| 44 |
|
\begin{doublespace} |
| 45 |
|
|
| 46 |
|
\begin{abstract} |
| 47 |
< |
|
| 48 |
< |
With the Non-Isotropic Velocity Scaling algorithm (NIVS) we have |
| 49 |
< |
developed, an unphysical thermal flux can be effectively set up even |
| 50 |
< |
for non-homogeneous systems like interfaces in non-equilibrium |
| 51 |
< |
molecular dynamics simulations. In this work, this algorithm is |
| 52 |
< |
applied for simulating thermal conductance at metal / organic solvent |
| 53 |
< |
interfaces with various coverages of butanethiol capping |
| 54 |
< |
agents. Different solvents and force field models were tested. Our |
| 55 |
< |
results suggest that the United-Atom models are able to provide an |
| 56 |
< |
estimate of the interfacial thermal conductivity comparable to |
| 57 |
< |
experiments in our simulations with satisfactory computational |
| 58 |
< |
efficiency. From our results, the acoustic impedance mismatch between |
| 59 |
< |
metal and liquid phase is effectively reduced by the capping |
| 60 |
< |
agents, and thus leads to interfacial thermal conductance |
| 61 |
< |
enhancement. Furthermore, this effect is closely related to the |
| 62 |
< |
capping agent coverage on the metal surfaces and the type of solvent |
| 63 |
< |
molecules, and is affected by the models used in the simulations. |
| 64 |
< |
|
| 47 |
> |
With the Non-Isotropic Velocity Scaling (NIVS) approach to Reverse |
| 48 |
> |
Non-Equilibrium Molecular Dynamics (RNEMD) it is possible to impose |
| 49 |
> |
an unphysical thermal flux between different regions of |
| 50 |
> |
inhomogeneous systems such as solid / liquid interfaces. We have |
| 51 |
> |
applied NIVS to compute the interfacial thermal conductance at a |
| 52 |
> |
metal / organic solvent interface that has been chemically capped by |
| 53 |
> |
butanethiol molecules. Our calculations suggest that the acoustic |
| 54 |
> |
impedance mismatch between the metal and liquid phases is |
| 55 |
> |
effectively reduced by the capping agents, leading to a greatly |
| 56 |
> |
enhanced conductivity at the interface. Specifically, the chemical |
| 57 |
> |
bond between the metal and the capping agent introduces a |
| 58 |
> |
vibrational overlap that is not present without the capping agent, |
| 59 |
> |
and the overlap between the vibrational spectra (metal to cap, cap |
| 60 |
> |
to solvent) provides a mechanism for rapid thermal transport across |
| 61 |
> |
the interface. Our calculations also suggest that this is a |
| 62 |
> |
non-monotonic function of the fractional coverage of the surface, as |
| 63 |
> |
moderate coverages allow convective heat transport of solvent |
| 64 |
> |
molecules that have been in close contact with the capping agent. |
| 65 |
|
\end{abstract} |
| 66 |
|
|
| 67 |
|
\newpage |
| 73 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 74 |
|
|
| 75 |
|
\section{Introduction} |
| 76 |
< |
Due to the importance of heat flow in nanotechnology, interfacial |
| 77 |
< |
thermal conductance has been studied extensively both experimentally |
| 78 |
< |
and computationally.\cite{cahill:793} Unlike bulk materials, nanoscale |
| 79 |
< |
materials have a significant fraction of their atoms at interfaces, |
| 80 |
< |
and the chemical details of these interfaces govern the heat transfer |
| 81 |
< |
behavior. Furthermore, the interfaces are |
| 76 |
> |
Due to the importance of heat flow (and heat removal) in |
| 77 |
> |
nanotechnology, interfacial thermal conductance has been studied |
| 78 |
> |
extensively both experimentally and computationally.\cite{cahill:793} |
| 79 |
> |
Nanoscale materials have a significant fraction of their atoms at |
| 80 |
> |
interfaces, and the chemical details of these interfaces govern the |
| 81 |
> |
thermal transport properties. Furthermore, the interfaces are often |
| 82 |
|
heterogeneous (e.g. solid - liquid), which provides a challenge to |
| 83 |
< |
traditional methods developed for homogeneous systems. |
| 83 |
> |
computational methods which have been developed for homogeneous or |
| 84 |
> |
bulk systems. |
| 85 |
|
|
| 86 |
< |
Experimentally, various interfaces have been investigated for their |
| 87 |
< |
thermal conductance. Cahill and coworkers studied nanoscale thermal |
| 86 |
> |
Experimentally, the thermal properties of a number of interfaces have |
| 87 |
> |
been investigated. Cahill and coworkers studied nanoscale thermal |
| 88 |
|
transport from metal nanoparticle/fluid interfaces, to epitaxial |
| 89 |
< |
TiN/single crystal oxides interfaces, to hydrophilic and hydrophobic |
| 89 |
> |
TiN/single crystal oxides interfaces, and hydrophilic and hydrophobic |
| 90 |
|
interfaces between water and solids with different self-assembled |
| 91 |
|
monolayers.\cite{Wilson:2002uq,PhysRevB.67.054302,doi:10.1021/jp048375k,PhysRevLett.96.186101} |
| 92 |
< |
Wang {\it et al.} studied heat transport through |
| 93 |
< |
long-chain hydrocarbon monolayers on gold substrate at individual |
| 94 |
< |
molecular level,\cite{Wang10082007} Schmidt {\it et al.} studied the |
| 95 |
< |
role of CTAB on thermal transport between gold nanorods and |
| 96 |
< |
solvent,\cite{doi:10.1021/jp8051888} and Juv\'e {\it et al.} studied |
| 97 |
< |
the cooling dynamics, which is controlled by thermal interface |
| 98 |
< |
resistence of glass-embedded metal |
| 92 |
> |
Wang {\it et al.} studied heat transport through long-chain |
| 93 |
> |
hydrocarbon monolayers on gold substrate at individual molecular |
| 94 |
> |
level,\cite{Wang10082007} Schmidt {\it et al.} studied the role of |
| 95 |
> |
cetyltrimethylammonium bromide (CTAB) on the thermal transport between |
| 96 |
> |
gold nanorods and solvent,\cite{doi:10.1021/jp8051888} and Juv\'e {\it |
| 97 |
> |
et al.} studied the cooling dynamics, which is controlled by thermal |
| 98 |
> |
interface resistance of glass-embedded metal |
| 99 |
|
nanoparticles.\cite{PhysRevB.80.195406} Although interfaces are |
| 100 |
|
normally considered barriers for heat transport, Alper {\it et al.} |
| 101 |
|
suggested that specific ligands (capping agents) could completely |
| 115 |
|
difficult to measure with Equilibrium |
| 116 |
|
MD\cite{doi:10.1080/0026897031000068578} or forward NEMD simulation |
| 117 |
|
methods. Therefore, the Reverse NEMD (RNEMD) |
| 118 |
< |
methods\cite{MullerPlathe:1997xw,kuang:164101} would have the |
| 119 |
< |
advantage of applying this difficult to measure flux (while measuring |
| 120 |
< |
the resulting gradient), given that the simulation methods being able |
| 121 |
< |
to effectively apply an unphysical flux in non-homogeneous systems. |
| 118 |
> |
methods\cite{MullerPlathe:1997xw,kuang:164101} would be advantageous |
| 119 |
> |
in that they {\it apply} the difficult to measure quantity (flux), |
| 120 |
> |
while {\it measuring} the easily-computed quantity (the thermal |
| 121 |
> |
gradient). This is particularly true for inhomogeneous interfaces |
| 122 |
> |
where it would not be clear how to apply a gradient {\it a priori}. |
| 123 |
|
Garde and coworkers\cite{garde:nl2005,garde:PhysRevLett2009} applied |
| 124 |
|
this approach to various liquid interfaces and studied how thermal |
| 125 |
< |
conductance (or resistance) is dependent on chemistry details of |
| 126 |
< |
interfaces, e.g. hydrophobic and hydrophilic aqueous interfaces. |
| 125 |
> |
conductance (or resistance) is dependent on chemical details of a |
| 126 |
> |
number of hydrophobic and hydrophilic aqueous interfaces. {\bf And |
| 127 |
> |
Luo {\it et al.} studied the thermal conductance of Au-SAM-Au |
| 128 |
> |
junctions using the same approach, with comparison to a constant |
| 129 |
> |
temperature difference method\cite{Luo20101}. While this latter |
| 130 |
> |
approach establishes more thermal distributions compared to the |
| 131 |
> |
former RNEMD methods, it does not guarantee momentum or kinetic |
| 132 |
> |
energy conservations.} |
| 133 |
|
|
| 134 |
|
Recently, we have developed a Non-Isotropic Velocity Scaling (NIVS) |
| 135 |
|
algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm |
| 143 |
|
The work presented here deals with the Au(111) surface covered to |
| 144 |
|
varying degrees by butanethiol, a capping agent with short carbon |
| 145 |
|
chain, and solvated with organic solvents of different molecular |
| 146 |
< |
properties. Different models were used for both the capping agent and |
| 147 |
< |
the solvent force field parameters. Using the NIVS algorithm, the |
| 148 |
< |
thermal transport across these interfaces was studied and the |
| 149 |
< |
underlying mechanism for the phenomena was investigated. |
| 146 |
> |
properties. {\bf To our knowledge, few previous MD inverstigations |
| 147 |
> |
have been found to address to these systems yet.} Different models |
| 148 |
> |
were used for both the capping agent and the solvent force field |
| 149 |
> |
parameters. Using the NIVS algorithm, the thermal transport across |
| 150 |
> |
these interfaces was studied and the underlying mechanism for the |
| 151 |
> |
phenomena was investigated. |
| 152 |
|
|
| 153 |
|
\section{Methodology} |
| 154 |
< |
\subsection{Imposd-Flux Methods in MD Simulations} |
| 154 |
> |
\subsection{Imposed-Flux Methods in MD Simulations} |
| 155 |
|
Steady state MD simulations have an advantage in that not many |
| 156 |
|
trajectories are needed to study the relationship between thermal flux |
| 157 |
|
and thermal gradients. For systems with low interfacial conductance, |
| 175 |
|
kinetic energy fluxes without obvious perturbation to the velocity |
| 176 |
|
distributions of the simulated systems. Furthermore, this approach has |
| 177 |
|
the advantage in heterogeneous interfaces in that kinetic energy flux |
| 178 |
< |
can be applied between regions of particles of arbitary identity, and |
| 178 |
> |
can be applied between regions of particles of arbitrary identity, and |
| 179 |
|
the flux will not be restricted by difference in particle mass. |
| 180 |
|
|
| 181 |
|
The NIVS algorithm scales the velocity vectors in two separate regions |
| 182 |
< |
of a simulation system with respective diagonal scaling matricies. To |
| 183 |
< |
determine these scaling factors in the matricies, a set of equations |
| 182 |
> |
of a simulation system with respective diagonal scaling matrices. To |
| 183 |
> |
determine these scaling factors in the matrices, a set of equations |
| 184 |
|
including linear momentum conservation and kinetic energy conservation |
| 185 |
|
constraints and target energy flux satisfaction is solved. With the |
| 186 |
|
scaling operation applied to the system in a set frequency, bulk |
| 212 |
|
discrete on the two sides of the interface. $G$ can be calculated |
| 213 |
|
using the applied thermal flux $J$ and the maximum temperature |
| 214 |
|
difference measured along the thermal gradient max($\Delta T$), which |
| 215 |
< |
occurs at the Gibbs deviding surface (Figure \ref{demoPic}). This is |
| 215 |
> |
occurs at the Gibbs dividing surface (Figure \ref{demoPic}). This is |
| 216 |
|
known as the Kapitza conductance, which is the inverse of the Kapitza |
| 217 |
|
resistance. |
| 218 |
|
\begin{equation} |
| 225 |
|
\caption{Interfacial conductance can be calculated by applying an |
| 226 |
|
(unphysical) kinetic energy flux between two slabs, one located |
| 227 |
|
within the metal and another on the edge of the periodic box. The |
| 228 |
< |
system responds by forming a thermal response or a gradient. In |
| 229 |
< |
bulk liquids, this gradient typically has a single slope, but in |
| 230 |
< |
interfacial systems, there are distinct thermal conductivity |
| 231 |
< |
domains. The interfacial conductance, $G$ is found by measuring the |
| 232 |
< |
temperature gap at the Gibbs dividing surface, or by using second |
| 233 |
< |
derivatives of the thermal profile.} |
| 228 |
> |
system responds by forming a thermal gradient. In bulk liquids, |
| 229 |
> |
this gradient typically has a single slope, but in interfacial |
| 230 |
> |
systems, there are distinct thermal conductivity domains. The |
| 231 |
> |
interfacial conductance, $G$ is found by measuring the temperature |
| 232 |
> |
gap at the Gibbs dividing surface, or by using second derivatives of |
| 233 |
> |
the thermal profile.} |
| 234 |
|
\label{demoPic} |
| 235 |
|
\end{figure} |
| 236 |
|
|
| 269 |
|
|
| 270 |
|
\begin{figure} |
| 271 |
|
\includegraphics[width=\linewidth]{gradT} |
| 272 |
< |
\caption{A sample of Au-butanethiol/hexane interfacial system and the |
| 273 |
< |
temperature profile after a kinetic energy flux is imposed to |
| 274 |
< |
it. The 1st and 2nd derivatives of the temperature profile can be |
| 275 |
< |
obtained with finite difference approximation (lower panel).} |
| 272 |
> |
\caption{A sample of Au (111) / butanethiol / hexane interfacial |
| 273 |
> |
system with the temperature profile after a kinetic energy flux has |
| 274 |
> |
been imposed. Note that the largest temperature jump in the thermal |
| 275 |
> |
profile (corresponding to the lowest interfacial conductance) is at |
| 276 |
> |
the interface between the butanethiol molecules (blue) and the |
| 277 |
> |
solvent (grey). First and second derivatives of the temperature |
| 278 |
> |
profile are obtained using a finite difference approximation (lower |
| 279 |
> |
panel).} |
| 280 |
|
\label{gradT} |
| 281 |
|
\end{figure} |
| 282 |
|
|
| 323 |
|
solvent molecules would change the normal behavior of the liquid |
| 324 |
|
phase. Therefore, our $N_{solvent}$ values were chosen to ensure that |
| 325 |
|
these extreme cases did not happen to our simulations. The spacing |
| 326 |
< |
between periodic images of the gold interfaces is $45 \sim 75$\AA. |
| 326 |
> |
between periodic images of the gold interfaces is $45 \sim 75$\AA in |
| 327 |
> |
our simulations. |
| 328 |
|
|
| 329 |
|
The initial configurations generated are further equilibrated with the |
| 330 |
|
$x$ and $y$ dimensions fixed, only allowing the $z$-length scale to |
| 342 |
|
$\sim$200K. Therefore, thermal flux usually came from the metal to the |
| 343 |
|
liquid so that the liquid has a higher temperature and would not |
| 344 |
|
freeze due to lowered temperatures. After this induced temperature |
| 345 |
< |
gradient had stablized, the temperature profile of the simulation cell |
| 346 |
< |
was recorded. To do this, the simulation cell is devided evenly into |
| 345 |
> |
gradient had stabilized, the temperature profile of the simulation cell |
| 346 |
> |
was recorded. To do this, the simulation cell is divided evenly into |
| 347 |
|
$N$ slabs along the $z$-axis. The average temperatures of each slab |
| 348 |
|
are recorded for 1$\sim$2 ns. When the slab width $d$ of each slab is |
| 349 |
|
the same, the derivatives of $T$ with respect to slab number $n$ can |
| 374 |
|
\caption{Structures of the capping agent and solvents utilized in |
| 375 |
|
these simulations. The chemically-distinct sites (a-e) are expanded |
| 376 |
|
in terms of constituent atoms for both United Atom (UA) and All Atom |
| 377 |
< |
(AA) force fields. Most parameters are from |
| 378 |
< |
Refs. \protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes,TraPPE-UA.thiols} |
| 377 |
> |
(AA) force fields. Most parameters are from References |
| 378 |
> |
\protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes,TraPPE-UA.thiols} |
| 379 |
|
(UA) and \protect\cite{OPLSAA} (AA). Cross-interactions with the Au |
| 380 |
|
atoms are given in Table \ref{MnM}.} |
| 381 |
|
\label{demoMol} |
| 399 |
|
|
| 400 |
|
By eliminating explicit hydrogen atoms, the TraPPE-UA models are |
| 401 |
|
simple and computationally efficient, while maintaining good accuracy. |
| 402 |
< |
However, the TraPPE-UA model for alkanes is known to predict a slighly |
| 402 |
> |
However, the TraPPE-UA model for alkanes is known to predict a slightly |
| 403 |
|
lower boiling point than experimental values. This is one of the |
| 404 |
|
reasons we used a lower average temperature (200K) for our |
| 405 |
|
simulations. If heat is transferred to the liquid phase during the |
| 518 |
|
|
| 519 |
|
\begin{figure} |
| 520 |
|
\includegraphics[width=\linewidth]{coverage} |
| 521 |
< |
\caption{Comparison of interfacial thermal conductivity ($G$) values |
| 522 |
< |
for the Au-butanethiol/solvent interface with various UA models and |
| 523 |
< |
different capping agent coverages at $\langle T\rangle\sim$200K.} |
| 521 |
> |
\caption{The interfacial thermal conductivity ($G$) has a |
| 522 |
> |
non-monotonic dependence on the degree of surface capping. This |
| 523 |
> |
data is for the Au(111) / butanethiol / solvent interface with |
| 524 |
> |
various UA force fields at $\langle T\rangle \sim $200K.} |
| 525 |
|
\label{coverage} |
| 526 |
|
\end{figure} |
| 527 |
|
|
| 535 |
|
From Figure \ref{coverage}, one can see the significance of the |
| 536 |
|
presence of capping agents. When even a small fraction of the Au(111) |
| 537 |
|
surface sites are covered with butanethiols, the conductivity exhibits |
| 538 |
< |
an enhancement by at least a factor of 3. Cappping agents are clearly |
| 538 |
> |
an enhancement by at least a factor of 3. Capping agents are clearly |
| 539 |
|
playing a major role in thermal transport at metal / organic solvent |
| 540 |
|
surfaces. |
| 541 |
|
|
| 593 |
|
\caption{Computed interfacial thermal conductance ($G$ and |
| 594 |
|
$G^\prime$) values for interfaces using various models for |
| 595 |
|
solvent and capping agent (or without capping agent) at |
| 596 |
< |
$\langle T\rangle\sim$200K. (D stands for deuterated solvent |
| 597 |
< |
or capping agent molecules; ``Avg.'' denotes results that are |
| 598 |
< |
averages of simulations under different applied thermal flux values $(J_z)$. Error |
| 599 |
< |
estimates are indicated in parentheses.)} |
| 596 |
> |
$\langle T\rangle\sim$200K. Here ``D'' stands for deuterated |
| 597 |
> |
solvent or capping agent molecules; ``Avg.'' denotes results |
| 598 |
> |
that are averages of simulations under different applied |
| 599 |
> |
thermal flux $(J_z)$ values. Error estimates are indicated in |
| 600 |
> |
parentheses.} |
| 601 |
|
|
| 602 |
|
\begin{tabular}{llccc} |
| 603 |
|
\hline\hline |
| 644 |
|
phases. |
| 645 |
|
|
| 646 |
|
For the fully-covered surfaces, the choice of force field for the |
| 647 |
< |
capping agent and solvent has a large impact on the calulated values |
| 647 |
> |
capping agent and solvent has a large impact on the calculated values |
| 648 |
|
of $G$ and $G^\prime$. The AA thiol to AA solvent conductivities are |
| 649 |
|
much larger than their UA to UA counterparts, and these values exceed |
| 650 |
|
the experimental estimates by a large measure. The AA force field |
| 699 |
|
flow simply by changing the sign of the flux, and thermal gradients |
| 700 |
|
which would be difficult to obtain experimentally ($5$ K/\AA) can be |
| 701 |
|
easily simulated. However, the magnitude of the applied flux is not |
| 702 |
< |
arbitary if one aims to obtain a stable and reliable thermal gradient. |
| 702 |
> |
arbitrary if one aims to obtain a stable and reliable thermal gradient. |
| 703 |
|
A temperature gradient can be lost in the noise if $|J_z|$ is too |
| 704 |
|
small, and excessive $|J_z|$ values can cause phase transitions if the |
| 705 |
|
extremes of the simulation cell become widely separated in |
| 724 |
|
\begin{table*} |
| 725 |
|
\begin{minipage}{\linewidth} |
| 726 |
|
\begin{center} |
| 727 |
< |
\caption{Computed interfacial thermal conductivity ($G$ and |
| 728 |
< |
$G^\prime$) values for the 100\% covered Au-butanethiol/hexane |
| 729 |
< |
interfaces with UA model and different hexane molecule numbers |
| 730 |
< |
at different temperatures using a range of energy |
| 731 |
< |
fluxes. Error estimates indicated in parenthesis.} |
| 727 |
> |
\caption{In the hexane-solvated interfaces, the system size has |
| 728 |
> |
little effect on the calculated values for interfacial |
| 729 |
> |
conductance ($G$ and $G^\prime$), but the direction of heat |
| 730 |
> |
flow (i.e. the sign of $J_z$) can alter the average |
| 731 |
> |
temperature of the liquid phase and this can alter the |
| 732 |
> |
computed conductivity.} |
| 733 |
|
|
| 734 |
|
\begin{tabular}{ccccccc} |
| 735 |
|
\hline\hline |
| 778 |
|
between the hexane and butanethiol, and this accounts for our |
| 779 |
|
observation of lower conductance at higher temperatures as shown in |
| 780 |
|
Table \ref{AuThiolHexaneUA}. In raising the average temperature from |
| 781 |
< |
200K to 250K, the density drop of ~20\% in the solvent phase leads to |
| 782 |
< |
a ~65\% drop in the conductance. |
| 781 |
> |
200K to 250K, the density drop of $\sim$20\% in the solvent phase |
| 782 |
> |
leads to a $\sim$40\% drop in the conductance. |
| 783 |
|
|
| 784 |
|
Similar behavior is observed in the TraPPE-UA model for toluene, |
| 785 |
|
although this model has better agreement with the experimental |
| 786 |
|
densities of toluene. The expansion of the toluene liquid phase is |
| 787 |
|
not as significant as that of the hexane (8.3\% over 100K), and this |
| 788 |
< |
limits the effect to ~20\% drop in thermal conductivity (Table |
| 788 |
> |
limits the effect to $\sim$20\% drop in thermal conductivity (Table |
| 789 |
|
\ref{AuThiolToluene}). |
| 790 |
|
|
| 791 |
|
Although we have not mapped out the behavior at a large number of |
| 797 |
|
\begin{table*} |
| 798 |
|
\begin{minipage}{\linewidth} |
| 799 |
|
\begin{center} |
| 800 |
< |
\caption{Computed interfacial thermal conductivity ($G$ and |
| 801 |
< |
$G^\prime$) values for a 90\% coverage Au-butanethiol/toluene |
| 802 |
< |
interface at different temperatures using a range of energy |
| 803 |
< |
fluxes. Error estimates indicated in parenthesis.} |
| 800 |
> |
\caption{When toluene is the solvent, the interfacial thermal |
| 801 |
> |
conductivity is less sensitive to temperature, but again, the |
| 802 |
> |
direction of the heat flow can alter the solvent temperature |
| 803 |
> |
and can change the computed conductance values.} |
| 804 |
|
|
| 805 |
|
\begin{tabular}{ccccc} |
| 806 |
|
\hline\hline |
| 827 |
|
S atom layer, and butanethiol molecules which embed into the surface |
| 828 |
|
Au layer. The driving force for this behavior is the strong Au-S |
| 829 |
|
interactions which are modeled here with a deep Lennard-Jones |
| 830 |
< |
potential. This phenomenon agrees with reconstructions that have beeen |
| 830 |
> |
potential. This phenomenon agrees with reconstructions that have been |
| 831 |
|
experimentally |
| 832 |
|
observed.\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt |
| 833 |
|
{\it et al.} kept their Au(111) slab rigid so that their simulations |
| 840 |
|
|
| 841 |
|
However, when the surface is not completely covered by butanethiols, |
| 842 |
|
the simulated system appears to be more resistent to the |
| 843 |
< |
reconstruction. O ur Au / butanethiol / toluene system had the Au(111) |
| 843 |
> |
reconstruction. Our Au / butanethiol / toluene system had the Au(111) |
| 844 |
|
surfaces 90\% covered by butanethiols, but did not see this above |
| 845 |
|
phenomena even at $\langle T\rangle\sim$300K. That said, we did |
| 846 |
|
observe butanethiols migrating to neighboring three-fold sites during |
| 847 |
< |
a simulation. Since the interface persisted in these simulations, |
| 847 |
> |
a simulation. Since the interface persisted in these simulations, we |
| 848 |
|
were able to obtain $G$'s for these interfaces even at a relatively |
| 849 |
|
high temperature without being affected by surface reconstructions. |
| 850 |
|
|
| 863 |
|
spectra, simulations were run after equilibration in the |
| 864 |
|
microcanonical (NVE) ensemble and without a thermal |
| 865 |
|
gradient. Snapshots of configurations were collected at a frequency |
| 866 |
< |
that is higher than that of the fastest vibrations occuring in the |
| 866 |
> |
that is higher than that of the fastest vibrations occurring in the |
| 867 |
|
simulations. With these configurations, the velocity auto-correlation |
| 868 |
|
functions can be computed: |
| 869 |
|
\begin{equation} |
| 883 |
|
shown as in Figure \ref{specAu}. Regardless of the presence of |
| 884 |
|
solvent, the gold surfaces which are covered by butanethiol molecules |
| 885 |
|
exhibit an additional peak observed at a frequency of |
| 886 |
< |
$\sim$170cm$^{-1}$. We attribute this peak to the S-Au bonding |
| 886 |
> |
$\sim$165cm$^{-1}$. We attribute this peak to the S-Au bonding |
| 887 |
|
vibration. This vibration enables efficient thermal coupling of the |
| 888 |
|
surface Au layer to the capping agents. Therefore, in our simulations, |
| 889 |
|
the Au / S interfaces do not appear to be the primary barrier to |
| 890 |
|
thermal transport when compared with the butanethiol / solvent |
| 891 |
< |
interfaces. |
| 891 |
> |
interfaces. {\bf This confirms the results from Luo {\it et |
| 892 |
> |
al.}\cite{Luo20101}, which reported $G$ for Au-SAM junctions |
| 893 |
> |
generally twice larger than what we have computed for the |
| 894 |
> |
thiol-liquid interfaces.} |
| 895 |
|
|
| 896 |
|
\begin{figure} |
| 897 |
|
\includegraphics[width=\linewidth]{vibration} |
| 898 |
< |
\caption{Vibrational power spectra for gold in different solvent |
| 899 |
< |
environments. The presence of the butanethiol capping molecules |
| 900 |
< |
adds a vibrational peak at $\sim$170cm$^{-1}$.} |
| 898 |
> |
\caption{The vibrational power spectrum for thiol-capped gold has an |
| 899 |
> |
additional vibrational peak at $\sim $165cm$^{-1}$. Bare gold |
| 900 |
> |
surfaces (both with and without a solvent over-layer) are missing |
| 901 |
> |
this peak. A similar peak at $\sim $165cm$^{-1}$ also appears in |
| 902 |
> |
the vibrational power spectrum for the butanethiol capping agents.} |
| 903 |
|
\label{specAu} |
| 904 |
|
\end{figure} |
| 905 |
|
|
| 906 |
|
Also in this figure, we show the vibrational power spectrum for the |
| 907 |
|
bound butanethiol molecules, which also exhibits the same |
| 908 |
< |
$\sim$170cm$^{-1}$ peak. |
| 908 |
> |
$\sim$165cm$^{-1}$ peak. |
| 909 |
|
|
| 910 |
|
\subsection{Overlap of power spectra} |
| 911 |
|
A comparison of the results obtained from the two different organic |
| 917 |
|
vibrations were treated classically. The presence of extra degrees of |
| 918 |
|
freedom in the AA force field yields higher heat exchange rates |
| 919 |
|
between the two phases and results in a much higher conductivity than |
| 920 |
< |
in the UA force field. |
| 920 |
> |
in the UA force field. {\bf Due to the classical models used, this |
| 921 |
> |
even includes those high frequency modes which should be unpopulated |
| 922 |
> |
at our relatively low temperatures. This artifact causes high |
| 923 |
> |
frequency vibrations accountable for thermal transport in classical |
| 924 |
> |
MD simulations.} |
| 925 |
|
|
| 926 |
|
The similarity in the vibrational modes available to solvent and |
| 927 |
|
capping agent can be reduced by deuterating one of the two components |
| 966 |
|
|
| 967 |
|
\begin{figure} |
| 968 |
|
\includegraphics[width=\linewidth]{uahxnua} |
| 969 |
< |
\caption{Vibrational spectra obtained for normal (upper) and |
| 970 |
< |
deuterated (lower) hexane in Au-butanethiol/hexane |
| 971 |
< |
systems. Butanethiol spectra are shown as reference. Both hexane and |
| 972 |
< |
butanethiol were using United-Atom models.} |
| 969 |
> |
\caption{Vibrational power spectra for UA models for the butanethiol |
| 970 |
> |
and hexane solvent (upper panel) show the high degree of overlap |
| 971 |
> |
between these two molecules, particularly at lower frequencies. |
| 972 |
> |
Deuterating a UA model for the solvent (lower panel) does not |
| 973 |
> |
decouple the two spectra to the same degree as in the AA force |
| 974 |
> |
field (see Fig \ref{aahxntln}).} |
| 975 |
|
\label{uahxnua} |
| 976 |
|
\end{figure} |
| 977 |
|
|
| 989 |
|
presence of capping agent, compared with the bare gold / liquid |
| 990 |
|
interfaces. The acoustic impedance mismatch between the metal and the |
| 991 |
|
liquid phase is effectively eliminated by a chemically-bonded capping |
| 992 |
< |
agent. Furthermore, the coverage precentage of the capping agent plays |
| 992 |
> |
agent. Furthermore, the coverage percentage of the capping agent plays |
| 993 |
|
an important role in the interfacial thermal transport |
| 994 |
|
process. Moderately low coverages allow higher contact between capping |
| 995 |
|
agent and solvent, and thus could further enhance the heat transfer |
| 1026 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
| 1027 |
|
the Center for Research Computing (CRC) at the University of Notre |
| 1028 |
|
Dame. |
| 1029 |
+ |
|
| 1030 |
+ |
\section{Supporting Information} |
| 1031 |
+ |
This information is available free of charge via the Internet at |
| 1032 |
+ |
http://pubs.acs.org. |
| 1033 |
+ |
|
| 1034 |
|
\newpage |
| 1035 |
|
|
| 1036 |
|
\bibliography{interfacial} |
