Flux Methods in MD Simulations} |
| 140 |
< |
[CF. CAHILL] |
| 141 |
< |
For systems with low interfacial conductivity one must have a method |
| 142 |
< |
capable of generating relatively small fluxes, compared to those |
| 143 |
< |
required for bulk conductivity. This requirement makes the calculation |
| 144 |
< |
even more difficult for those slowly-converging equilibrium |
| 145 |
< |
methods\cite{Viscardy:2007lq}. |
| 146 |
< |
Forward methods impose gradient, but in interfacial conditions it is |
| 147 |
< |
not clear what behavior to impose at the boundary... |
| 148 |
< |
Imposed-flux reverse non-equilibrium |
| 140 |
> |
Steady state MD simulations has the advantage that not many |
| 141 |
> |
trajectories are needed to study the relationship between thermal flux |
| 142 |
> |
and thermal gradients. For systems including low conductance |
| 143 |
> |
interfaces one must have a method capable of generating or measuring |
| 144 |
> |
relatively small fluxes, compared to those required for bulk |
| 145 |
> |
conductivity. This requirement makes the calculation even more |
| 146 |
> |
difficult for those slowly-converging equilibrium |
| 147 |
> |
methods\cite{Viscardy:2007lq}. Forward methods may impose gradient, |
| 148 |
> |
but in interfacial conditions it is not clear what behavior to impose |
| 149 |
> |
at the interfacial boundaries. Imposed-flux reverse non-equilibrium |
| 150 |
|
methods\cite{MullerPlathe:1997xw} have the flux set {\it a priori} and |
| 151 |
< |
the thermal response becomes easier to |
| 152 |
< |
measure than the flux. Although M\"{u}ller-Plathe's original momentum |
| 153 |
< |
swapping approach can be used for exchanging energy between particles |
| 154 |
< |
of different identity, the kinetic energy transfer efficiency is |
| 155 |
< |
affected by the mass difference between the particles, which limits |
| 156 |
< |
its application on heterogeneous interfacial systems. |
| 151 |
> |
the thermal response becomes easier to measure than the flux. Although |
| 152 |
> |
M\"{u}ller-Plathe's original momentum swapping approach can be used |
| 153 |
> |
for exchanging energy between particles of different identity, the |
| 154 |
> |
kinetic energy transfer efficiency is affected by the mass difference |
| 155 |
> |
between the particles, which limits its application on heterogeneous |
| 156 |
> |
interfacial systems. |
| 157 |
|
|
| 158 |
|
The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach to |
| 159 |
|
non-equilibrium MD simulations is able to impose a wide range of |
| 275 |
|
they are not distinguished in our study. The maximum butanethiol |
| 276 |
|
capacity on Au surface is $1/3$ of the total number of surface Au |
| 277 |
|
atoms, and the packing forms a $(\sqrt{3}\times\sqrt{3})R30^\circ$ |
| 278 |
< |
structure[CITE PORTER]. |
| 279 |
< |
A series of different coverages was derived by evenly eliminating |
| 280 |
< |
butanethiols on the surfaces, and was investigated in order to study |
| 281 |
< |
the relation between coverage and interfacial conductance. |
| 278 |
> |
structure\cite{doi:10.1021/ja00008a001,doi:10.1021/cr9801317}. A |
| 279 |
> |
series of different coverages was derived by evenly eliminating |
| 280 |
> |
butanethiols on the surfaces, and was investigated in order to study |
| 281 |
> |
the relation between coverage and interfacial conductance. |
| 282 |
|
|
| 283 |
|
The capping agent molecules were allowed to migrate during the |
| 284 |
|
simulations. They distributed themselves uniformly and sampled a |
| 304 |
|
solvent molecules would change the normal behavior of the liquid |
| 305 |
|
phase. Therefore, our $N_{solvent}$ values were chosen to ensure that |
| 306 |
|
these extreme cases did not happen to our simulations. And the |
| 307 |
< |
corresponding spacing is usually $35[DOUBLE CHECK] \sim 75$\AA. |
| 307 |
> |
corresponding spacing is usually $35 \sim 75$\AA. |
| 308 |
|
|
| 309 |
|
The initial configurations generated are further equilibrated with the |
| 310 |
|
$x$ and $y$ dimensions fixed, only allowing length scale change in $z$ |
| 505 |
|
C_A (t) = \langle\vec{v}_A (t)\cdot\vec{v}_A (0)\rangle |
| 506 |
|
\label{vCorr} |
| 507 |
|
\end{equation} |
| 507 |
– |
|
| 508 |
|
Followed by Fourier transforms, the power spectrum can be constructed: |
| 509 |
|
\begin{equation} |
| 510 |
|
\hat{f}(\omega) = \int_{-\infty}^{\infty} C_A (t) e^{-2\pi it\omega}\,dt |
| 772 |
|
|
| 773 |
|
Furthermore, results for rigid body toluene solvent, as well as other |
| 774 |
|
UA-hexane solvents, are reasonable within the general experimental |
| 775 |
< |
ranges[CITATIONS]. This suggests that explicit hydrogen might not be a |
| 776 |
< |
required factor for modeling thermal transport phenomena of systems |
| 777 |
< |
such as Au-thiol/organic solvent. |
| 775 |
> |
ranges\cite{Wilson:2002uq,cahill:793,PhysRevB.80.195406}. This |
| 776 |
> |
suggests that explicit hydrogen might not be a required factor for |
| 777 |
> |
modeling thermal transport phenomena of systems such as |
| 778 |
> |
Au-thiol/organic solvent. |
| 779 |
|
|
| 780 |
|
However, results for Au-butanethiol/toluene do not show an identical |
| 781 |
|
trend with those for Au-butanethiol/hexane in that $G$ remains at |
| 886 |
|
measurement results. Compared to the C-H vibrational overlap between |
| 887 |
|
hexane and butanethiol, both of which have alkyl chains, that overlap |
| 888 |
|
between toluene and butanethiol is not so significant and thus does |
| 889 |
< |
not have as much contribution to the ``Intramolecular Vibration |
| 890 |
< |
Redistribution''[CITE HASE]. Conversely, extra degrees of freedom such |
| 891 |
< |
as the C-H vibrations could yield higher heat exchange rate between |
| 892 |
< |
these two phases and result in a much higher conductivity. |
| 889 |
> |
not have as much contribution to the heat exchange |
| 890 |
> |
process. Conversely, extra degrees of freedom such as the C-H |
| 891 |
> |
vibrations could yield higher heat exchange rate between these two |
| 892 |
> |
phases and result in a much higher conductivity. |
| 893 |
|
|
| 894 |
|
Although the QSC model for Au is known to predict an overly low value |
| 895 |
|
for bulk metal gold conductivity\cite{kuang:164101}, our computational |
| 918 |
|
transfer efficiency between butanethiol and organic solvents is closer |
| 919 |
|
to that within bulk liquid phase. |
| 920 |
|
|
| 921 |
< |
As a combinational effects of the above two, butanethiol acts as a |
| 922 |
< |
channel to expedite thermal transport process. The acoustic impedance |
| 923 |
< |
mismatch between the metal and the liquid phase can be effectively |
| 924 |
< |
reduced with the presence of suitable capping agents. |
| 921 |
> |
Furthermore, our observation validated previous |
| 922 |
> |
results\cite{hase:2010} that the intramolecular heat transport of |
| 923 |
> |
alkylthiols is highly effecient. As a combinational effects of these |
| 924 |
> |
phenomena, butanethiol acts as a channel to expedite thermal transport |
| 925 |
> |
process. The acoustic impedance mismatch between the metal and the |
| 926 |
> |
liquid phase can be effectively reduced with the presence of suitable |
| 927 |
> |
capping agents. |
| 928 |
|
|
| 929 |
|
\begin{figure} |
| 930 |
|
\includegraphics[width=\linewidth]{vibration} |
