| 86 |
|
Previously, reverse nonequilibrium molecular dynamics (RNEMD) methods |
| 87 |
|
have been applied to calculate the interfacial thermal conductance at |
| 88 |
|
flat (111) metal / organic solvent interfaces that had been chemically |
| 89 |
< |
protected by mixed-chain alkanethiolate groups.\cite{kuang:AuThl} |
| 89 |
> |
protected by varying coverages of alkanethiolate groups.\cite{kuang:AuThl} |
| 90 |
|
These simulations suggested an explanation for the increased thermal |
| 91 |
|
conductivity at alkanethiol-capped metal surfaces compared with bare |
| 92 |
|
metal interfaces. Specifically, the chemical bond between the metal |
| 119 |
|
curvature that creates gaps in well-ordered self-assembled monolayers, |
| 120 |
|
and the effect of those gaps on the thermal conductance is unknown. |
| 121 |
|
|
| 122 |
– |
|
| 123 |
– |
|
| 122 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 123 |
|
% INTERFACIAL THERMAL CONDUCTANCE OF METALLIC NANOPARTICLES |
| 124 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 176 |
|
|
| 177 |
|
In this work, thiolated gold nanospheres were modeled using a united atom force field and non-equilibrium molecular dynamics. Gold nanoparticles |
| 178 |
|
with radii ranging from 10 - 25 \AA\ were created from a bulk fcc |
| 179 |
< |
lattice. To match surface coverages previously reported by Badia, |
| 180 |
< |
\textit{et al.}\cite{Badia1996:2}, these particles were passivated |
| 183 |
< |
with a 50\% coverage of a selection of alkyl thiolates of varying |
| 179 |
> |
lattice. These particles were passivated |
| 180 |
> |
with a 50\% coverage -- based on coverage densities reported by Badia \textit{et al.} -- of a selection of alkyl thiolates of varying |
| 181 |
|
chain lengths. The passivated particles were then solvated in hexane. |
| 182 |
|
Details of the models and simulation protocol follow in the next |
| 183 |
|
section. |
| 184 |
|
|
| 185 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 186 |
+ |
% COMPUTATIONAL DETAILS |
| 187 |
+ |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 188 |
+ |
\section{Computational Details} |
| 189 |
+ |
|
| 190 |
+ |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 191 |
|
% NON-PERIODIC VSS-RNEMD METHODOLOGY |
| 192 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 193 |
|
\subsection{Creating a thermal flux between particles and solvent} |
| 258 |
|
interfacial thermal conductance of the ligand layer. |
| 259 |
|
|
| 260 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 259 |
– |
% COMPUTATIONAL DETAILS |
| 260 |
– |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 261 |
– |
\section{Computational Details} |
| 262 |
– |
|
| 263 |
– |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 261 |
|
% FORCE FIELDS |
| 262 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 263 |
|
\subsection{Force Fields} |
| 264 |
|
|
| 265 |
|
Throughout this work, gold -- gold interactions are described by the |
| 266 |
< |
quantum Sutton-Chen (QSC) model.\cite{PhysRevB.59.3527} The hexane |
| 266 |
> |
quantum Sutton-Chen (QSC) model.\cite{PhysRevB.59.3527} Previous work\cite{kuang:AuThl} has demonstrated that the electronic contributions to heat conduction (which are missing from the QSC model) across heterogeneous metal / non-metal interfaces are negligible compared to phonon excitation, which is captured by the classical model. The hexane |
| 267 |
|
solvent is described by the TraPPE united atom |
| 268 |
|
model,\cite{TraPPE-UA.alkanes} where sites are located at the carbon |
| 269 |
|
centers for alkyl groups. The TraPPE-UA model for hexane provides both |
| 281 |
|
widely-used effective potential of Hautman and Klein for the Au(111) |
| 282 |
|
surface.\cite{hautman:4994} |
| 283 |
|
|
| 287 |
– |
|
| 288 |
– |
|
| 284 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 285 |
|
% SIMULATION PROTOCOL |
| 286 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 324 |
|
coupling to the external temperature bath was removed to avoid |
| 325 |
|
interference with the imposed RNEMD flux. |
| 326 |
|
|
| 327 |
+ |
\begin{figure} |
| 328 |
+ |
\includegraphics[width=\linewidth]{figures/temp_profile} |
| 329 |
+ |
\caption{Radial temperature profile for a 25 \AA\ radius particle protected with a 50\% coverage of TraPPE-UA butanethiolate (C$_4$) ligands and solvated in TraPPE-UA hexane. A kinetic energy flux is applied between RNEMD region A and RNEMD region B. The size of the temperature discontinuity at the interface is governed by the interfacial thermal conductance.} |
| 330 |
+ |
\label{fig:temp_profile} |
| 331 |
+ |
\end{figure} |
| 332 |
+ |
|
| 333 |
|
Because the method conserves \emph{total} angular momentum and energy, |
| 334 |
|
systems which contain a metal nanoparticle embedded in a significant |
| 335 |
|
volume of solvent will still experience nanoparticle diffusion inside |
| 395 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 396 |
|
\section{Mechanisms for Ligand-Enhanced Heat Transfer} |
| 397 |
|
|
| 398 |
+ |
corrugation |
| 399 |
+ |
|
| 400 |
+ |
escape rate |
| 401 |
+ |
|
| 402 |
+ |
orientation of ligand |
| 403 |
+ |
|
| 404 |
+ |
orientation of solvent |
| 405 |
+ |
|
| 406 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 407 |
|
% CORRUGATION OF PARTICLE SURFACE |
| 408 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 660 |
|
and a lower ligand packing density creates a disordered ligand layer |
| 661 |
|
that lacks well-formed channels for the solvent molecules to occupy. |
| 662 |
|
|
| 654 |
– |
% \begin{figure} |
| 655 |
– |
% \includegraphics[width=\linewidth]{figures/hex_pAngle} |
| 656 |
– |
% \caption{} |
| 657 |
– |
% \label{fig:hex_pAngle} |
| 658 |
– |
% \end{figure} |
| 659 |
– |
|
| 663 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 664 |
|
% SOLVENT PENETRATION OF LIGAND LAYER |
| 665 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 700 |
|
vibrational overlap that is not present between the bare metal surface |
| 701 |
|
and solvent. Thus, regardless of ligand chain length, the presence of |
| 702 |
|
a half-monolayer ligand coverage yields a higher interfacial thermal |
| 703 |
< |
conductance value than the bare nanoparticle. The dependence of the |
| 701 |
< |
interfacial thermal conductance on ligand chain length is primarily |
| 702 |
< |
explained by increased ligand flexibility and a corresponding decrease |
| 703 |
< |
in solvent mobility away from the particles. The shortest and least |
| 703 |
> |
conductance value than the bare nanoparticle. The shortest and least |
| 704 |
|
flexible ligand ($C_4$), which exhibits the highest interfacial |
| 705 |
|
thermal conductance value, has a smaller range of available angles relative to |
| 706 |
< |
the surface normal and is least likely to trap solvent molecules |
| 707 |
< |
within the ligand layer. The longer $C_8$ and $C_{12}$ ligands have |
| 706 |
> |
the surface normal. The longer $C_8$ and $C_{12}$ ligands have |
| 707 |
|
increasingly disordered orientations and correspondingly lower solvent |
| 708 |
< |
escape rates. |
| 710 |
< |
|
| 711 |
< |
When the ligands are less tightly packed, the cooperative |
| 708 |
> |
escape rates. When the ligands are less tightly packed, the cooperative |
| 709 |
|
orientational ordering between the ligand and solvent decreases |
| 710 |
< |
dramatically and the conductive heat transfer model plays a much |
| 714 |
< |
smaller role in determining the total interfacial thermal |
| 715 |
< |
conductance. Thus, heat transfer into the solvent relies primarily on |
| 716 |
< |
the convective model, where solvent molecules pick up thermal energy |
| 717 |
< |
from the ligands and diffuse into the bulk solvent. This mode of heat |
| 718 |
< |
transfer is hampered by a slow solvent escape rate, which is clearly |
| 719 |
< |
present in the randomly ordered long ligand layers. |
| 710 |
> |
dramatically. |
| 711 |
|
|
| 712 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 713 |
|
% **ACKNOWLEDGMENTS** |
