| 131 |
|
properties. Different models were used for both the capping agent and |
| 132 |
|
the solvent force field parameters. Using the NIVS algorithm, the |
| 133 |
|
thermal transport across these interfaces was studied and the |
| 134 |
< |
underlying mechanism for this phenomena was investigated. |
| 134 |
> |
underlying mechanism for the phenomena was investigated. |
| 135 |
|
|
| 136 |
|
[MAY ADD WHY STUDY AU-THIOL SURFACE; CITE SHAOYI JIANG] |
| 137 |
|
|
| 138 |
|
\section{Methodology} |
| 139 |
|
\subsection{Imposd-Flux Methods in MD Simulations} |
| 140 |
< |
For systems with low interfacial conductivity one must have a method |
| 141 |
< |
capable of generating relatively small fluxes, compared to those |
| 142 |
< |
required for bulk conductivity. This requirement makes the calculation |
| 143 |
< |
even more difficult for those slowly-converging equilibrium |
| 144 |
< |
methods\cite{Viscardy:2007lq}. |
| 145 |
< |
Forward methods impose gradient, but in interfacail conditions it is |
| 146 |
< |
not clear what behavior to impose at the boundary... |
| 147 |
< |
Imposed-flux reverse non-equilibrium |
| 140 |
> |
Steady state MD simulations has the advantage that not many |
| 141 |
> |
trajectories are needed to study the relationship between thermal flux |
| 142 |
> |
and thermal gradients. For systems including low conductance |
| 143 |
> |
interfaces one must have a method capable of generating or measuring |
| 144 |
> |
relatively small fluxes, compared to those required for bulk |
| 145 |
> |
conductivity. This requirement makes the calculation even more |
| 146 |
> |
difficult for those slowly-converging equilibrium |
| 147 |
> |
methods\cite{Viscardy:2007lq}. Forward methods may impose gradient, |
| 148 |
> |
but in interfacial conditions it is not clear what behavior to impose |
| 149 |
> |
at the interfacial boundaries. Imposed-flux reverse non-equilibrium |
| 150 |
|
methods\cite{MullerPlathe:1997xw} have the flux set {\it a priori} and |
| 151 |
< |
the thermal response becomes easier to |
| 152 |
< |
measure than the flux. Although M\"{u}ller-Plathe's original momentum |
| 153 |
< |
swapping approach can be used for exchanging energy between particles |
| 154 |
< |
of different identity, the kinetic energy transfer efficiency is |
| 155 |
< |
affected by the mass difference between the particles, which limits |
| 156 |
< |
its application on heterogeneous interfacial systems. |
| 151 |
> |
the thermal response becomes easier to measure than the flux. Although |
| 152 |
> |
M\"{u}ller-Plathe's original momentum swapping approach can be used |
| 153 |
> |
for exchanging energy between particles of different identity, the |
| 154 |
> |
kinetic energy transfer efficiency is affected by the mass difference |
| 155 |
> |
between the particles, which limits its application on heterogeneous |
| 156 |
> |
interfacial systems. |
| 157 |
|
|
| 158 |
|
The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach to |
| 159 |
|
non-equilibrium MD simulations is able to impose a wide range of |
| 174 |
|
momenta and energy and does not depend on an external thermostat. |
| 175 |
|
|
| 176 |
|
\subsection{Defining Interfacial Thermal Conductivity $G$} |
| 177 |
< |
For interfaces with a relatively low interfacial conductance, the bulk |
| 178 |
< |
regions on either side of an interface rapidly come to a state in |
| 179 |
< |
which the two phases have relatively homogeneous (but distinct) |
| 180 |
< |
temperatures. The interfacial thermal conductivity $G$ can therefore |
| 181 |
< |
be approximated as: |
| 177 |
> |
Given a system with thermal gradients and the corresponding thermal |
| 178 |
> |
flux, for interfaces with a relatively low interfacial conductance, |
| 179 |
> |
the bulk regions on either side of an interface rapidly come to a |
| 180 |
> |
state in which the two phases have relatively homogeneous (but |
| 181 |
> |
distinct) temperatures. The interfacial thermal conductivity $G$ can |
| 182 |
> |
therefore be approximated as: |
| 183 |
|
\begin{equation} |
| 184 |
|
G = \frac{E_{total}}{2 t L_x L_y \left( \langle T_\mathrm{hot}\rangle - |
| 185 |
|
\langle T_\mathrm{cold}\rangle \right)} |
| 241 |
|
a metal slab with its (111) surfaces perpendicular to the $z$-axis of |
| 242 |
|
our simulation cells. Both with and without capping agents on the |
| 243 |
|
surfaces, the metal slab is solvated with simple organic solvents, as |
| 244 |
< |
illustrated in Figure \ref{demoPic}. |
| 244 |
> |
illustrated in Figure \ref{gradT}. |
| 245 |
|
|
| 246 |
|
With the simulation cell described above, we are able to equilibrate |
| 247 |
|
the system and impose an unphysical thermal flux between the liquid |
| 249 |
|
the unphysical flux, we are able to obtain a temperature profile and |
| 250 |
|
its spatial derivatives. These quantities enable the evaluation of the |
| 251 |
|
interfacial thermal conductance of a surface. Figure \ref{gradT} is an |
| 252 |
< |
example how those applied thermal fluxes can be used to obtain the 1st |
| 252 |
> |
example of how an applied thermal flux can be used to obtain the 1st |
| 253 |
|
and 2nd derivatives of the temperature profile. |
| 254 |
|
|
| 255 |
|
\begin{figure} |
| 265 |
|
\subsection{Simulation Protocol} |
| 266 |
|
The NIVS algorithm has been implemented in our MD simulation code, |
| 267 |
|
OpenMD\cite{Meineke:2005gd,openmd}, and was used for our |
| 268 |
< |
simulations. Different slab thickness (layer numbers of Au) were |
| 268 |
> |
simulations. Different metal slab thickness (layer numbers of Au) was |
| 269 |
|
simulated. Metal slabs were first equilibrated under atmospheric |
| 270 |
|
pressure (1 atm) and a desired temperature (e.g. 200K). After |
| 271 |
|
equilibration, butanethiol capping agents were placed at three-fold |
| 272 |
< |
sites on the Au(111) surfaces. The maximum butanethiol capacity on Au |
| 273 |
< |
surface is $1/3$ of the total number of surface Au |
| 274 |
< |
atoms\cite{vlugt:cpc2007154}. A series of different coverages was |
| 275 |
< |
investigated in order to study the relation between coverage and |
| 276 |
< |
interfacial conductance. |
| 272 |
> |
hollow sites on the Au(111) surfaces. These sites could be either a |
| 273 |
> |
{\it fcc} or {\it hcp} site. However, Hase {\it et al.} found that |
| 274 |
> |
they are equivalent in a heat transfer process\cite{hase:2010}, so |
| 275 |
> |
they are not distinguished in our study. The maximum butanethiol |
| 276 |
> |
capacity on Au surface is $1/3$ of the total number of surface Au |
| 277 |
> |
atoms, and the packing forms a $(\sqrt{3}\times\sqrt{3})R30^\circ$ |
| 278 |
> |
structure\cite{doi:10.1021/ja00008a001,doi:10.1021/cr9801317}. A |
| 279 |
> |
series of different coverages was derived by evenly eliminating |
| 280 |
> |
butanethiols on the surfaces, and was investigated in order to study |
| 281 |
> |
the relation between coverage and interfacial conductance. |
| 282 |
|
|
| 283 |
|
The capping agent molecules were allowed to migrate during the |
| 284 |
|
simulations. They distributed themselves uniformly and sampled a |
| 286 |
|
initial configuration would not noticeably affect the sampling of a |
| 287 |
|
variety of configurations of the same coverage, and the final |
| 288 |
|
conductance measurement would be an average effect of these |
| 289 |
< |
configurations explored in the simulations. [MAY NEED FIGURES] |
| 289 |
> |
configurations explored in the simulations. [MAY NEED SNAPSHOTS] |
| 290 |
|
|
| 291 |
|
After the modified Au-butanethiol surface systems were equilibrated |
| 292 |
|
under canonical ensemble, organic solvent molecules were packed in the |
| 306 |
|
these extreme cases did not happen to our simulations. And the |
| 307 |
|
corresponding spacing is usually $35 \sim 75$\AA. |
| 308 |
|
|
| 309 |
< |
The initial configurations generated by Packmol are further |
| 310 |
< |
equilibrated with the $x$ and $y$ dimensions fixed, only allowing |
| 311 |
< |
length scale change in $z$ dimension. This is to ensure that the |
| 312 |
< |
equilibration of liquid phase does not affect the metal crystal |
| 313 |
< |
structure in $x$ and $y$ dimensions. Further equilibration are run |
| 314 |
< |
under NVT and then NVE ensembles. |
| 309 |
> |
The initial configurations generated are further equilibrated with the |
| 310 |
> |
$x$ and $y$ dimensions fixed, only allowing length scale change in $z$ |
| 311 |
> |
dimension. This is to ensure that the equilibration of liquid phase |
| 312 |
> |
does not affect the metal crystal structure in $x$ and $y$ dimensions. |
| 313 |
> |
To investigate this effect, comparisons were made with simulations |
| 314 |
> |
that allow changes of $L_x$ and $L_y$ during NPT equilibration, and |
| 315 |
> |
the results are shown in later sections. After ensuring the liquid |
| 316 |
> |
phase reaches equilibrium at atmospheric pressure (1 atm), further |
| 317 |
> |
equilibration are followed under NVT and then NVE ensembles. |
| 318 |
|
|
| 319 |
|
After the systems reach equilibrium, NIVS is implemented to impose a |
| 320 |
|
periodic unphysical thermal flux between the metal and the liquid |
| 321 |
|
phase. Most of our simulations are under an average temperature of |
| 322 |
|
$\sim$200K. Therefore, this flux usually comes from the metal to the |
| 323 |
|
liquid so that the liquid has a higher temperature and would not |
| 324 |
< |
freeze due to excessively low temperature. This induced temperature |
| 325 |
< |
gradient is stablized and the simulation cell is devided evenly into |
| 326 |
< |
N slabs along the $z$-axis and the temperatures of each slab are |
| 327 |
< |
recorded. When the slab width $d$ of each slab is the same, the |
| 328 |
< |
derivatives of $T$ with respect to slab number $n$ can be directly |
| 329 |
< |
used for $G^\prime$ calculations: |
| 324 |
> |
freeze due to excessively low temperature. After this induced |
| 325 |
> |
temperature gradient is stablized, the temperature profile of the |
| 326 |
> |
simulation cell is recorded. To do this, the simulation cell is |
| 327 |
> |
devided evenly into $N$ slabs along the $z$-axis and $N$ is maximized |
| 328 |
> |
for highest possible spatial resolution but not too many to have some |
| 329 |
> |
slabs empty most of the time. The average temperatures of each slab |
| 330 |
> |
are recorded for 1$\sim$2 ns. When the slab width $d$ of each slab is |
| 331 |
> |
the same, the derivatives of $T$ with respect to slab number $n$ can |
| 332 |
> |
be directly used for $G^\prime$ calculations: |
| 333 |
|
\begin{equation} |
| 334 |
|
G^\prime = |J_z|\Big|\frac{\partial^2 T}{\partial z^2}\Big| |
| 335 |
|
\Big/\left(\frac{\partial T}{\partial z}\right)^2 |
| 340 |
|
\label{derivativeG2} |
| 341 |
|
\end{equation} |
| 342 |
|
|
| 343 |
+ |
All of the above simulation procedures use a time step of 1 fs. And |
| 344 |
+ |
each equilibration / stabilization step usually takes 100 ps, or |
| 345 |
+ |
longer, if necessary. |
| 346 |
+ |
|
| 347 |
|
\subsection{Force Field Parameters} |
| 348 |
|
Our simulations include various components. Figure \ref{demoMol} |
| 349 |
|
demonstrates the sites defined for both United-Atom and All-Atom |
| 378 |
|
the carbon centers for alkyl groups. Bonding interactions, including |
| 379 |
|
bond stretches and bends and torsions, were used for intra-molecular |
| 380 |
|
sites not separated by more than 3 bonds. Otherwise, for non-bonded |
| 381 |
< |
interactions, Lennard-Jones potentials are used. [MORE CITATION?] |
| 381 |
> |
interactions, Lennard-Jones potentials are used. [CHECK CITATION] |
| 382 |
|
|
| 383 |
|
By eliminating explicit hydrogen atoms, these models are simple and |
| 384 |
|
computationally efficient, while maintains good accuracy. However, the |
| 385 |
|
TraPPE-UA for alkanes is known to predict a lower boiling point than |
| 386 |
|
experimental values. Considering that after an unphysical thermal flux |
| 387 |
|
is applied to a system, the temperature of ``hot'' area in the liquid |
| 388 |
< |
phase would be significantly higher than the average, to prevent over |
| 389 |
< |
heating and boiling of the liquid phase, the average temperature in |
| 390 |
< |
our simulations should be much lower than the liquid boiling point. |
| 388 |
> |
phase would be significantly higher than the average of the system, to |
| 389 |
> |
prevent over heating and boiling of the liquid phase, the average |
| 390 |
> |
temperature in our simulations should be much lower than the liquid |
| 391 |
> |
boiling point. |
| 392 |
|
|
| 393 |
|
For UA-toluene model, the non-bonded potentials between |
| 394 |
|
inter-molecular sites have a similar Lennard-Jones formulation. For |
| 407 |
|
adopted. Without the rigid body constraints, bonding interactions were |
| 408 |
|
included. For the aromatic ring, improper torsions (inversions) were |
| 409 |
|
added as an extra potential for maintaining the planar shape. |
| 410 |
< |
[MORE CITATION?] |
| 410 |
> |
[CHECK CITATION] |
| 411 |
|
|
| 412 |
|
The capping agent in our simulations, the butanethiol molecules can |
| 413 |
|
either use UA or AA model. The TraPPE-UA force fields includes |
| 417 |
|
surfaces do not have the hydrogen atom bonded to sulfur. To adapt this |
| 418 |
|
change and derive suitable parameters for butanethiol adsorbed on |
| 419 |
|
Au(111) surfaces, we adopt the S parameters from Luedtke and |
| 420 |
< |
Landman\cite{landman:1998} and modify parameters for its neighbor C |
| 420 |
> |
Landman\cite{landman:1998}[CHECK CITATION] |
| 421 |
> |
and modify parameters for its neighbor C |
| 422 |
|
atom for charge balance in the molecule. Note that the model choice |
| 423 |
|
(UA or AA) of capping agent can be different from the |
| 424 |
|
solvent. Regardless of model choice, the force field parameters for |
| 492 |
|
\end{minipage} |
| 493 |
|
\end{table*} |
| 494 |
|
|
| 495 |
+ |
\subsection{Vibrational Spectrum} |
| 496 |
+ |
To investigate the mechanism of interfacial thermal conductance, the |
| 497 |
+ |
vibrational spectrum is utilized as a complementary tool. Vibrational |
| 498 |
+ |
spectra were taken for individual components in different |
| 499 |
+ |
simulations. To obtain these spectra, simulations were run after |
| 500 |
+ |
equilibration, in the NVE ensemble. Snapshots of configurations were |
| 501 |
+ |
collected at a frequency that is higher than that of the fastest |
| 502 |
+ |
vibrations occuring in the simulations. With these configurations, the |
| 503 |
+ |
velocity auto-correlation functions can be computed: |
| 504 |
+ |
\begin{equation} |
| 505 |
+ |
C_A (t) = \langle\vec{v}_A (t)\cdot\vec{v}_A (0)\rangle |
| 506 |
+ |
\label{vCorr} |
| 507 |
+ |
\end{equation} |
| 508 |
+ |
Followed by Fourier transforms, the power spectrum can be constructed: |
| 509 |
+ |
\begin{equation} |
| 510 |
+ |
\hat{f}(\omega) = \int_{-\infty}^{\infty} C_A (t) e^{-2\pi it\omega}\,dt |
| 511 |
+ |
\label{fourier} |
| 512 |
+ |
\end{equation} |
| 513 |
|
|
| 514 |
|
\section{Results and Discussions} |
| 515 |
< |
[MAY HAVE A BRIEF SUMMARY] |
| 515 |
> |
In what follows, how the parameters and protocol of simulations would |
| 516 |
> |
affect the measurement of $G$'s is first discussed. With a reliable |
| 517 |
> |
protocol and set of parameters, the influence of capping agent |
| 518 |
> |
coverage on thermal conductance is investigated. Besides, different |
| 519 |
> |
force field models for both solvents and selected deuterated models |
| 520 |
> |
were tested and compared. Finally, a summary of the role of capping |
| 521 |
> |
agent in the interfacial thermal transport process is given. |
| 522 |
> |
|
| 523 |
|
\subsection{How Simulation Parameters Affects $G$} |
| 479 |
– |
[MAY NOT PUT AT FIRST] |
| 524 |
|
We have varied our protocol or other parameters of the simulations in |
| 525 |
|
order to investigate how these factors would affect the measurement of |
| 526 |
|
$G$'s. It turned out that while some of these parameters would not |
| 707 |
|
effect in interfacial thermal conductance, deuterated UA-hexane is |
| 708 |
|
included as well. |
| 709 |
|
|
| 710 |
+ |
\begin{figure} |
| 711 |
+ |
\includegraphics[width=\linewidth]{coverage} |
| 712 |
+ |
\caption{Comparison of interfacial thermal conductivity ($G$) values |
| 713 |
+ |
for the Au-butanethiol/solvent interface with various UA models and |
| 714 |
+ |
different capping agent coverages at $\langle T\rangle\sim$200K |
| 715 |
+ |
using certain energy flux respectively.} |
| 716 |
+ |
\label{coverage} |
| 717 |
+ |
\end{figure} |
| 718 |
+ |
|
| 719 |
|
It turned out that with partial covered butanethiol on the Au(111) |
| 720 |
|
surface, the derivative definition for $G^\prime$ |
| 721 |
|
(Eq. \ref{derivativeG}) was difficult to apply, due to the difficulty |
| 749 |
|
continues to decrease, solvent-capping agent contact actually |
| 750 |
|
decreases with the disappearing of butanethiol molecules. In this |
| 751 |
|
case, $G$ decrease could not be offset but instead accelerated. [NEED |
| 752 |
< |
SNAPSHOT SHOWING THE PHENOMENA] |
| 752 |
> |
SNAPSHOT SHOWING THE PHENOMENA / SLAB DENSITY ANALYSIS] |
| 753 |
|
|
| 754 |
|
A comparison of the results obtained from differenet organic solvents |
| 755 |
|
can also provide useful information of the interfacial thermal |
| 759 |
|
studies, even though eliminating C-H vibration samplings, still have |
| 760 |
|
C-C vibrational frequencies different from each other. However, these |
| 761 |
|
differences in the infrared range do not seem to produce an observable |
| 762 |
< |
difference for the results of $G$. [MAY NEED SPECTRA FIGURE] |
| 762 |
> |
difference for the results of $G$ (Figure \ref{uahxnua}). |
| 763 |
|
|
| 764 |
+ |
\begin{figure} |
| 765 |
+ |
\includegraphics[width=\linewidth]{uahxnua} |
| 766 |
+ |
\caption{Vibrational spectra obtained for normal (upper) and |
| 767 |
+ |
deuterated (lower) hexane in Au-butanethiol/hexane |
| 768 |
+ |
systems. Butanethiol spectra are shown as reference. Both hexane and |
| 769 |
+ |
butanethiol were using United-Atom models.} |
| 770 |
+ |
\label{uahxnua} |
| 771 |
+ |
\end{figure} |
| 772 |
+ |
|
| 773 |
|
Furthermore, results for rigid body toluene solvent, as well as other |
| 774 |
|
UA-hexane solvents, are reasonable within the general experimental |
| 775 |
< |
ranges[CITATIONS]. This suggests that explicit hydrogen might not be a |
| 776 |
< |
required factor for modeling thermal transport phenomena of systems |
| 777 |
< |
such as Au-thiol/organic solvent. |
| 775 |
> |
ranges\cite{Wilson:2002uq,cahill:793,PhysRevB.80.195406}. This |
| 776 |
> |
suggests that explicit hydrogen might not be a required factor for |
| 777 |
> |
modeling thermal transport phenomena of systems such as |
| 778 |
> |
Au-thiol/organic solvent. |
| 779 |
|
|
| 780 |
|
However, results for Au-butanethiol/toluene do not show an identical |
| 781 |
|
trend with those for Au-butanethiol/hexane in that $G$ remains at |
| 790 |
|
its effect to the process of interfacial thermal transport. Thus, one |
| 791 |
|
can see a plateau of $G$ vs. butanethiol coverage in our results. |
| 792 |
|
|
| 730 |
– |
\begin{figure} |
| 731 |
– |
\includegraphics[width=\linewidth]{coverage} |
| 732 |
– |
\caption{Comparison of interfacial thermal conductivity ($G$) values |
| 733 |
– |
for the Au-butanethiol/solvent interface with various UA models and |
| 734 |
– |
different capping agent coverages at $\langle T\rangle\sim$200K |
| 735 |
– |
using certain energy flux respectively.} |
| 736 |
– |
\label{coverage} |
| 737 |
– |
\end{figure} |
| 738 |
– |
|
| 793 |
|
\subsection{Influence of Chosen Molecule Model on $G$} |
| 740 |
– |
[MAY COMBINE W MECHANISM STUDY] |
| 741 |
– |
|
| 794 |
|
In addition to UA solvent/capping agent models, AA models are included |
| 795 |
|
in our simulations as well. Besides simulations of the same (UA or AA) |
| 796 |
|
model for solvent and capping agent, different models can be applied |
| 865 |
|
temperatures. In comparison, once either the hexanes or the |
| 866 |
|
butanethiols are deuterated, one can see a significantly lower $G$ and |
| 867 |
|
$G^\prime$. In either of these cases, the C-H(D) vibrational overlap |
| 868 |
< |
between the solvent and the capping agent is removed. |
| 869 |
< |
[MAY NEED SPECTRA FIGURE] Conclusively, the |
| 870 |
< |
improperly treated C-H vibration in the AA model produced |
| 871 |
< |
over-predicted results accordingly. Compared to the AA model, the UA |
| 872 |
< |
model yields more reasonable results with higher computational |
| 821 |
< |
efficiency. |
| 868 |
> |
between the solvent and the capping agent is removed (Figure |
| 869 |
> |
\ref{aahxntln}). Conclusively, the improperly treated C-H vibration in |
| 870 |
> |
the AA model produced over-predicted results accordingly. Compared to |
| 871 |
> |
the AA model, the UA model yields more reasonable results with higher |
| 872 |
> |
computational efficiency. |
| 873 |
|
|
| 874 |
+ |
\begin{figure} |
| 875 |
+ |
\includegraphics[width=\linewidth]{aahxntln} |
| 876 |
+ |
\caption{Spectra obtained for All-Atom model Au-butanethil/solvent |
| 877 |
+ |
systems. When butanethiol is deuterated (lower left), its |
| 878 |
+ |
vibrational overlap with hexane would decrease significantly, |
| 879 |
+ |
compared with normal butanethiol (upper left). However, this |
| 880 |
+ |
dramatic change does not apply to toluene as much (right).} |
| 881 |
+ |
\label{aahxntln} |
| 882 |
+ |
\end{figure} |
| 883 |
+ |
|
| 884 |
|
However, for Au-butanethiol/toluene interfaces, having the AA |
| 885 |
|
butanethiol deuterated did not yield a significant change in the |
| 886 |
|
measurement results. Compared to the C-H vibrational overlap between |
| 887 |
|
hexane and butanethiol, both of which have alkyl chains, that overlap |
| 888 |
|
between toluene and butanethiol is not so significant and thus does |
| 889 |
< |
not have as much contribution to the ``Intramolecular Vibration |
| 890 |
< |
Redistribution''[CITE HASE]. Conversely, extra degrees of freedom such |
| 891 |
< |
as the C-H vibrations could yield higher heat exchange rate between |
| 892 |
< |
these two phases and result in a much higher conductivity. |
| 889 |
> |
not have as much contribution to the heat exchange |
| 890 |
> |
process. Conversely, extra degrees of freedom such as the C-H |
| 891 |
> |
vibrations could yield higher heat exchange rate between these two |
| 892 |
> |
phases and result in a much higher conductivity. |
| 893 |
|
|
| 894 |
|
Although the QSC model for Au is known to predict an overly low value |
| 895 |
|
for bulk metal gold conductivity\cite{kuang:164101}, our computational |
| 899 |
|
the accuracy of the interaction descriptions between components |
| 900 |
|
occupying the interfaces. |
| 901 |
|
|
| 902 |
< |
\subsection{Mechanism of Interfacial Thermal Conductance Enhancement |
| 903 |
< |
by Capping Agent} |
| 904 |
< |
[OR: Vibrational Spectrum Study on Conductance Mechanism] |
| 905 |
< |
|
| 906 |
< |
[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S] |
| 907 |
< |
|
| 908 |
< |
To investigate the mechanism of this interfacial thermal conductance, |
| 909 |
< |
the vibrational spectra of various gold systems were obtained and are |
| 910 |
< |
shown as in the upper panel of Fig. \ref{vibration}. To obtain these |
| 911 |
< |
spectra, one first runs a simulation in the NVE ensemble and collects |
| 851 |
< |
snapshots of configurations; these configurations are used to compute |
| 852 |
< |
the velocity auto-correlation functions, which is used to construct a |
| 853 |
< |
power spectrum via a Fourier transform. |
| 902 |
> |
\subsection{Role of Capping Agent in Interfacial Thermal Conductance} |
| 903 |
> |
The vibrational spectra for gold slabs in different environments are |
| 904 |
> |
shown as in Figure \ref{specAu}. Regardless of the presence of |
| 905 |
> |
solvent, the gold surfaces covered by butanethiol molecules, compared |
| 906 |
> |
to bare gold surfaces, exhibit an additional peak observed at the |
| 907 |
> |
frequency of $\sim$170cm$^{-1}$, which is attributed to the S-Au |
| 908 |
> |
bonding vibration. This vibration enables efficient thermal transport |
| 909 |
> |
from surface Au layer to the capping agents. Therefore, in our |
| 910 |
> |
simulations, the Au/S interfaces do not appear major heat barriers |
| 911 |
> |
compared to the butanethiol / solvent interfaces. |
| 912 |
|
|
| 913 |
< |
[MAY RELATE TO HASE'S] |
| 914 |
< |
The gold surfaces covered by butanethiol molecules, compared to bare |
| 915 |
< |
gold surfaces, exhibit an additional peak observed at the frequency of |
| 916 |
< |
$\sim$170cm$^{-1}$, which is attributed to the S-Au bonding |
| 917 |
< |
vibration. This vibration enables efficient thermal transport from |
| 918 |
< |
surface Au layer to the capping agents. |
| 919 |
< |
[MAY PUT IN OTHER SECTION] Simultaneously, as shown in |
| 862 |
< |
the lower panel of Fig. \ref{vibration}, the large overlap of the |
| 863 |
< |
vibration spectra of butanethiol and hexane in the All-Atom model, |
| 864 |
< |
including the C-H vibration, also suggests high thermal exchange |
| 865 |
< |
efficiency. The combination of these two effects produces the drastic |
| 866 |
< |
interfacial thermal conductance enhancement in the All-Atom model. |
| 913 |
> |
Simultaneously, the vibrational overlap between butanethiol and |
| 914 |
> |
organic solvents suggests higher thermal exchange efficiency between |
| 915 |
> |
these two components. Even exessively high heat transport was observed |
| 916 |
> |
when All-Atom models were used and C-H vibrations were treated |
| 917 |
> |
classically. Compared to metal and organic liquid phase, the heat |
| 918 |
> |
transfer efficiency between butanethiol and organic solvents is closer |
| 919 |
> |
to that within bulk liquid phase. |
| 920 |
|
|
| 921 |
< |
[NEED SEPARATE FIGURE. MAY NEED TO CONVERT TO JPEG] |
| 921 |
> |
Furthermore, our observation validated previous |
| 922 |
> |
results\cite{hase:2010} that the intramolecular heat transport of |
| 923 |
> |
alkylthiols is highly effecient. As a combinational effects of these |
| 924 |
> |
phenomena, butanethiol acts as a channel to expedite thermal transport |
| 925 |
> |
process. The acoustic impedance mismatch between the metal and the |
| 926 |
> |
liquid phase can be effectively reduced with the presence of suitable |
| 927 |
> |
capping agents. |
| 928 |
> |
|
| 929 |
|
\begin{figure} |
| 930 |
|
\includegraphics[width=\linewidth]{vibration} |
| 931 |
|
\caption{Vibrational spectra obtained for gold in different |
| 932 |
|
environments.} |
| 933 |
< |
\label{vibration} |
| 933 |
> |
\label{specAu} |
| 934 |
|
\end{figure} |
| 935 |
|
|
| 936 |
< |
[MAY ADD COMPARISON OF G AND G', AU SLAB WIDTHS, ETC] |
| 877 |
< |
% The results show that the two definitions used for $G$ yield |
| 878 |
< |
% comparable values, though $G^\prime$ tends to be smaller. |
| 936 |
> |
[MAY ADD COMPARISON OF AU SLAB WIDTHS] |
| 937 |
|
|
| 938 |
|
\section{Conclusions} |
| 939 |
|
The NIVS algorithm we developed has been applied to simulations of |
| 941 |
|
effective unphysical thermal flux transferred between the metal and |
| 942 |
|
the liquid phase. With the flux applied, we were able to measure the |
| 943 |
|
corresponding thermal gradient and to obtain interfacial thermal |
| 944 |
< |
conductivities. Our simulations have seen significant conductance |
| 945 |
< |
enhancement with the presence of capping agent, compared to the bare |
| 946 |
< |
gold / liquid interfaces. The acoustic impedance mismatch between the |
| 947 |
< |
metal and the liquid phase is effectively eliminated by proper capping |
| 944 |
> |
conductivities. Under steady states, single trajectory simulation |
| 945 |
> |
would be enough for accurate measurement. This would be advantageous |
| 946 |
> |
compared to transient state simulations, which need multiple |
| 947 |
> |
trajectories to produce reliable average results. |
| 948 |
> |
|
| 949 |
> |
Our simulations have seen significant conductance enhancement with the |
| 950 |
> |
presence of capping agent, compared to the bare gold / liquid |
| 951 |
> |
interfaces. The acoustic impedance mismatch between the metal and the |
| 952 |
> |
liquid phase is effectively eliminated by proper capping |
| 953 |
|
agent. Furthermore, the coverage precentage of the capping agent plays |
| 954 |
< |
an important role in the interfacial thermal transport process. |
| 954 |
> |
an important role in the interfacial thermal transport |
| 955 |
> |
process. Moderately lower coverages allow higher contact between |
| 956 |
> |
capping agent and solvent, and thus could further enhance the heat |
| 957 |
> |
transfer process. |
| 958 |
|
|
| 959 |
|
Our measurement results, particularly of the UA models, agree with |
| 960 |
|
available experimental data. This indicates that our force field |
| 964 |
|
vibration would be overly sampled. Compared to the AA models, the UA |
| 965 |
|
models have higher computational efficiency with satisfactory |
| 966 |
|
accuracy, and thus are preferable in interfacial thermal transport |
| 967 |
< |
modelings. |
| 967 |
> |
modelings. Of the two definitions for $G$, the discrete form |
| 968 |
> |
(Eq. \ref{discreteG}) was easier to use and gives out relatively |
| 969 |
> |
consistent results, while the derivative form (Eq. \ref{derivativeG}) |
| 970 |
> |
is not as versatile. Although $G^\prime$ gives out comparable results |
| 971 |
> |
and follows similar trend with $G$ when measuring close to fully |
| 972 |
> |
covered or bare surfaces, the spatial resolution of $T$ profile is |
| 973 |
> |
limited for accurate computation of derivatives data. |
| 974 |
|
|
| 975 |
|
Vlugt {\it et al.} has investigated the surface thiol structures for |
| 976 |
|
nanocrystal gold and pointed out that they differs from those of the |
| 980 |
|
and measure the corresponding thermal gradient is desirable for |
| 981 |
|
simulating structures with spherical symmetry. |
| 982 |
|
|
| 911 |
– |
|
| 983 |
|
\section{Acknowledgments} |
| 984 |
|
Support for this project was provided by the National Science |
| 985 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
