| 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 TWO PAPERS]. However, emsemble average measurements for heat |
| 107 |
< |
conductance of interfaces between the capping monolayer on Au and a |
| 108 |
< |
solvent phase has yet to be studied. The relatively low thermal flux |
| 109 |
< |
through interfaces is difficult to measure with Equilibrium MD or |
| 110 |
< |
forward NEMD simulation methods. Therefore, the Reverse NEMD (RNEMD) |
| 111 |
< |
methods would have the advantage of having this difficult to measure |
| 112 |
< |
flux known when studying the thermal transport |
| 113 |
< |
across interfaces, given that the simulation |
| 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 |
|
|
| 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 |
| 253 |
|
|
| 254 |
|
\section{Computational Details} |
| 255 |
|
\subsection{Simulation Protocol} |
| 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 |
| 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). [MAY |
| 284 |
< |
EXPLAIN WHY WE CHOOSE THEM] |
| 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 |
| 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] demonstrates how we name our pseudo-atoms of the |
| 341 |
< |
molecules in our simulations. |
| 342 |
< |
[FIGURE FOR MOLECULE NOMENCLATURE] |
| 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 |
| 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 [CITATION CF VLUGT] |
| 382 |
< |
and modify parameters for its neighbor C atom for charge balance in |
| 383 |
< |
the molecule. Note that the model choice (UA or AA) of capping agent |
| 384 |
< |
can be different from the solvent. Regardless of model choice, the |
| 385 |
< |
force field parameters for interactions between capping agent and |
| 386 |
< |
solvent can be derived using Lorentz-Berthelot Mixing Rule: |
| 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 |
|
To describe the interactions between metal Au and non-metal capping |
| 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[CITATION] for the Au(111) |
| 397 |
< |
surface. As our simulations require the gold lattice slab to be |
| 398 |
< |
non-rigid so that it could accommodate kinetic energy for thermal |
| 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 |
|
|
