| 28 |
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|
| 29 |
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\begin{document} |
| 30 |
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|
| 31 |
< |
\title{Simulating interfacial thermal conductance at metal-solvent |
| 32 |
< |
interfaces: the role of chemical capping agents} |
| 31 |
> |
\title{Simulating Interfacial Thermal Conductance at Metal-Solvent |
| 32 |
> |
Interfaces: the Role of Chemical Capping Agents} |
| 33 |
|
|
| 34 |
|
\author{Shenyu Kuang and J. Daniel |
| 35 |
|
Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
| 50 |
|
inhomogeneous systems such as solid / liquid interfaces. We have |
| 51 |
|
applied NIVS to compute the interfacial thermal conductance at a |
| 52 |
|
metal / organic solvent interface that has been chemically capped by |
| 53 |
< |
butanethiol molecules. Our calculations suggest that the acoustic |
| 54 |
< |
impedance mismatch between the metal and liquid phases is |
| 55 |
< |
effectively reduced by the capping agents, leading to a greatly |
| 56 |
< |
enhanced conductivity at the interface. Specifically, the chemical |
| 57 |
< |
bond between the metal and the capping agent introduces a |
| 58 |
< |
vibrational overlap that is not present without the capping agent, |
| 59 |
< |
and the overlap between the vibrational spectra (metal to cap, cap |
| 60 |
< |
to solvent) provides a mechanism for rapid thermal transport across |
| 61 |
< |
the interface. Our calculations also suggest that this is a |
| 62 |
< |
non-monotonic function of the fractional coverage of the surface, as |
| 63 |
< |
moderate coverages allow convective heat transport of solvent |
| 64 |
< |
molecules that have been in close contact with the capping agent. |
| 53 |
> |
butanethiol molecules. Our calculations suggest that vibrational |
| 54 |
> |
coupling between the metal and liquid phases is enhanced by the |
| 55 |
> |
capping agents, leading to a greatly enhanced conductivity at the |
| 56 |
> |
interface. Specifically, the chemical bond between the metal and |
| 57 |
> |
the capping agent introduces a vibrational overlap that is not |
| 58 |
> |
present without the capping agent, and the overlap between the |
| 59 |
> |
vibrational spectra (metal to cap, cap to solvent) provides a |
| 60 |
> |
mechanism for rapid thermal transport across the interface. Our |
| 61 |
> |
calculations also suggest that this is a non-monotonic function of |
| 62 |
> |
the fractional coverage of the surface, as moderate coverages allow |
| 63 |
> |
diffusive heat transport of solvent molecules that have been in |
| 64 |
> |
close contact with the capping agent. |
| 65 |
> |
|
| 66 |
> |
Keywords: non-equilibrium, molecular dynamics, vibrational overlap, |
| 67 |
> |
coverage dependent. |
| 68 |
|
\end{abstract} |
| 69 |
|
|
| 70 |
|
\newpage |
| 105 |
|
eliminate this barrier |
| 106 |
|
($G\rightarrow\infty$).\cite{doi:10.1021/la904855s} |
| 107 |
|
|
| 108 |
< |
Theoretical and computational models have also been used to study the |
| 108 |
> |
The acoustic mismatch model for interfacial conductance utilizes the |
| 109 |
> |
acoustic impedance ($Z_a = \rho_a v^s_a$) on both sides of the |
| 110 |
> |
interface.\cite{schwartz} Here, $\rho_a$ and $v^s_a$ are the density |
| 111 |
> |
and speed of sound in material $a$. The phonon transmission |
| 112 |
> |
probability at the $a-b$ interface is |
| 113 |
> |
\begin{equation} |
| 114 |
> |
t_{ab} = \frac{4 Z_a Z_b}{\left(Z_a + Z_b \right)^2}, |
| 115 |
> |
\end{equation} |
| 116 |
> |
and the interfacial conductance can then be approximated as |
| 117 |
> |
\begin{equation} |
| 118 |
> |
G_{ab} \approx \frac{1}{4} C_D v_D t_{ab} |
| 119 |
> |
\end{equation} |
| 120 |
> |
where $C_D$ is the Debye heat capacity of the hot side, and $v_D$ is |
| 121 |
> |
the Debye phonon velocity ($1/v_D^3 = 1/3v_L^3 + 2/3 v_T^3$) where |
| 122 |
> |
$v_L$ and $v_T$ are the longitudinal and transverse speeds of sound, |
| 123 |
> |
respectively. For the Au/hexane and Au/toluene interfaces, the |
| 124 |
> |
acoustic mismatch model predicts room-temperature $G \approx 87 \mbox{ |
| 125 |
> |
and } 129$ MW m$^{-2}$ K$^{-1}$, respectively. However, it is not |
| 126 |
> |
clear how one might apply the acoustic mismatch model to a |
| 127 |
> |
chemically-modified surface, particularly when the acoustic properties |
| 128 |
> |
of a monolayer film may not be well characterized. |
| 129 |
> |
|
| 130 |
> |
More precise computational models have also been used to study the |
| 131 |
|
interfacial thermal transport in order to gain an understanding of |
| 132 |
|
this phenomena at the molecular level. Recently, Hase and coworkers |
| 133 |
|
employed Non-Equilibrium Molecular Dynamics (NEMD) simulations to |
| 148 |
|
Garde and coworkers\cite{garde:nl2005,garde:PhysRevLett2009} applied |
| 149 |
|
this approach to various liquid interfaces and studied how thermal |
| 150 |
|
conductance (or resistance) is dependent on chemical details of a |
| 151 |
< |
number of hydrophobic and hydrophilic aqueous interfaces. {\bf And |
| 152 |
< |
Luo {\it et al.} studied the thermal conductance of Au-SAM-Au |
| 153 |
< |
junctions using the same approach, with comparison to a constant |
| 154 |
< |
temperature difference method\cite{Luo20101}. While this latter |
| 155 |
< |
approach establishes more thermal distributions compared to the |
| 156 |
< |
former RNEMD methods, it does not guarantee momentum or kinetic |
| 157 |
< |
energy conservations.} |
| 151 |
> |
number of hydrophobic and hydrophilic aqueous interfaces. And |
| 152 |
> |
recently, Luo {\it et al.} studied the thermal conductance of |
| 153 |
> |
Au-SAM-Au junctions using the same approach, comparing to a constant |
| 154 |
> |
temperature difference method.\cite{Luo20101} While this latter |
| 155 |
> |
approach establishes more ideal Maxwell-Boltzmann distributions than |
| 156 |
> |
previous RNEMD methods, it does not guarantee momentum or kinetic |
| 157 |
> |
energy conservation. |
| 158 |
|
|
| 159 |
|
Recently, we have developed a Non-Isotropic Velocity Scaling (NIVS) |
| 160 |
|
algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm |
| 168 |
|
The work presented here deals with the Au(111) surface covered to |
| 169 |
|
varying degrees by butanethiol, a capping agent with short carbon |
| 170 |
|
chain, and solvated with organic solvents of different molecular |
| 171 |
< |
properties. {\bf To our knowledge, few previous MD inverstigations |
| 172 |
< |
have been found to address to these systems yet.} Different models |
| 173 |
< |
were used for both the capping agent and the solvent force field |
| 174 |
< |
parameters. Using the NIVS algorithm, the thermal transport across |
| 150 |
< |
these interfaces was studied and the underlying mechanism for the |
| 151 |
< |
phenomena was investigated. |
| 171 |
> |
properties. Different models were used for both the capping agent and |
| 172 |
> |
the solvent force field parameters. Using the NIVS algorithm, the |
| 173 |
> |
thermal transport across these interfaces was studied and the |
| 174 |
> |
underlying mechanism for the phenomena was investigated. |
| 175 |
|
|
| 176 |
|
\section{Methodology} |
| 177 |
|
\subsection{Imposed-Flux Methods in MD Simulations} |
| 257 |
|
\label{demoPic} |
| 258 |
|
\end{figure} |
| 259 |
|
|
| 260 |
< |
The other approach is to assume a continuous temperature profile along |
| 261 |
< |
the thermal gradient axis (e.g. $z$) and define $G$ at the point where |
| 262 |
< |
the magnitude of thermal conductivity ($\lambda$) change reaches its |
| 263 |
< |
maximum, given that $\lambda$ is well-defined throughout the space: |
| 264 |
< |
\begin{equation} |
| 265 |
< |
G^\prime = \Big|\frac{\partial\lambda}{\partial z}\Big| |
| 266 |
< |
= \Big|\frac{\partial}{\partial z}\left(-J_z\Big/ |
| 267 |
< |
\left(\frac{\partial T}{\partial z}\right)\right)\Big| |
| 268 |
< |
= |J_z|\Big|\frac{\partial^2 T}{\partial z^2}\Big| |
| 269 |
< |
\Big/\left(\frac{\partial T}{\partial z}\right)^2 |
| 270 |
< |
\label{derivativeG} |
| 271 |
< |
\end{equation} |
| 260 |
> |
Another approach is to assume that the temperature is continuous and |
| 261 |
> |
differentiable throughout the space. Given that $\lambda$ is also |
| 262 |
> |
differentiable, $G$ can be defined as its gradient ($\nabla\lambda$) |
| 263 |
> |
projected along a vector normal to the interface ($\mathbf{\hat{n}}$) |
| 264 |
> |
and evaluated at the interface location ($z_0$). This quantity, |
| 265 |
> |
\begin{align} |
| 266 |
> |
G^\prime &= \left(\nabla\lambda \cdot \mathbf{\hat{n}}\right)_{z_0} \\ |
| 267 |
> |
&= \frac{\partial}{\partial z}\left(-\frac{J_z}{ |
| 268 |
> |
\left(\frac{\partial T}{\partial z}\right)}\right)_{z_0} \\ |
| 269 |
> |
&= J_z\left(\frac{\partial^2 T}{\partial z^2}\right)_{z_0} \Big/ |
| 270 |
> |
\left(\frac{\partial T}{\partial z}\right)_{z_0}^2 \label{derivativeG} |
| 271 |
> |
\end{align} |
| 272 |
> |
has the same units as the common definition for $G$, and the maximum |
| 273 |
> |
of its magnitude denotes where thermal conductivity has the largest |
| 274 |
> |
change, i.e. the interface. In the geometry used in this study, the |
| 275 |
> |
vector normal to the interface points along the $z$ axis, as do |
| 276 |
> |
$\vec{J}$ and the thermal gradient. This yields the simplified |
| 277 |
> |
expressions in Eq. \ref{derivativeG}. |
| 278 |
|
|
| 279 |
|
With temperature profiles obtained from simulation, one is able to |
| 280 |
|
approximate the first and second derivatives of $T$ with finite |
| 385 |
|
\Big/\left(\frac{\partial T}{\partial n}\right)^2 |
| 386 |
|
\label{derivativeG2} |
| 387 |
|
\end{equation} |
| 388 |
+ |
The absolute values in Eq. \ref{derivativeG2} appear because the |
| 389 |
+ |
direction of the flux $\vec{J}$ is in an opposing direction on either |
| 390 |
+ |
side of the metal slab. |
| 391 |
|
|
| 392 |
|
All of the above simulation procedures use a time step of 1 fs. Each |
| 393 |
|
equilibration stage took a minimum of 100 ps, although in some cases, |
| 626 |
|
$G^\prime$) values for interfaces using various models for |
| 627 |
|
solvent and capping agent (or without capping agent) at |
| 628 |
|
$\langle T\rangle\sim$200K. Here ``D'' stands for deuterated |
| 629 |
< |
solvent or capping agent molecules; ``Avg.'' denotes results |
| 630 |
< |
that are averages of simulations under different applied |
| 599 |
< |
thermal flux $(J_z)$ values. Error estimates are indicated in |
| 600 |
< |
parentheses.} |
| 629 |
> |
solvent or capping agent molecules. Error estimates are |
| 630 |
> |
indicated in parentheses.} |
| 631 |
|
|
| 632 |
|
\begin{tabular}{llccc} |
| 633 |
|
\hline\hline |
| 634 |
< |
Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\ |
| 635 |
< |
(or bare surface) & model & (GW/m$^2$) & |
| 634 |
> |
Butanethiol model & Solvent & $G$ & $G^\prime$ \\ |
| 635 |
> |
(or bare surface) & model & |
| 636 |
|
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 637 |
|
\hline |
| 638 |
< |
UA & UA hexane & Avg. & 131(9) & 87(10) \\ |
| 639 |
< |
& UA hexane(D) & 1.95 & 153(5) & 136(13) \\ |
| 640 |
< |
& AA hexane & Avg. & 131(6) & 122(10) \\ |
| 641 |
< |
& UA toluene & 1.96 & 187(16) & 151(11) \\ |
| 642 |
< |
& AA toluene & 1.89 & 200(36) & 149(53) \\ |
| 638 |
> |
UA & UA hexane & 131(9) & 87(10) \\ |
| 639 |
> |
& UA hexane(D) & 153(5) & 136(13) \\ |
| 640 |
> |
& AA hexane & 131(6) & 122(10) \\ |
| 641 |
> |
& UA toluene & 187(16) & 151(11) \\ |
| 642 |
> |
& AA toluene & 200(36) & 149(53) \\ |
| 643 |
|
\hline |
| 644 |
< |
AA & UA hexane & 1.94 & 116(9) & 129(8) \\ |
| 645 |
< |
& AA hexane & Avg. & 442(14) & 356(31) \\ |
| 646 |
< |
& AA hexane(D) & 1.93 & 222(12) & 234(54) \\ |
| 647 |
< |
& UA toluene & 1.98 & 125(25) & 97(60) \\ |
| 648 |
< |
& AA toluene & 3.79 & 487(56) & 290(42) \\ |
| 619 |
< |
\hline |
| 620 |
< |
AA(D) & UA hexane & 1.94 & 158(25) & 172(4) \\ |
| 621 |
< |
& AA hexane & 1.92 & 243(29) & 191(11) \\ |
| 622 |
< |
& AA toluene & 1.93 & 364(36) & 322(67) \\ |
| 644 |
> |
AA & UA hexane & 116(9) & 129(8) \\ |
| 645 |
> |
& AA hexane & 442(14) & 356(31) \\ |
| 646 |
> |
& AA hexane(D) & 222(12) & 234(54) \\ |
| 647 |
> |
& UA toluene & 125(25) & 97(60) \\ |
| 648 |
> |
& AA toluene & 487(56) & 290(42) \\ |
| 649 |
|
\hline |
| 650 |
< |
bare & UA hexane & Avg. & 46.5(3.2) & 49.4(4.5) \\ |
| 651 |
< |
& UA hexane(D) & 0.98 & 43.9(4.6) & 43.0(2.0) \\ |
| 652 |
< |
& AA hexane & 0.96 & 31.0(1.4) & 29.4(1.3) \\ |
| 653 |
< |
& UA toluene & 1.99 & 70.1(1.3) & 65.8(0.5) \\ |
| 650 |
> |
AA(D) & UA hexane & 158(25) & 172(4) \\ |
| 651 |
> |
& AA hexane & 243(29) & 191(11) \\ |
| 652 |
> |
& AA toluene & 364(36) & 322(67) \\ |
| 653 |
> |
\hline |
| 654 |
> |
bare & UA hexane & 46.5(3.2) & 49.4(4.5) \\ |
| 655 |
> |
& UA hexane(D) & 43.9(4.6) & 43.0(2.0) \\ |
| 656 |
> |
& AA hexane & 31.0(1.4) & 29.4(1.3) \\ |
| 657 |
> |
& UA toluene & 70.1(1.3) & 65.8(0.5) \\ |
| 658 |
|
\hline\hline |
| 659 |
|
\end{tabular} |
| 660 |
|
\label{modelTest} |
| 669 |
|
On bare metal / solvent surfaces, different force field models for |
| 670 |
|
hexane yield similar results for both $G$ and $G^\prime$, and these |
| 671 |
|
two definitions agree with each other very well. This is primarily an |
| 672 |
< |
indicator of weak interactions between the metal and the solvent, and |
| 643 |
< |
is a typical case for acoustic impedance mismatch between these two |
| 644 |
< |
phases. |
| 672 |
> |
indicator of weak interactions between the metal and the solvent. |
| 673 |
|
|
| 674 |
|
For the fully-covered surfaces, the choice of force field for the |
| 675 |
|
capping agent and solvent has a large impact on the calculated values |
| 742 |
|
The resulting gradient therefore has a higher temperature in the |
| 743 |
|
liquid phase. Negative flux values reverse this transfer, and result |
| 744 |
|
in higher temperature metal phases. The conductance measured under |
| 745 |
< |
different applied $J_z$ values is listed in Tables |
| 746 |
< |
\ref{AuThiolHexaneUA} and \ref{AuThiolToluene}. These results do not |
| 747 |
< |
indicate that $G$ depends strongly on $J_z$ within this flux |
| 748 |
< |
range. The linear response of flux to thermal gradient simplifies our |
| 749 |
< |
investigations in that we can rely on $G$ measurement with only a |
| 722 |
< |
small number $J_z$ values. |
| 745 |
> |
different applied $J_z$ values is listed in Tables 1 and 2 in the |
| 746 |
> |
supporting information. These results do not indicate that $G$ depends |
| 747 |
> |
strongly on $J_z$ within this flux range. The linear response of flux |
| 748 |
> |
to thermal gradient simplifies our investigations in that we can rely |
| 749 |
> |
on $G$ measurement with only a small number $J_z$ values. |
| 750 |
|
|
| 724 |
– |
\begin{table*} |
| 725 |
– |
\begin{minipage}{\linewidth} |
| 726 |
– |
\begin{center} |
| 727 |
– |
\caption{In the hexane-solvated interfaces, the system size has |
| 728 |
– |
little effect on the calculated values for interfacial |
| 729 |
– |
conductance ($G$ and $G^\prime$), but the direction of heat |
| 730 |
– |
flow (i.e. the sign of $J_z$) can alter the average |
| 731 |
– |
temperature of the liquid phase and this can alter the |
| 732 |
– |
computed conductivity.} |
| 733 |
– |
|
| 734 |
– |
\begin{tabular}{ccccccc} |
| 735 |
– |
\hline\hline |
| 736 |
– |
$\langle T\rangle$ & $N_{hexane}$ & $\rho_{hexane}$ & |
| 737 |
– |
$J_z$ & $G$ & $G^\prime$ \\ |
| 738 |
– |
(K) & & (g/cm$^3$) & (GW/m$^2$) & |
| 739 |
– |
\multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 740 |
– |
\hline |
| 741 |
– |
200 & 266 & 0.672 & -0.96 & 102(3) & 80.0(0.8) \\ |
| 742 |
– |
& 200 & 0.688 & 0.96 & 125(16) & 90.2(15) \\ |
| 743 |
– |
& & & 1.91 & 139(10) & 101(10) \\ |
| 744 |
– |
& & & 2.83 & 141(6) & 89.9(9.8) \\ |
| 745 |
– |
& 166 & 0.681 & 0.97 & 141(30) & 78(22) \\ |
| 746 |
– |
& & & 1.92 & 138(4) & 98.9(9.5) \\ |
| 747 |
– |
\hline |
| 748 |
– |
250 & 200 & 0.560 & 0.96 & 75(10) & 61.8(7.3) \\ |
| 749 |
– |
& & & -0.95 & 49.4(0.3) & 45.7(2.1) \\ |
| 750 |
– |
& 166 & 0.569 & 0.97 & 80.3(0.6) & 67(11) \\ |
| 751 |
– |
& & & 1.44 & 76.2(5.0) & 64.8(3.8) \\ |
| 752 |
– |
& & & -0.95 & 56.4(2.5) & 54.4(1.1) \\ |
| 753 |
– |
& & & -1.85 & 47.8(1.1) & 53.5(1.5) \\ |
| 754 |
– |
\hline\hline |
| 755 |
– |
\end{tabular} |
| 756 |
– |
\label{AuThiolHexaneUA} |
| 757 |
– |
\end{center} |
| 758 |
– |
\end{minipage} |
| 759 |
– |
\end{table*} |
| 760 |
– |
|
| 751 |
|
The sign of $J_z$ is a different matter, however, as this can alter |
| 752 |
|
the temperature on the two sides of the interface. The average |
| 753 |
|
temperature values reported are for the entire system, and not for the |
| 754 |
|
liquid phase, so at a given $\langle T \rangle$, the system with |
| 755 |
|
positive $J_z$ has a warmer liquid phase. This means that if the |
| 756 |
< |
liquid carries thermal energy via convective transport, {\it positive} |
| 756 |
> |
liquid carries thermal energy via diffusive transport, {\it positive} |
| 757 |
|
$J_z$ values will result in increased molecular motion on the liquid |
| 758 |
|
side of the interface, and this will increase the measured |
| 759 |
|
conductivity. |
| 766 |
|
predict a lower boiling point (and liquid state density) than |
| 767 |
|
experiments. This lower-density liquid phase leads to reduced contact |
| 768 |
|
between the hexane and butanethiol, and this accounts for our |
| 769 |
< |
observation of lower conductance at higher temperatures as shown in |
| 770 |
< |
Table \ref{AuThiolHexaneUA}. In raising the average temperature from |
| 771 |
< |
200K to 250K, the density drop of $\sim$20\% in the solvent phase |
| 772 |
< |
leads to a $\sim$40\% drop in the conductance. |
| 769 |
> |
observation of lower conductance at higher temperatures. In raising |
| 770 |
> |
the average temperature from 200K to 250K, the density drop of |
| 771 |
> |
$\sim$20\% in the solvent phase leads to a $\sim$40\% drop in the |
| 772 |
> |
conductance. |
| 773 |
|
|
| 774 |
|
Similar behavior is observed in the TraPPE-UA model for toluene, |
| 775 |
|
although this model has better agreement with the experimental |
| 776 |
|
densities of toluene. The expansion of the toluene liquid phase is |
| 777 |
|
not as significant as that of the hexane (8.3\% over 100K), and this |
| 778 |
< |
limits the effect to $\sim$20\% drop in thermal conductivity (Table |
| 789 |
< |
\ref{AuThiolToluene}). |
| 778 |
> |
limits the effect to $\sim$20\% drop in thermal conductivity. |
| 779 |
|
|
| 780 |
|
Although we have not mapped out the behavior at a large number of |
| 781 |
|
temperatures, is clear that there will be a strong temperature |
| 783 |
|
of one side of the interface (notably the density) change rapidly as a |
| 784 |
|
function of temperature. |
| 785 |
|
|
| 797 |
– |
\begin{table*} |
| 798 |
– |
\begin{minipage}{\linewidth} |
| 799 |
– |
\begin{center} |
| 800 |
– |
\caption{When toluene is the solvent, the interfacial thermal |
| 801 |
– |
conductivity is less sensitive to temperature, but again, the |
| 802 |
– |
direction of the heat flow can alter the solvent temperature |
| 803 |
– |
and can change the computed conductance values.} |
| 804 |
– |
|
| 805 |
– |
\begin{tabular}{ccccc} |
| 806 |
– |
\hline\hline |
| 807 |
– |
$\langle T\rangle$ & $\rho_{toluene}$ & $J_z$ & $G$ & $G^\prime$ \\ |
| 808 |
– |
(K) & (g/cm$^3$) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 809 |
– |
\hline |
| 810 |
– |
200 & 0.933 & 2.15 & 204(12) & 113(12) \\ |
| 811 |
– |
& & -1.86 & 180(3) & 135(21) \\ |
| 812 |
– |
& & -3.93 & 176(5) & 113(12) \\ |
| 813 |
– |
\hline |
| 814 |
– |
300 & 0.855 & -1.91 & 143(5) & 125(2) \\ |
| 815 |
– |
& & -4.19 & 135(9) & 113(12) \\ |
| 816 |
– |
\hline\hline |
| 817 |
– |
\end{tabular} |
| 818 |
– |
\label{AuThiolToluene} |
| 819 |
– |
\end{center} |
| 820 |
– |
\end{minipage} |
| 821 |
– |
\end{table*} |
| 822 |
– |
|
| 786 |
|
Besides the lower interfacial thermal conductance, surfaces at |
| 787 |
|
relatively high temperatures are susceptible to reconstructions, |
| 788 |
|
particularly when butanethiols fully cover the Au(111) surface. These |
| 851 |
|
surface Au layer to the capping agents. Therefore, in our simulations, |
| 852 |
|
the Au / S interfaces do not appear to be the primary barrier to |
| 853 |
|
thermal transport when compared with the butanethiol / solvent |
| 854 |
< |
interfaces. {\bf This confirms the results from Luo {\it et |
| 855 |
< |
al.}\cite{Luo20101}, which reported $G$ for Au-SAM junctions |
| 856 |
< |
generally twice larger than what we have computed for the |
| 857 |
< |
thiol-liquid interfaces.} |
| 854 |
> |
interfaces. This supports the results of Luo {\it et |
| 855 |
> |
al.}\cite{Luo20101}, who reported $G$ for Au-SAM junctions roughly |
| 856 |
> |
twice as large as what we have computed for the thiol-liquid |
| 857 |
> |
interfaces. |
| 858 |
|
|
| 859 |
|
\begin{figure} |
| 860 |
|
\includegraphics[width=\linewidth]{vibration} |
| 877 |
|
between the butanethiol and the organic solvents suggests a highly |
| 878 |
|
efficient thermal exchange between these components. Very high |
| 879 |
|
thermal conductivity was observed when AA models were used and C-H |
| 880 |
< |
vibrations were treated classically. The presence of extra degrees of |
| 880 |
> |
vibrations were treated classically. The presence of extra degrees of |
| 881 |
|
freedom in the AA force field yields higher heat exchange rates |
| 882 |
|
between the two phases and results in a much higher conductivity than |
| 883 |
< |
in the UA force field. {\bf Due to the classical models used, this |
| 884 |
< |
even includes those high frequency modes which should be unpopulated |
| 885 |
< |
at our relatively low temperatures. This artifact causes high |
| 886 |
< |
frequency vibrations accountable for thermal transport in classical |
| 924 |
< |
MD simulations.} |
| 883 |
> |
in the UA force field. The all-atom classical models include high |
| 884 |
> |
frequency modes which should be unpopulated at our relatively low |
| 885 |
> |
temperatures. This artifact is likely the cause of the high thermal |
| 886 |
> |
conductance in all-atom MD simulations. |
| 887 |
|
|
| 888 |
|
The similarity in the vibrational modes available to solvent and |
| 889 |
|
capping agent can be reduced by deuterating one of the two components |
| 913 |
|
highly efficient. Combining our observations with those of Zhang {\it |
| 914 |
|
et al.}, it appears that butanethiol acts as a channel to expedite |
| 915 |
|
heat flow from the gold surface and into the alkyl chain. The |
| 916 |
< |
acoustic impedance mismatch between the metal and the liquid phase can |
| 917 |
< |
therefore be effectively reduced with the presence of suitable capping |
| 956 |
< |
agents. |
| 916 |
> |
vibrational coupling between the metal and the liquid phase can |
| 917 |
> |
therefore be enhanced with the presence of suitable capping agents. |
| 918 |
|
|
| 919 |
|
Deuterated models in the UA force field did not decouple the thermal |
| 920 |
|
transport as well as in the AA force field. The UA models, even |
| 948 |
|
|
| 949 |
|
Our simulations have seen significant conductance enhancement in the |
| 950 |
|
presence of capping agent, compared with the bare gold / liquid |
| 951 |
< |
interfaces. The acoustic impedance mismatch between the metal and the |
| 952 |
< |
liquid phase is effectively eliminated by a chemically-bonded capping |
| 953 |
< |
agent. Furthermore, the coverage percentage of the capping agent plays |
| 954 |
< |
an important role in the interfacial thermal transport |
| 955 |
< |
process. Moderately low coverages allow higher contact between capping |
| 956 |
< |
agent and solvent, and thus could further enhance the heat transfer |
| 957 |
< |
process, giving a non-monotonic behavior of conductance with |
| 997 |
< |
increasing coverage. |
| 951 |
> |
interfaces. The vibrational coupling between the metal and the liquid |
| 952 |
> |
phase is enhanced by a chemically-bonded capping agent. Furthermore, |
| 953 |
> |
the coverage percentage of the capping agent plays an important role |
| 954 |
> |
in the interfacial thermal transport process. Moderately low coverages |
| 955 |
> |
allow higher contact between capping agent and solvent, and thus could |
| 956 |
> |
further enhance the heat transfer process, giving a non-monotonic |
| 957 |
> |
behavior of conductance with increasing coverage. |
| 958 |
|
|
| 959 |
|
Our results, particularly using the UA models, agree well with |
| 960 |
|
available experimental data. The AA models tend to overestimate the |
