| 45 |
|
|
| 46 |
|
\begin{abstract} |
| 47 |
|
|
| 48 |
< |
We have developed a Non-Isotropic Velocity Scaling algorithm for |
| 49 |
< |
setting up and maintaining stable thermal gradients in non-equilibrium |
| 50 |
< |
molecular dynamics simulations. This approach effectively imposes |
| 51 |
< |
unphysical thermal flux even between particles of different |
| 52 |
< |
identities, conserves linear momentum and kinetic energy, and |
| 53 |
< |
minimally perturbs the velocity profile of a system when compared with |
| 54 |
< |
previous RNEMD methods. We have used this method to simulate thermal |
| 55 |
< |
conductance at metal / organic solvent interfaces both with and |
| 56 |
< |
without the presence of thiol-based capping agents. We obtained |
| 57 |
< |
values comparable with experimental values, and observed significant |
| 58 |
< |
conductance enhancement with the presence of capping agents. Computed |
| 59 |
< |
power spectra indicate the acoustic impedance mismatch between metal |
| 60 |
< |
and liquid phase is greatly reduced by the capping agents and thus |
| 61 |
< |
leads to higher interfacial thermal transfer efficiency. |
| 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 |
|
|
| 65 |
|
\end{abstract} |
| 66 |
|
|
| 73 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 74 |
|
|
| 75 |
|
\section{Introduction} |
| 74 |
– |
[BACKGROUND FOR INTERFACIAL THERMAL CONDUCTANCE PROBLEM] |
| 76 |
|
Interfacial thermal conductance is extensively studied both |
| 77 |
< |
experimentally and computationally, and systems with interfaces |
| 78 |
< |
present are generally heterogeneous. Although interfaces are commonly |
| 79 |
< |
barriers to heat transfer, it has been |
| 80 |
< |
reported\cite{doi:10.1021/la904855s} that under specific circustances, |
| 81 |
< |
e.g. with certain capping agents present on the surface, interfacial |
| 82 |
< |
conductance can be significantly enhanced. However, heat conductance |
| 83 |
< |
of molecular and nano-scale interfaces will be affected by the |
| 83 |
< |
chemical details of the surface and is challenging to |
| 84 |
< |
experimentalist. The lower thermal flux through interfaces is even |
| 85 |
< |
more difficult to measure with EMD and forward NEMD simulation |
| 86 |
< |
methods. Therefore, developing good simulation methods will be |
| 87 |
< |
desirable in order to investigate thermal transport across interfaces. |
| 77 |
> |
experimentally and computationally, due to its importance in nanoscale |
| 78 |
> |
science and technology. Reliability of nanoscale devices depends on |
| 79 |
> |
their thermal transport properties. Unlike bulk homogeneous materials, |
| 80 |
> |
nanoscale materials features significant presence of interfaces, and |
| 81 |
> |
these interfaces could dominate the heat transfer behavior of these |
| 82 |
> |
materials. Furthermore, these materials are generally heterogeneous, |
| 83 |
> |
which challenges traditional research methods for homogeneous systems. |
| 84 |
|
|
| 85 |
+ |
Heat conductance of molecular and nano-scale interfaces will be |
| 86 |
+ |
affected by the chemical details of the surface. Experimentally, |
| 87 |
+ |
various interfaces have been investigated for their thermal |
| 88 |
+ |
conductance properties. Wang {\it et al.} studied heat transport |
| 89 |
+ |
through long-chain hydrocarbon monolayers on gold substrate at |
| 90 |
+ |
individual molecular level\cite{Wang10082007}; Schmidt {\it et al.} |
| 91 |
+ |
studied the role of CTAB on thermal transport between gold nanorods |
| 92 |
+ |
and solvent\cite{doi:10.1021/jp8051888}; Juv\'e {\it et al.} studied |
| 93 |
+ |
the cooling dynamics, which is controlled by thermal interface |
| 94 |
+ |
resistence of glass-embedded metal |
| 95 |
+ |
nanoparticles\cite{PhysRevB.80.195406}. Although interfaces are |
| 96 |
+ |
commonly barriers for heat transport, Alper {\it et al.} suggested |
| 97 |
+ |
that specific ligands (capping agents) could completely eliminate this |
| 98 |
+ |
barrier ($G\rightarrow\infty$)\cite{doi:10.1021/la904855s}. |
| 99 |
+ |
|
| 100 |
+ |
Theoretical and computational studies were also engaged in the |
| 101 |
+ |
interfacial thermal transport research in order to gain an |
| 102 |
+ |
understanding of this phenomena at the molecular level. Hase and |
| 103 |
+ |
coworkers employed Non-Equilibrium Molecular Dynamics (NEMD) |
| 104 |
+ |
simulations to study thermal transport from hot Au(111) substrate to a |
| 105 |
+ |
self-assembled monolayer of alkylthiolate with relatively long chain |
| 106 |
+ |
(8-20 carbon atoms)\cite{hase:2010,hase:2011}. However, |
| 107 |
+ |
emsemble average measurements for heat conductance of interfaces |
| 108 |
+ |
between the capping monolayer on Au and a solvent phase has yet to be |
| 109 |
+ |
studied. The relatively low thermal flux through interfaces is |
| 110 |
+ |
difficult to measure with Equilibrium MD or forward NEMD simulation |
| 111 |
+ |
methods. Therefore, the Reverse NEMD (RNEMD) methods would have the |
| 112 |
+ |
advantage of having this difficult to measure flux known when studying |
| 113 |
+ |
the thermal transport across interfaces, given that the simulation |
| 114 |
+ |
methods being able to effectively apply an unphysical flux in |
| 115 |
+ |
non-homogeneous systems. |
| 116 |
+ |
|
| 117 |
|
Recently, we have developed the Non-Isotropic Velocity Scaling (NIVS) |
| 118 |
|
algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm |
| 119 |
|
retains the desirable features of RNEMD (conservation of linear |
| 121 |
|
conditions) while establishing true thermal distributions in each of |
| 122 |
|
the two slabs. Furthermore, it allows more effective thermal exchange |
| 123 |
|
between particles of different identities, and thus enables extensive |
| 124 |
< |
study of interfacial conductance. |
| 124 |
> |
study of interfacial conductance under steady states. |
| 125 |
|
|
| 126 |
+ |
Our work presented here investigated the Au(111) surface with various |
| 127 |
+ |
coverage of butanethiol, a capping agent with shorter carbon chain, |
| 128 |
+ |
solvated with organic solvents of different molecular shapes. And |
| 129 |
+ |
different models were used for both the capping agent and the solvent |
| 130 |
+ |
force field parameters. With the NIVS algorithm applied, the thermal |
| 131 |
+ |
transport through these interfacial systems was studied and the |
| 132 |
+ |
underlying mechanism for this phenomena was investigated. |
| 133 |
+ |
|
| 134 |
+ |
[WHY STUDY AU-THIOL SURFACE; MAY CITE SHAOYI JIANG] |
| 135 |
+ |
|
| 136 |
|
\section{Methodology} |
| 137 |
|
\subsection{Algorithm} |
| 138 |
|
[BACKGROUND FOR MD METHODS] |
| 162 |
|
of a simulation system with respective diagonal scaling matricies. To |
| 163 |
|
determine these scaling factors in the matricies, a set of equations |
| 164 |
|
including linear momentum conservation and kinetic energy conservation |
| 165 |
< |
constraints and target momentum/energy flux satisfaction is |
| 165 |
> |
constraints and target momentum / energy flux satisfaction is |
| 166 |
|
solved. With the scaling operation applied to the system in a set |
| 167 |
< |
frequency, corresponding momentum/temperature gradients can be built, |
| 168 |
< |
which can be used for computing transportation properties and other |
| 169 |
< |
applications related to momentum/temperature gradients. The NIVS |
| 167 |
> |
frequency, corresponding momentum / temperature gradients can be |
| 168 |
> |
built, which can be used for computing transport properties and other |
| 169 |
> |
applications related to momentum / temperature gradients. The NIVS |
| 170 |
|
algorithm conserves momenta and energy and does not depend on an |
| 171 |
< |
external thermostat. |
| 171 |
> |
external thermostat. |
| 172 |
|
|
| 173 |
|
\subsection{Defining Interfacial Thermal Conductivity $G$} |
| 174 |
|
For interfaces with a relatively low interfacial conductance, the bulk |
| 249 |
|
\label{gradT} |
| 250 |
|
\end{figure} |
| 251 |
|
|
| 252 |
+ |
[MAY INCLUDE POWER SPECTRUM PROTOCOL] |
| 253 |
+ |
|
| 254 |
|
\section{Computational Details} |
| 255 |
< |
\subsection{System Geometry} |
| 256 |
< |
In our simulations, Au is used to construct a metal slab with bare |
| 257 |
< |
(111) surface perpendicular to the $z$-axis. Different slab thickness |
| 258 |
< |
(layer numbers of Au) are simulated. This metal slab is first |
| 259 |
< |
equilibrated under normal pressure (1 atm) and a desired |
| 260 |
< |
temperature. After equilibration, butanethiol is used as the capping |
| 261 |
< |
agent molecule to cover the bare Au (111) surfaces evenly. The sulfur |
| 262 |
< |
atoms in the butanethiol molecules would occupy the three-fold sites |
| 263 |
< |
of the surfaces, and the maximal butanethiol capacity on Au surface is |
| 264 |
< |
$1/3$ of the total number of surface Au atoms[CITATION]. A series of |
| 255 |
> |
\subsection{Simulation Protocol} |
| 256 |
> |
Our MD simulation code, OpenMD\cite{Meineke:2005gd,openmd}, has the |
| 257 |
> |
NIVS algorithm integrated and was used for our simulations. In our |
| 258 |
> |
simulations, Au is used to construct a metal slab with bare (111) |
| 259 |
> |
surface perpendicular to the $z$-axis. Different slab thickness (layer |
| 260 |
> |
numbers of Au) are simulated. This metal slab is first equilibrated |
| 261 |
> |
under normal pressure (1 atm) and a desired temperature. After |
| 262 |
> |
equilibration, butanethiol is used as the capping agent molecule to |
| 263 |
> |
cover the bare Au (111) surfaces evenly. The sulfur atoms in the |
| 264 |
> |
butanethiol molecules would occupy the three-fold sites of the |
| 265 |
> |
surfaces, and the maximal butanethiol capacity on Au surface is $1/3$ |
| 266 |
> |
of the total number of surface Au atoms[CITATIONs]. A series of |
| 267 |
|
different coverage surfaces is investigated in order to study the |
| 268 |
|
relation between coverage and conductance. |
| 269 |
|
|
| 270 |
< |
[COVERAGE DISCRIPTION] However, since the interactions between surface |
| 271 |
< |
Au and butanethiol is non-bonded, the capping agent molecules are |
| 270 |
> |
[COVERAGE DISCRIPTION] |
| 271 |
> |
In the initial configurations for each coverage precentage, |
| 272 |
> |
butanethiols were distributed evenly on the Au(111) surfaces. However, |
| 273 |
> |
since the interaction descriptions between surface Au and butanethiol |
| 274 |
> |
is non-bonded in our simulations, the capping agent molecules are |
| 275 |
|
allowed to migrate to an empty neighbor three-fold site during a |
| 276 |
|
simulation. Therefore, the initial configuration would not severely |
| 277 |
|
affect the sampling of a variety of configurations of the same |
| 279 |
|
effect of these configurations explored in the simulations. [MAY NEED FIGURES] |
| 280 |
|
|
| 281 |
|
After the modified Au-butanethiol surface systems are equilibrated |
| 282 |
< |
under canonical ensemble, Packmol\cite{packmol} is used to pack |
| 283 |
< |
organic solvent molecules in the previously vacuum part of the |
| 284 |
< |
simulation cells, which guarantees that short range repulsive |
| 285 |
< |
interactions do not disrupt the simulations. Two solvents are |
| 286 |
< |
investigated, one which has little vibrational overlap with the |
| 287 |
< |
alkanethiol and plane-like shape (toluene), and one which has similar |
| 288 |
< |
vibrational frequencies and chain-like shape ({\it n}-hexane). The |
| 244 |
< |
spacing filled by solvent molecules, i.e. the gap between periodically |
| 245 |
< |
repeated Au-butanethiol surfaces should be carefully chosen so that it |
| 246 |
< |
would not be too short to affect the liquid phase structure, nor too |
| 247 |
< |
long, leading to over cooling (freezing) or heating (boiling) when a |
| 248 |
< |
thermal flux is applied. In our simulations, this spacing is usually |
| 249 |
< |
$35 \sim 60$\AA. |
| 282 |
> |
under canonical ensemble, organic solvent molecules are packed in the |
| 283 |
> |
previously vacuum part of the simulation cells and guarantees that |
| 284 |
> |
short range repulsive interactions do not disrupt the |
| 285 |
> |
simulations\cite{packmol}. Two solvents are investigated, one which |
| 286 |
> |
has little vibrational overlap with the alkanethiol and plane-like |
| 287 |
> |
shape (toluene), and one which has similar vibrational frequencies and |
| 288 |
> |
chain-like shape ({\it n}-hexane). [MAY EXPLAIN WHY WE CHOOSE THEM] |
| 289 |
|
|
| 290 |
+ |
The spacing filled by solvent molecules, i.e. the gap between |
| 291 |
+ |
periodically repeated Au-butanethiol surfaces should be carefully |
| 292 |
+ |
chosen. A very long length scale for the thermal gradient axis ($z$) |
| 293 |
+ |
may cause excessively hot or cold temperatures in the middle of the |
| 294 |
+ |
solvent region and lead to undesired phenomena such as solvent boiling |
| 295 |
+ |
or freezing when a thermal flux is applied. Conversely, too few |
| 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. |
| 300 |
+ |
|
| 301 |
|
The initial configurations generated by Packmol are further |
| 302 |
|
equilibrated with the $x$ and $y$ dimensions fixed, only allowing |
| 303 |
|
length scale change in $z$ dimension. This is to ensure that the |
| 332 |
|
same type of particles and between particles of different species. |
| 333 |
|
|
| 334 |
|
The Au-Au interactions in metal lattice slab is described by the |
| 335 |
< |
quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC |
| 335 |
> |
quantum Sutton-Chen (QSC) formulation\cite{PhysRevB.59.3527}. The QSC |
| 336 |
|
potentials include zero-point quantum corrections and are |
| 337 |
|
reparametrized for accurate surface energies compared to the |
| 338 |
|
Sutton-Chen potentials\cite{Chen90}. |
| 339 |
|
|
| 340 |
+ |
Figure \ref{demoMol} demonstrates how we name our pseudo-atoms of the |
| 341 |
+ |
organic solvent molecules in our simulations. |
| 342 |
+ |
|
| 343 |
+ |
\begin{figure} |
| 344 |
+ |
\includegraphics[width=\linewidth]{demoMol} |
| 345 |
+ |
\caption{Denomination of atoms or pseudo-atoms in our simulations: a) |
| 346 |
+ |
UA-hexane; b) AA-hexane; c) UA-toluene; d) AA-toluene.} |
| 347 |
+ |
\label{demoMol} |
| 348 |
+ |
\end{figure} |
| 349 |
+ |
|
| 350 |
|
For both solvent molecules, straight chain {\it n}-hexane and aromatic |
| 351 |
|
toluene, United-Atom (UA) and All-Atom (AA) models are used |
| 352 |
|
respectively. The TraPPE-UA |
| 360 |
|
to a system, the temperature of ``hot'' area in the liquid phase would be |
| 361 |
|
significantly higher than the average, to prevent over heating and |
| 362 |
|
boiling of the liquid phase, the average temperature in our |
| 363 |
< |
simulations should be much lower than the liquid boiling point. [NEED MORE DISCUSSION] |
| 363 |
> |
simulations should be much lower than the liquid boiling point. [MORE DISCUSSION] |
| 364 |
|
For UA-toluene model, rigid body constraints are applied, so that the |
| 365 |
< |
benzene ring and the methyl-C(aromatic) bond are kept rigid. This |
| 366 |
< |
would save computational time.[MORE DETAILS NEEDED] |
| 365 |
> |
benzene ring and the methyl-CRar bond are kept rigid. This would save |
| 366 |
> |
computational time.[MORE DETAILS] |
| 367 |
|
|
| 368 |
|
Besides the TraPPE-UA models, AA models for both organic solvents are |
| 369 |
< |
included in our studies as well. For hexane, the OPLS |
| 370 |
< |
all-atom\cite{OPLSAA} force field is used. [MORE DETAILS] |
| 369 |
> |
included in our studies as well. For hexane, the OPLS-AA\cite{OPLSAA} |
| 370 |
> |
force field is used. [MORE DETAILS] |
| 371 |
|
For toluene, the United Force Field developed by Rapp\'{e} {\it et |
| 372 |
|
al.}\cite{doi:10.1021/ja00051a040} is adopted.[MORE DETAILS] |
| 373 |
|
|
| 374 |
|
The capping agent in our simulations, the butanethiol molecules can |
| 375 |
|
either use UA or AA model. The TraPPE-UA force fields includes |
| 376 |
< |
parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used in |
| 377 |
< |
our simulations corresponding to our TraPPE-UA models for solvent. |
| 378 |
< |
and All-Atom models [NEED CITATIONS] |
| 379 |
< |
However, the model choice (UA or AA) of capping agent can be different |
| 380 |
< |
from the solvent. Regardless of model choice, the force field |
| 381 |
< |
parameters for interactions between capping agent and solvent can be |
| 382 |
< |
derived using Lorentz-Berthelot Mixing Rule. |
| 383 |
< |
|
| 384 |
< |
To describe the interactions between metal Au and non-metal capping |
| 385 |
< |
agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive |
| 386 |
< |
other interactions which are not yet finely parametrized. [can add |
| 387 |
< |
hautman and klein's paper here and more discussion; need to put |
| 328 |
< |
aromatic-metal interaction approximation here]\cite{doi:10.1021/jp034405s} |
| 329 |
< |
|
| 330 |
< |
[TABULATED FORCE FIELD PARAMETERS NEEDED] |
| 331 |
< |
|
| 332 |
< |
|
| 333 |
< |
[SURFACE RECONSTRUCTION PREVENTS SIMULATION TEMP TO GO HIGHER] |
| 376 |
> |
parameters for thiol molecules\cite{TraPPE-UA.thiols} and are used for |
| 377 |
> |
UA butanethiol model in our simulations. The OPLS-AA also provides |
| 378 |
> |
parameters for alkyl thiols. However, alkyl thiols adsorbed on Au(111) |
| 379 |
> |
surfaces do not have the hydrogen atom bonded to sulfur. To adapt this |
| 380 |
> |
change and derive suitable parameters for butanethiol adsorbed on |
| 381 |
> |
Au(111) surfaces, we adopt the S parameters from Luedtke and |
| 382 |
> |
Landman\cite{landman:1998} and modify parameters for its neighbor C |
| 383 |
> |
atom for charge balance in the molecule. Note that the model choice |
| 384 |
> |
(UA or AA) of capping agent can be different from the |
| 385 |
> |
solvent. Regardless of model choice, the force field parameters for |
| 386 |
> |
interactions between capping agent and solvent can be derived using |
| 387 |
> |
Lorentz-Berthelot Mixing Rule:[EQN'S] |
| 388 |
|
|
| 389 |
|
|
| 390 |
< |
\section{Results} |
| 391 |
< |
[REARRANGEMENT NEEDED] |
| 392 |
< |
\subsection{Toluene Solvent} |
| 390 |
> |
To describe the interactions between metal Au and non-metal capping |
| 391 |
> |
agent and solvent particles, we refer to an adsorption study of alkyl |
| 392 |
> |
thiols on gold surfaces by Vlugt {\it et |
| 393 |
> |
al.}\cite{vlugt:cpc2007154} They fitted an effective Lennard-Jones |
| 394 |
> |
form of potential parameters for the interaction between Au and |
| 395 |
> |
pseudo-atoms CH$_x$ and S based on a well-established and widely-used |
| 396 |
> |
effective potential of Hautman and Klein\cite{hautman:4994} for the |
| 397 |
> |
Au(111) surface. As our simulations require the gold lattice slab to |
| 398 |
> |
be non-rigid so that it could accommodate kinetic energy for thermal |
| 399 |
> |
transport study purpose, the pair-wise form of potentials is |
| 400 |
> |
preferred. |
| 401 |
|
|
| 402 |
< |
The results (Table \ref{AuThiolToluene}) show a |
| 403 |
< |
significant conductance enhancement compared to the gold/water |
| 404 |
< |
interface without capping agent and agree with available experimental |
| 343 |
< |
data. This indicates that the metal-metal potential, though not |
| 344 |
< |
predicting an accurate bulk metal thermal conductivity, does not |
| 345 |
< |
greatly interfere with the simulation of the thermal conductance |
| 346 |
< |
behavior across a non-metal interface. The solvent model is not |
| 347 |
< |
particularly volatile, so the simulation cell does not expand |
| 348 |
< |
significantly under higher temperature. We did not observe a |
| 349 |
< |
significant conductance decrease when the temperature was increased to |
| 350 |
< |
300K. The results show that the two definitions used for $G$ yield |
| 351 |
< |
comparable values, though $G^\prime$ tends to be smaller. |
| 402 |
> |
Besides, the potentials developed from {\it ab initio} calculations by |
| 403 |
> |
Leng {\it et al.}\cite{doi:10.1021/jp034405s} are adopted for the |
| 404 |
> |
interactions between Au and aromatic C/H atoms in toluene.[MORE DETAILS] |
| 405 |
|
|
| 406 |
+ |
However, the Lennard-Jones parameters between Au and other types of |
| 407 |
+ |
particles in our simulations are not yet well-established. For these |
| 408 |
+ |
interactions, we attempt to derive their parameters using the Mixing |
| 409 |
+ |
Rule. To do this, the ``Metal-non-Metal'' (MnM) interaction parameters |
| 410 |
+ |
for Au is first extracted from the Au-CH$_x$ parameters by applying |
| 411 |
+ |
the Mixing Rule reversely. Table \ref{MnM} summarizes these ``MnM'' |
| 412 |
+ |
parameters in our simulations. |
| 413 |
+ |
|
| 414 |
|
\begin{table*} |
| 415 |
|
\begin{minipage}{\linewidth} |
| 416 |
|
\begin{center} |
| 417 |
< |
\caption{Computed interfacial thermal conductivity ($G$ and |
| 418 |
< |
$G^\prime$) values for the Au/butanethiol/toluene interface at |
| 358 |
< |
different temperatures using a range of energy fluxes.} |
| 417 |
> |
\caption{Lennard-Jones parameters for Au-non-Metal |
| 418 |
> |
interactions in our simulations.} |
| 419 |
|
|
| 420 |
< |
\begin{tabular}{cccc} |
| 420 |
> |
\begin{tabular}{ccc} |
| 421 |
|
\hline\hline |
| 422 |
< |
$\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\ |
| 423 |
< |
(K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 422 |
> |
Non-metal atom & $\sigma$ & $\epsilon$ \\ |
| 423 |
> |
(or pseudo-atom) & \AA & kcal/mol \\ |
| 424 |
|
\hline |
| 425 |
< |
200 & 1.86 & 180 & 135 \\ |
| 426 |
< |
& 2.15 & 204 & 113 \\ |
| 427 |
< |
& 3.93 & 175 & 114 \\ |
| 428 |
< |
300 & 1.91 & 143 & 125 \\ |
| 429 |
< |
& 4.19 & 134 & 113 \\ |
| 425 |
> |
S & 2.40 & 8.465 \\ |
| 426 |
> |
CH3 & 3.54 & 0.2146 \\ |
| 427 |
> |
CH2 & 3.54 & 0.1749 \\ |
| 428 |
> |
CT3 & 3.365 & 0.1373 \\ |
| 429 |
> |
CT2 & 3.365 & 0.1373 \\ |
| 430 |
> |
CTT & 3.365 & 0.1373 \\ |
| 431 |
> |
HC & 2.865 & 0.09256 \\ |
| 432 |
> |
CHar & 3.4625 & 0.1680 \\ |
| 433 |
> |
CRar & 3.555 & 0.1604 \\ |
| 434 |
> |
CA & 3.173 & 0.0640 \\ |
| 435 |
> |
HA & 2.746 & 0.0414 \\ |
| 436 |
|
\hline\hline |
| 437 |
|
\end{tabular} |
| 438 |
< |
\label{AuThiolToluene} |
| 438 |
> |
\label{MnM} |
| 439 |
|
\end{center} |
| 440 |
|
\end{minipage} |
| 441 |
|
\end{table*} |
| 442 |
|
|
| 377 |
– |
\subsection{Hexane Solvent} |
| 443 |
|
|
| 444 |
< |
Using the united-atom model, different coverages of capping agent, |
| 445 |
< |
temperatures of simulations and numbers of solvent molecules were all |
| 446 |
< |
investigated and Table \ref{AuThiolHexaneUA} shows the results of |
| 447 |
< |
these computations. The number of hexane molecules in our simulations |
| 448 |
< |
does not affect the calculations significantly. However, a very long |
| 449 |
< |
length scale for the thermal gradient axis ($z$) may cause excessively |
| 450 |
< |
hot or cold temperatures in the middle of the solvent region and lead |
| 451 |
< |
to undesired phenomena such as solvent boiling or freezing, while too |
| 452 |
< |
few solvent molecules would change the normal behavior of the liquid |
| 453 |
< |
phase. Our $N_{hexane}$ values were chosen to ensure that these |
| 389 |
< |
extreme cases did not happen to our simulations. |
| 444 |
> |
\section{Results and Discussions} |
| 445 |
> |
[MAY HAVE A BRIEF SUMMARY] |
| 446 |
> |
\subsection{How Simulation Parameters Affects $G$} |
| 447 |
> |
[MAY NOT PUT AT FIRST] |
| 448 |
> |
We have varied our protocol or other parameters of the simulations in |
| 449 |
> |
order to investigate how these factors would affect the measurement of |
| 450 |
> |
$G$'s. It turned out that while some of these parameters would not |
| 451 |
> |
affect the results substantially, some other changes to the |
| 452 |
> |
simulations would have a significant impact on the measurement |
| 453 |
> |
results. |
| 454 |
|
|
| 455 |
< |
Table \ref{AuThiolHexaneUA} enables direct comparison between |
| 456 |
< |
different coverages of capping agent, when other system parameters are |
| 457 |
< |
held constant. With high coverage of butanethiol on the gold surface, |
| 458 |
< |
the interfacial thermal conductance is enhanced |
| 459 |
< |
significantly. Interestingly, a slightly lower butanethiol coverage |
| 460 |
< |
leads to a moderately higher conductivity. This is probably due to |
| 461 |
< |
more solvent/capping agent contact when butanethiol molecules are |
| 462 |
< |
not densely packed, which enhances the interactions between the two |
| 463 |
< |
phases and lowers the thermal transfer barrier of this interface. |
| 400 |
< |
% [COMPARE TO AU/WATER IN PAPER] |
| 455 |
> |
In some of our simulations, we allowed $L_x$ and $L_y$ to change |
| 456 |
> |
during equilibrating the liquid phase. Due to the stiffness of the Au |
| 457 |
> |
slab, $L_x$ and $L_y$ would not change noticeably after |
| 458 |
> |
equilibration. Although $L_z$ could fluctuate $\sim$1\% after a system |
| 459 |
> |
is fully equilibrated in the NPT ensemble, this fluctuation, as well |
| 460 |
> |
as those comparably smaller to $L_x$ and $L_y$, would not be magnified |
| 461 |
> |
on the calculated $G$'s, as shown in Table \ref{AuThiolHexaneUA}. This |
| 462 |
> |
insensivity to $L_i$ fluctuations allows reliable measurement of $G$'s |
| 463 |
> |
without the necessity of extremely cautious equilibration process. |
| 464 |
|
|
| 465 |
< |
It is also noted that the overall simulation temperature is another |
| 466 |
< |
factor that affects the interfacial thermal conductance. One |
| 467 |
< |
possibility of this effect may be rooted in the decrease in density of |
| 468 |
< |
the liquid phase. We observed that when the average temperature |
| 469 |
< |
increases from 200K to 250K, the bulk hexane density becomes lower |
| 470 |
< |
than experimental value, as the system is equilibrated under NPT |
| 471 |
< |
ensemble. This leads to lower contact between solvent and capping |
| 472 |
< |
agent, and thus lower conductivity. |
| 465 |
> |
As stated in our computational details, the spacing filled with |
| 466 |
> |
solvent molecules can be chosen within a range. This allows some |
| 467 |
> |
change of solvent molecule numbers for the same Au-butanethiol |
| 468 |
> |
surfaces. We did this study on our Au-butanethiol/hexane |
| 469 |
> |
simulations. Nevertheless, the results obtained from systems of |
| 470 |
> |
different $N_{hexane}$ did not indicate that the measurement of $G$ is |
| 471 |
> |
susceptible to this parameter. For computational efficiency concern, |
| 472 |
> |
smaller system size would be preferable, given that the liquid phase |
| 473 |
> |
structure is not affected. |
| 474 |
|
|
| 475 |
< |
Conductivity values are more difficult to obtain under higher |
| 476 |
< |
temperatures. This is because the Au surface tends to undergo |
| 477 |
< |
reconstructions in relatively high temperatures. Surface Au atoms can |
| 478 |
< |
migrate outward to reach higher Au-S contact; and capping agent |
| 479 |
< |
molecules can be embedded into the surface Au layer due to the same |
| 480 |
< |
driving force. This phenomenon agrees with experimental |
| 481 |
< |
results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. A surface |
| 482 |
< |
fully covered in capping agent is more susceptible to reconstruction, |
| 483 |
< |
possibly because fully coverage prevents other means of capping agent |
| 484 |
< |
relaxation, such as migration to an empty neighbor three-fold site. |
| 475 |
> |
Our NIVS algorithm allows change of unphysical thermal flux both in |
| 476 |
> |
direction and in quantity. This feature extends our investigation of |
| 477 |
> |
interfacial thermal conductance. However, the magnitude of this |
| 478 |
> |
thermal flux is not arbitary if one aims to obtain a stable and |
| 479 |
> |
reliable thermal gradient. A temperature profile would be |
| 480 |
> |
substantially affected by noise when $|J_z|$ has a much too low |
| 481 |
> |
magnitude; while an excessively large $|J_z|$ that overwhelms the |
| 482 |
> |
conductance capacity of the interface would prevent a thermal gradient |
| 483 |
> |
to reach a stablized steady state. NIVS has the advantage of allowing |
| 484 |
> |
$J$ to vary in a wide range such that the optimal flux range for $G$ |
| 485 |
> |
measurement can generally be simulated by the algorithm. Within the |
| 486 |
> |
optimal range, we were able to study how $G$ would change according to |
| 487 |
> |
the thermal flux across the interface. For our simulations, we denote |
| 488 |
> |
$J_z$ to be positive when the physical thermal flux is from the liquid |
| 489 |
> |
to metal, and negative vice versa. The $G$'s measured under different |
| 490 |
> |
$J_z$ is listed in Table \ref{AuThiolHexaneUA} and [REF]. These |
| 491 |
> |
results do not suggest that $G$ is dependent on $J_z$ within this flux |
| 492 |
> |
range. The linear response of flux to thermal gradient simplifies our |
| 493 |
> |
investigations in that we can rely on $G$ measurement with only a |
| 494 |
> |
couple $J_z$'s and do not need to test a large series of fluxes. |
| 495 |
|
|
| 496 |
< |
%MAY ADD MORE DATA TO TABLE |
| 496 |
> |
%ADD MORE TO TABLE |
| 497 |
|
\begin{table*} |
| 498 |
|
\begin{minipage}{\linewidth} |
| 499 |
|
\begin{center} |
| 500 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
| 501 |
< |
$G^\prime$) values for the Au/butanethiol/hexane interface |
| 502 |
< |
with united-atom model and different capping agent coverage |
| 503 |
< |
and solvent molecule numbers at different temperatures using a |
| 430 |
< |
range of energy fluxes.} |
| 501 |
> |
$G^\prime$) values for the 100\% covered Au-butanethiol/hexane |
| 502 |
> |
interfaces with UA model and different hexane molecule numbers |
| 503 |
> |
at different temperatures using a range of energy fluxes.} |
| 504 |
|
|
| 505 |
< |
\begin{tabular}{cccccc} |
| 505 |
> |
\begin{tabular}{cccccccc} |
| 506 |
|
\hline\hline |
| 507 |
< |
Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\ |
| 508 |
< |
coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) & |
| 507 |
> |
$\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ & |
| 508 |
> |
$G$ & $G^\prime$ \\ |
| 509 |
> |
(K) & $N_{hexane}$ & \multicolumn{3}{c}{(\AA)} & (GW/m$^2$) & |
| 510 |
|
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 511 |
|
\hline |
| 512 |
< |
0.0 & 200 & 200 & 0.96 & 43.3 & 42.7 \\ |
| 513 |
< |
& & & 1.91 & 45.7 & 42.9 \\ |
| 514 |
< |
& & 166 & 0.96 & 43.1 & 53.4 \\ |
| 515 |
< |
88.9 & 200 & 166 & 1.94 & 172 & 108 \\ |
| 516 |
< |
100.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\ |
| 517 |
< |
& & 166 & 0.98 & 79.0 & 62.9 \\ |
| 518 |
< |
& & & 1.44 & 76.2 & 64.8 \\ |
| 519 |
< |
& 200 & 200 & 1.92 & 129 & 87.3 \\ |
| 520 |
< |
& & & 1.93 & 131 & 77.5 \\ |
| 521 |
< |
& & 166 & 0.97 & 115 & 69.3 \\ |
| 522 |
< |
& & & 1.94 & 125 & 87.1 \\ |
| 512 |
> |
200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 & |
| 513 |
> |
102() & 80.0() \\ |
| 514 |
> |
& 200 & 29.84 & 25.81 & 93.9 & 1.92 & |
| 515 |
> |
129() & 87.3() \\ |
| 516 |
> |
& & 29.84 & 25.81 & 95.3 & 1.93 & |
| 517 |
> |
131() & 77.5() \\ |
| 518 |
> |
& 166 & 29.84 & 25.81 & 85.7 & 0.97 & |
| 519 |
> |
115() & 69.3() \\ |
| 520 |
> |
& & & & & 1.94 & |
| 521 |
> |
125() & 87.1() \\ |
| 522 |
> |
250 & 200 & 29.84 & 25.87 & 106.8 & 0.96 & |
| 523 |
> |
81.8() & 67.0() \\ |
| 524 |
> |
& 166 & 29.87 & 25.84 & 94.8 & 0.98 & |
| 525 |
> |
79.0() & 62.9() \\ |
| 526 |
> |
& & 29.84 & 25.85 & 95.0 & 1.44 & |
| 527 |
> |
76.2() & 64.8() \\ |
| 528 |
|
\hline\hline |
| 529 |
|
\end{tabular} |
| 530 |
|
\label{AuThiolHexaneUA} |
| 532 |
|
\end{minipage} |
| 533 |
|
\end{table*} |
| 534 |
|
|
| 535 |
< |
For the all-atom model, the liquid hexane phase was not stable under NPT |
| 536 |
< |
conditions. Therefore, the simulation length scale parameters are |
| 537 |
< |
adopted from previous equilibration results of the united-atom model |
| 538 |
< |
at 200K. Table \ref{AuThiolHexaneAA} shows the results of these |
| 539 |
< |
simulations. The conductivity values calculated with full capping |
| 540 |
< |
agent coverage are substantially larger than observed in the |
| 541 |
< |
united-atom model, and is even higher than predicted by |
| 542 |
< |
experiments. It is possible that our parameters for metal-non-metal |
| 543 |
< |
particle interactions lead to an overestimate of the interfacial |
| 544 |
< |
thermal conductivity, although the active C-H vibrations in the |
| 545 |
< |
all-atom model (which should not be appreciably populated at normal |
| 467 |
< |
temperatures) could also account for this high conductivity. The major |
| 468 |
< |
thermal transfer barrier of Au/butanethiol/hexane interface is between |
| 469 |
< |
the liquid phase and the capping agent, so extra degrees of freedom |
| 470 |
< |
such as the C-H vibrations could enhance heat exchange between these |
| 471 |
< |
two phases and result in a much higher conductivity. |
| 535 |
> |
Furthermore, we also attempted to increase system average temperatures |
| 536 |
> |
to above 200K. These simulations are first equilibrated in the NPT |
| 537 |
> |
ensemble under normal pressure. As stated above, the TraPPE-UA model |
| 538 |
> |
for hexane tends to predict a lower boiling point. In our simulations, |
| 539 |
> |
hexane had diffculty to remain in liquid phase when NPT equilibration |
| 540 |
> |
temperature is higher than 250K. Additionally, the equilibrated liquid |
| 541 |
> |
hexane density under 250K becomes lower than experimental value. This |
| 542 |
> |
expanded liquid phase leads to lower contact between hexane and |
| 543 |
> |
butanethiol as well.[MAY NEED FIGURE] And this reduced contact would |
| 544 |
> |
probably be accountable for a lower interfacial thermal conductance, |
| 545 |
> |
as shown in Table \ref{AuThiolHexaneUA}. |
| 546 |
|
|
| 547 |
+ |
A similar study for TraPPE-UA toluene agrees with the above result as |
| 548 |
+ |
well. Having a higher boiling point, toluene tends to remain liquid in |
| 549 |
+ |
our simulations even equilibrated under 300K in NPT |
| 550 |
+ |
ensembles. Furthermore, the expansion of the toluene liquid phase is |
| 551 |
+ |
not as significant as that of the hexane. This prevents severe |
| 552 |
+ |
decrease of liquid-capping agent contact and the results (Table |
| 553 |
+ |
\ref{AuThiolToluene}) show only a slightly decreased interface |
| 554 |
+ |
conductance. Therefore, solvent-capping agent contact should play an |
| 555 |
+ |
important role in the thermal transport process across the interface |
| 556 |
+ |
in that higher degree of contact could yield increased conductance. |
| 557 |
+ |
|
| 558 |
+ |
[ADD Lxyz AND ERROR ESTIMATE TO TABLE] |
| 559 |
|
\begin{table*} |
| 560 |
|
\begin{minipage}{\linewidth} |
| 561 |
|
\begin{center} |
| 476 |
– |
|
| 562 |
|
\caption{Computed interfacial thermal conductivity ($G$ and |
| 563 |
< |
$G^\prime$) values for the Au/butanethiol/hexane interface |
| 564 |
< |
with all-atom model and different capping agent coverage at |
| 565 |
< |
200K using a range of energy fluxes.} |
| 563 |
> |
$G^\prime$) values for a 90\% coverage Au-butanethiol/toluene |
| 564 |
> |
interface at different temperatures using a range of energy |
| 565 |
> |
fluxes.} |
| 566 |
|
|
| 567 |
|
\begin{tabular}{cccc} |
| 568 |
|
\hline\hline |
| 569 |
< |
Thiol & $J_z$ & $G$ & $G^\prime$ \\ |
| 570 |
< |
coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 569 |
> |
$\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\ |
| 570 |
> |
(K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 571 |
|
\hline |
| 572 |
< |
0.0 & 0.95 & 28.5 & 27.2 \\ |
| 573 |
< |
& 1.88 & 30.3 & 28.9 \\ |
| 574 |
< |
100.0 & 2.87 & 551 & 294 \\ |
| 575 |
< |
& 3.81 & 494 & 193 \\ |
| 572 |
> |
200 & -1.86 & 180() & 135() \\ |
| 573 |
> |
& 2.15 & 204() & 113() \\ |
| 574 |
> |
& -3.93 & 175() & 114() \\ |
| 575 |
> |
300 & -1.91 & 143() & 125() \\ |
| 576 |
> |
& -4.19 & 134() & 113() \\ |
| 577 |
|
\hline\hline |
| 578 |
|
\end{tabular} |
| 579 |
< |
\label{AuThiolHexaneAA} |
| 579 |
> |
\label{AuThiolToluene} |
| 580 |
|
\end{center} |
| 581 |
|
\end{minipage} |
| 582 |
|
\end{table*} |
| 583 |
|
|
| 584 |
< |
%subsubsection{Vibrational spectrum study on conductance mechanism} |
| 584 |
> |
Besides lower interfacial thermal conductance, surfaces in relatively |
| 585 |
> |
high temperatures are susceptible to reconstructions, when |
| 586 |
> |
butanethiols have a full coverage on the Au(111) surface. These |
| 587 |
> |
reconstructions include surface Au atoms migrated outward to the S |
| 588 |
> |
atom layer, and butanethiol molecules embedded into the original |
| 589 |
> |
surface Au layer. The driving force for this behavior is the strong |
| 590 |
> |
Au-S interactions in our simulations. And these reconstructions lead |
| 591 |
> |
to higher ratio of Au-S attraction and thus is energetically |
| 592 |
> |
favorable. Furthermore, this phenomenon agrees with experimental |
| 593 |
> |
results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. Vlugt |
| 594 |
> |
{\it et al.} had kept their Au(111) slab rigid so that their |
| 595 |
> |
simulations can reach 300K without surface reconstructions. Without |
| 596 |
> |
this practice, simulating 100\% thiol covered interfaces under higher |
| 597 |
> |
temperatures could hardly avoid surface reconstructions. However, our |
| 598 |
> |
measurement is based on assuming homogeneity on $x$ and $y$ dimensions |
| 599 |
> |
so that measurement of $T$ at particular $z$ would be an effective |
| 600 |
> |
average of the particles of the same type. Since surface |
| 601 |
> |
reconstructions could eliminate the original $x$ and $y$ dimensional |
| 602 |
> |
homogeneity, measurement of $G$ is more difficult to conduct under |
| 603 |
> |
higher temperatures. Therefore, most of our measurements are |
| 604 |
> |
undertaken at $\langle T\rangle\sim$200K. |
| 605 |
> |
|
| 606 |
> |
However, when the surface is not completely covered by butanethiols, |
| 607 |
> |
the simulated system is more resistent to the reconstruction |
| 608 |
> |
above. Our Au-butanethiol/toluene system did not see this phenomena |
| 609 |
> |
even at $\langle T\rangle\sim$300K. The Au(111) surfaces have a 90\% coverage of |
| 610 |
> |
butanethiols and have empty three-fold sites. These empty sites could |
| 611 |
> |
help prevent surface reconstruction in that they provide other means |
| 612 |
> |
of capping agent relaxation. It is observed that butanethiols can |
| 613 |
> |
migrate to their neighbor empty sites during a simulation. Therefore, |
| 614 |
> |
we were able to obtain $G$'s for these interfaces even at a relatively |
| 615 |
> |
high temperature without being affected by surface reconstructions. |
| 616 |
> |
|
| 617 |
> |
\subsection{Influence of Capping Agent Coverage on $G$} |
| 618 |
> |
To investigate the influence of butanethiol coverage on interfacial |
| 619 |
> |
thermal conductance, a series of different coverage Au-butanethiol |
| 620 |
> |
surfaces is prepared and solvated with various organic |
| 621 |
> |
molecules. These systems are then equilibrated and their interfacial |
| 622 |
> |
thermal conductivity are measured with our NIVS algorithm. Table |
| 623 |
> |
\ref{tlnUhxnUhxnD} lists these results for direct comparison between |
| 624 |
> |
different coverages of butanethiol. To study the isotope effect in |
| 625 |
> |
interfacial thermal conductance, deuterated UA-hexane is included as |
| 626 |
> |
well. |
| 627 |
> |
|
| 628 |
> |
It turned out that with partial covered butanethiol on the Au(111) |
| 629 |
> |
surface, the derivative definition for $G$ (Eq. \ref{derivativeG}) has |
| 630 |
> |
difficulty to apply, due to the difficulty in locating the maximum of |
| 631 |
> |
change of $\lambda$. Instead, the discrete definition |
| 632 |
> |
(Eq. \ref{discreteG}) is easier to apply, as max($\Delta T$) can still |
| 633 |
> |
be well-defined. Therefore, $G$'s (not $G^\prime$) are used for this |
| 634 |
> |
section. |
| 635 |
> |
|
| 636 |
> |
From Table \ref{tlnUhxnUhxnD}, one can see the significance of the |
| 637 |
> |
presence of capping agents. Even when a fraction of the Au(111) |
| 638 |
> |
surface sites are covered with butanethiols, the conductivity would |
| 639 |
> |
see an enhancement by at least a factor of 3. This indicates the |
| 640 |
> |
important role cappping agent is playing for thermal transport |
| 641 |
> |
phenomena on metal/organic solvent surfaces. |
| 642 |
> |
|
| 643 |
> |
Interestingly, as one could observe from our results, the maximum |
| 644 |
> |
conductance enhancement (largest $G$) happens while the surfaces are |
| 645 |
> |
about 75\% covered with butanethiols. This again indicates that |
| 646 |
> |
solvent-capping agent contact has an important role of the thermal |
| 647 |
> |
transport process. Slightly lower butanethiol coverage allows small |
| 648 |
> |
gaps between butanethiols to form. And these gaps could be filled with |
| 649 |
> |
solvent molecules, which acts like ``heat conductors'' on the |
| 650 |
> |
surface. The higher degree of interaction between these solvent |
| 651 |
> |
molecules and capping agents increases the enhancement effect and thus |
| 652 |
> |
produces a higher $G$ than densely packed butanethiol arrays. However, |
| 653 |
> |
once this maximum conductance enhancement is reached, $G$ decreases |
| 654 |
> |
when butanethiol coverage continues to decrease. Each capping agent |
| 655 |
> |
molecule reaches its maximum capacity for thermal |
| 656 |
> |
conductance. Therefore, even higher solvent-capping agent contact |
| 657 |
> |
would not offset this effect. Eventually, when butanethiol coverage |
| 658 |
> |
continues to decrease, solvent-capping agent contact actually |
| 659 |
> |
decreases with the disappearing of butanethiol molecules. In this |
| 660 |
> |
case, $G$ decrease could not be offset but instead accelerated. |
| 661 |
> |
|
| 662 |
> |
A comparison of the results obtained from differenet organic solvents |
| 663 |
> |
can also provide useful information of the interfacial thermal |
| 664 |
> |
transport process. The deuterated hexane (UA) results do not appear to |
| 665 |
> |
be much different from those of normal hexane (UA), given that |
| 666 |
> |
butanethiol (UA) is non-deuterated for both solvents. These UA model |
| 667 |
> |
studies, even though eliminating C-H vibration samplings, still have |
| 668 |
> |
C-C vibrational frequencies different from each other. However, these |
| 669 |
> |
differences in the infrared range do not seem to produce an observable |
| 670 |
> |
difference for the results of $G$. [MAY NEED FIGURE] |
| 671 |
> |
|
| 672 |
> |
Furthermore, results for rigid body toluene solvent, as well as other |
| 673 |
> |
UA-hexane solvents, are reasonable within the general experimental |
| 674 |
> |
ranges[CITATIONS]. This suggests that explicit hydrogen might not be a |
| 675 |
> |
required factor for modeling thermal transport phenomena of systems |
| 676 |
> |
such as Au-thiol/organic solvent. |
| 677 |
> |
|
| 678 |
> |
However, results for Au-butanethiol/toluene do not show an identical |
| 679 |
> |
trend with those for Au-butanethiol/hexane in that $G$'s remain at |
| 680 |
> |
approximately the same magnitue when butanethiol coverage differs from |
| 681 |
> |
25\% to 75\%. This might be rooted in the molecule shape difference |
| 682 |
> |
for plane-like toluene and chain-like {\it n}-hexane. Due to this |
| 683 |
> |
difference, toluene molecules have more difficulty in occupying |
| 684 |
> |
relatively small gaps among capping agents when their coverage is not |
| 685 |
> |
too low. Therefore, the solvent-capping agent contact may keep |
| 686 |
> |
increasing until the capping agent coverage reaches a relatively low |
| 687 |
> |
level. This becomes an offset for decreasing butanethiol molecules on |
| 688 |
> |
its effect to the process of interfacial thermal transport. Thus, one |
| 689 |
> |
can see a plateau of $G$ vs. butanethiol coverage in our results. |
| 690 |
> |
|
| 691 |
> |
[NEED ERROR ESTIMATE, MAY ALSO PUT J HERE] |
| 692 |
> |
\begin{table*} |
| 693 |
> |
\begin{minipage}{\linewidth} |
| 694 |
> |
\begin{center} |
| 695 |
> |
\caption{Computed interfacial thermal conductivity ($G$) values |
| 696 |
> |
for the Au-butanethiol/solvent interface with various UA |
| 697 |
> |
models and different capping agent coverages at $\langle |
| 698 |
> |
T\rangle\sim$200K using certain energy flux respectively.} |
| 699 |
> |
|
| 700 |
> |
\begin{tabular}{cccc} |
| 701 |
> |
\hline\hline |
| 702 |
> |
Thiol & \multicolumn{3}{c}{$G$(MW/m$^2$/K)} \\ |
| 703 |
> |
coverage (\%) & hexane & hexane(D) & toluene \\ |
| 704 |
> |
\hline |
| 705 |
> |
0.0 & 46.5() & 43.9() & 70.1() \\ |
| 706 |
> |
25.0 & 151() & 153() & 249() \\ |
| 707 |
> |
50.0 & 172() & 182() & 214() \\ |
| 708 |
> |
75.0 & 242() & 229() & 244() \\ |
| 709 |
> |
88.9 & 178() & - & - \\ |
| 710 |
> |
100.0 & 137() & 153() & 187() \\ |
| 711 |
> |
\hline\hline |
| 712 |
> |
\end{tabular} |
| 713 |
> |
\label{tlnUhxnUhxnD} |
| 714 |
> |
\end{center} |
| 715 |
> |
\end{minipage} |
| 716 |
> |
\end{table*} |
| 717 |
> |
|
| 718 |
> |
\subsection{Influence of Chosen Molecule Model on $G$} |
| 719 |
> |
[MAY COMBINE W MECHANISM STUDY] |
| 720 |
> |
|
| 721 |
> |
In addition to UA solvent/capping agent models, AA models are included |
| 722 |
> |
in our simulations as well. Besides simulations of the same (UA or AA) |
| 723 |
> |
model for solvent and capping agent, different models can be applied |
| 724 |
> |
to different components. Furthermore, regardless of models chosen, |
| 725 |
> |
either the solvent or the capping agent can be deuterated, similar to |
| 726 |
> |
the previous section. Table \ref{modelTest} summarizes the results of |
| 727 |
> |
these studies. |
| 728 |
> |
|
| 729 |
> |
[MORE DATA; ERROR ESTIMATE] |
| 730 |
> |
\begin{table*} |
| 731 |
> |
\begin{minipage}{\linewidth} |
| 732 |
> |
\begin{center} |
| 733 |
> |
|
| 734 |
> |
\caption{Computed interfacial thermal conductivity ($G$ and |
| 735 |
> |
$G^\prime$) values for interfaces using various models for |
| 736 |
> |
solvent and capping agent (or without capping agent) at |
| 737 |
> |
$\langle T\rangle\sim$200K.} |
| 738 |
> |
|
| 739 |
> |
\begin{tabular}{ccccc} |
| 740 |
> |
\hline\hline |
| 741 |
> |
Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\ |
| 742 |
> |
(or bare surface) & model & (GW/m$^2$) & |
| 743 |
> |
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 744 |
> |
\hline |
| 745 |
> |
UA & AA hexane & 1.94 & 135() & 129() \\ |
| 746 |
> |
& & 2.86 & 126() & 115() \\ |
| 747 |
> |
& AA toluene & 1.89 & 200() & 149() \\ |
| 748 |
> |
AA & UA hexane & 1.94 & 116() & 129() \\ |
| 749 |
> |
& AA hexane & 3.76 & 451() & 378() \\ |
| 750 |
> |
& & 4.71 & 432() & 334() \\ |
| 751 |
> |
& AA toluene & 3.79 & 487() & 290() \\ |
| 752 |
> |
AA(D) & UA hexane & 1.94 & 158() & 172() \\ |
| 753 |
> |
bare & AA hexane & 0.96 & 31.0() & 29.4() \\ |
| 754 |
> |
\hline\hline |
| 755 |
> |
\end{tabular} |
| 756 |
> |
\label{modelTest} |
| 757 |
> |
\end{center} |
| 758 |
> |
\end{minipage} |
| 759 |
> |
\end{table*} |
| 760 |
> |
|
| 761 |
> |
To facilitate direct comparison, the same system with differnt models |
| 762 |
> |
for different components uses the same length scale for their |
| 763 |
> |
simulation cells. Without the presence of capping agent, using |
| 764 |
> |
different models for hexane yields similar results for both $G$ and |
| 765 |
> |
$G^\prime$, and these two definitions agree with eath other very |
| 766 |
> |
well. This indicates very weak interaction between the metal and the |
| 767 |
> |
solvent, and is a typical case for acoustic impedance mismatch between |
| 768 |
> |
these two phases. |
| 769 |
> |
|
| 770 |
> |
As for Au(111) surfaces completely covered by butanethiols, the choice |
| 771 |
> |
of models for capping agent and solvent could impact the measurement |
| 772 |
> |
of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane |
| 773 |
> |
interfaces, using AA model for both butanethiol and hexane yields |
| 774 |
> |
substantially higher conductivity values than using UA model for at |
| 775 |
> |
least one component of the solvent and capping agent, which exceeds |
| 776 |
> |
the upper bond of experimental value range. This is probably due to |
| 777 |
> |
the classically treated C-H vibrations in the AA model, which should |
| 778 |
> |
not be appreciably populated at normal temperatures. In comparison, |
| 779 |
> |
once either the hexanes or the butanethiols are deuterated, one can |
| 780 |
> |
see a significantly lower $G$ and $G^\prime$. In either of these |
| 781 |
> |
cases, the C-H(D) vibrational overlap between the solvent and the |
| 782 |
> |
capping agent is removed. [MAY NEED FIGURE] Conclusively, the |
| 783 |
> |
improperly treated C-H vibration in the AA model produced |
| 784 |
> |
over-predicted results accordingly. Compared to the AA model, the UA |
| 785 |
> |
model yields more reasonable results with higher computational |
| 786 |
> |
efficiency. |
| 787 |
> |
|
| 788 |
> |
However, for Au-butanethiol/toluene interfaces, having the AA |
| 789 |
> |
butanethiol deuterated did not yield a significant change in the |
| 790 |
> |
measurement results. |
| 791 |
> |
. , so extra degrees of freedom |
| 792 |
> |
such as the C-H vibrations could enhance heat exchange between these |
| 793 |
> |
two phases and result in a much higher conductivity. |
| 794 |
> |
|
| 795 |
> |
|
| 796 |
> |
Although the QSC model for Au is known to predict an overly low value |
| 797 |
> |
for bulk metal gold conductivity[CITE NIVSRNEMD], our computational |
| 798 |
> |
results for $G$ and $G^\prime$ do not seem to be affected by this |
| 799 |
> |
drawback of the model for metal. Instead, the modeling of interfacial |
| 800 |
> |
thermal transport behavior relies mainly on an accurate description of |
| 801 |
> |
the interactions between components occupying the interfaces. |
| 802 |
> |
|
| 803 |
> |
\subsection{Mechanism of Interfacial Thermal Conductance Enhancement |
| 804 |
> |
by Capping Agent} |
| 805 |
> |
%OR\subsection{Vibrational spectrum study on conductance mechanism} |
| 806 |
> |
|
| 807 |
> |
[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S] |
| 808 |
> |
|
| 809 |
|
To investigate the mechanism of this interfacial thermal conductance, |
| 810 |
|
the vibrational spectra of various gold systems were obtained and are |
| 811 |
|
shown as in the upper panel of Fig. \ref{vibration}. To obtain these |
| 812 |
|
spectra, one first runs a simulation in the NVE ensemble and collects |
| 813 |
|
snapshots of configurations; these configurations are used to compute |
| 814 |
|
the velocity auto-correlation functions, which is used to construct a |
| 815 |
< |
power spectrum via a Fourier transform. The gold surfaces covered by |
| 506 |
< |
butanethiol molecules exhibit an additional peak observed at a |
| 507 |
< |
frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration |
| 508 |
< |
of the S-Au bond. This vibration enables efficient thermal transport |
| 509 |
< |
from surface Au atoms to the capping agents. Simultaneously, as shown |
| 510 |
< |
in the lower panel of Fig. \ref{vibration}, the large overlap of the |
| 511 |
< |
vibration spectra of butanethiol and hexane in the all-atom model, |
| 512 |
< |
including the C-H vibration, also suggests high thermal exchange |
| 513 |
< |
efficiency. The combination of these two effects produces the drastic |
| 514 |
< |
interfacial thermal conductance enhancement in the all-atom model. |
| 815 |
> |
power spectrum via a Fourier transform. |
| 816 |
|
|
| 817 |
+ |
The gold surfaces covered by |
| 818 |
+ |
butanethiol molecules, compared to bare gold surfaces, exhibit an |
| 819 |
+ |
additional peak observed at a frequency of $\sim$170cm$^{-1}$, which |
| 820 |
+ |
is attributed to the vibration of the S-Au bond. This vibration |
| 821 |
+ |
enables efficient thermal transport from surface Au atoms to the |
| 822 |
+ |
capping agents. Simultaneously, as shown in the lower panel of |
| 823 |
+ |
Fig. \ref{vibration}, the large overlap of the vibration spectra of |
| 824 |
+ |
butanethiol and hexane in the all-atom model, including the C-H |
| 825 |
+ |
vibration, also suggests high thermal exchange efficiency. The |
| 826 |
+ |
combination of these two effects produces the drastic interfacial |
| 827 |
+ |
thermal conductance enhancement in the all-atom model. |
| 828 |
+ |
|
| 829 |
+ |
[MAY NEED TO CONVERT TO JPEG] |
| 830 |
|
\begin{figure} |
| 831 |
|
\includegraphics[width=\linewidth]{vibration} |
| 832 |
|
\caption{Vibrational spectra obtained for gold in different |
| 834 |
|
all-atom model (lower panel).} |
| 835 |
|
\label{vibration} |
| 836 |
|
\end{figure} |
| 523 |
– |
% 600dpi, letter size. too large? |
| 837 |
|
|
| 838 |
+ |
[COMPARISON OF TWO G'S; AU SLAB WIDTHS; ETC] |
| 839 |
+ |
% The results show that the two definitions used for $G$ yield |
| 840 |
+ |
% comparable values, though $G^\prime$ tends to be smaller. |
| 841 |
|
|
| 842 |
+ |
\section{Conclusions} |
| 843 |
+ |
The NIVS algorithm we developed has been applied to simulations of |
| 844 |
+ |
Au-butanethiol surfaces with organic solvents. This algorithm allows |
| 845 |
+ |
effective unphysical thermal flux transferred between the metal and |
| 846 |
+ |
the liquid phase. With the flux applied, we were able to measure the |
| 847 |
+ |
corresponding thermal gradient and to obtain interfacial thermal |
| 848 |
+ |
conductivities. Our simulations have seen significant conductance |
| 849 |
+ |
enhancement with the presence of capping agent, compared to the bare |
| 850 |
+ |
gold/liquid interfaces. The acoustic impedance mismatch between the |
| 851 |
+ |
metal and the liquid phase is effectively eliminated by proper capping |
| 852 |
+ |
agent. Furthermore, the coverage precentage of the capping agent plays |
| 853 |
+ |
an important role in the interfacial thermal transport process. |
| 854 |
+ |
|
| 855 |
+ |
Our measurement results, particularly of the UA models, agree with |
| 856 |
+ |
available experimental data. This indicates that our force field |
| 857 |
+ |
parameters have a nice description of the interactions between the |
| 858 |
+ |
particles at the interfaces. AA models tend to overestimate the |
| 859 |
+ |
interfacial thermal conductance in that the classically treated C-H |
| 860 |
+ |
vibration would be overly sampled. Compared to the AA models, the UA |
| 861 |
+ |
models have higher computational efficiency with satisfactory |
| 862 |
+ |
accuracy, and thus are preferable in interfacial thermal transport |
| 863 |
+ |
modelings. |
| 864 |
+ |
|
| 865 |
+ |
Vlugt {\it et al.} has investigated the surface thiol structures for |
| 866 |
+ |
nanocrystal gold and pointed out that they differs from those of the |
| 867 |
+ |
Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to |
| 868 |
+ |
change of interfacial thermal transport behavior as well. To |
| 869 |
+ |
investigate this problem, an effective means to introduce thermal flux |
| 870 |
+ |
and measure the corresponding thermal gradient is desirable for |
| 871 |
+ |
simulating structures with spherical symmetry. |
| 872 |
+ |
|
| 873 |
+ |
|
| 874 |
|
\section{Acknowledgments} |
| 875 |
|
Support for this project was provided by the National Science |
| 876 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
| 877 |
|
the Center for Research Computing (CRC) at the University of Notre |
| 878 |
< |
Dame. \newpage |
| 878 |
> |
Dame. \newpage |
| 879 |
|
|
| 880 |
|
\bibliography{interfacial} |
| 881 |
|
|
