109 |
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straightforward. The major modifications to the method are the addition of a rotational shearing term and the use of more versatile hot / cold regions instead |
110 |
|
of rectangular slabs. A temperature profile along the $r$ coordinate is created by recording the average temperature of concentric spherical shells. |
111 |
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|
112 |
< |
\begin{figure} |
113 |
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\center{\includegraphics[width=7in]{figures/VSS}} |
114 |
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\caption{Schematics of periodic (left) and nonperiodic (right) Velocity Shearing and Scaling RNEMD. A kinetic energy or momentum flux is applied from region B to region A. Thermal gradients are depicted by a color gradient. Linear or angular velocity gradients are shown as arrows.} |
115 |
< |
\label{fig:VSS} |
116 |
< |
\end{figure} |
112 |
> |
% \begin{figure} |
113 |
> |
% \center{\includegraphics[width=7in]{figures/VSS}} |
114 |
> |
% \caption{Schematics of periodic (left) and nonperiodic (right) Velocity Shearing and Scaling RNEMD. A kinetic energy or momentum flux is applied from region B to region A. Thermal gradients are depicted by a color gradient. Linear or angular velocity gradients are shown as arrows.} |
115 |
> |
% \label{fig:VSS} |
116 |
> |
% \end{figure} |
117 |
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|
118 |
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At each time interval, the particle velocities ($\mathbf{v}_i$ and |
119 |
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$\mathbf{v}_j$) in the cold and hot shells ($C$ and $H$) are modified by a |
285 |
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\\ \hline \hline |
286 |
|
{$J_r$} & {$\langle dT / dr \rangle$} & {$\boldsymbol \lambda$}\\ |
287 |
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{\small(kcal fs$^{-1}$ \AA$^{-2}$)} & {\small(K \AA$^{-1}$)} & {\small(W m$^{-1}$ K$^{-1}$)}\\ \hline |
288 |
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\\ \hline \hline |
288 |
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1.00$\times 10^{-5}$ & 0.38683 & 1.79665486\\ |
289 |
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3.00$\times 10^{-5}$ & 1.1643 & 1.79077557\\ |
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> |
6.00$\times 10^{-5}$ & 2.2262 & 1.87314707\\ |
291 |
> |
\hline \hline |
292 |
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\label{table:waterconductivity} |
293 |
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\end{longtable} |
294 |
|
|
297 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
298 |
|
\subsection{Interfacial thermal conductance} |
299 |
|
|
300 |
+ |
\begin{longtable}{ccc} |
301 |
+ |
\caption{Caption.} |
302 |
+ |
\\ \hline \hline |
303 |
+ |
{Nanoparticle Radius} & {$\boldsymbol \lambda$}\\ |
304 |
+ |
{\small(\AA)} & {\small(W m$^{-1}$ K$^{-1}$)}\\ \hline |
305 |
+ |
20 & 59.66\\ |
306 |
+ |
30 & 57.88\\ |
307 |
+ |
40 & \\ |
308 |
+ |
$\infty$ & \\ |
309 |
+ |
\hline \hline |
310 |
+ |
\label{table:waterconductivity} |
311 |
+ |
\end{longtable} |
312 |
+ |
|
313 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
314 |
|
% INTERFACIAL FRICTION |
315 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
316 |
|
\subsection{Interfacial friction} |
317 |
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|
318 |
< |
Table \ref{table:interfacialfrictionstick} shows the calculated interfacial friction coefficients $\kappa$ for a spherical gold nanoparticle and prolate ellipsoidal gold nanorod in TraPPE-UA hexane. An angular momentum flux was applied between the A and B regions defined as the gold structure and hexane molecules beyond a certain radius, respectively. The resulting angular velocity gradient resulted in the gold structure rotating about the prescribed axis within the solvent. |
318 |
> |
Table \ref{table:interfacialfrictionstick} shows the calculated interfacial friction coefficients $\kappa$ for spherical gold nanoparticles and a prolate ellipsoidal gold nanorod in TraPPE-UA hexane. An angular momentum flux was applied between the A and B regions defined as the gold structure and hexane molecules beyond a certain radius, respectively. The resulting angular velocity gradient resulted in the gold structure rotating about the prescribed axis within the solvent. |
319 |
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|
320 |
|
\begin{longtable}{lccccc} |
321 |
< |
\caption{Calculated ``stick'' interfacial friction coefficients ($\kappa$) and friction factors ($f$) of gold nanostructures solvated in TraPPE-UA hexane. The ellipsoid is oriented with the long axis along the $z$ direction.} |
321 |
> |
\caption{Calculated ``stick'' interfacial friction coefficients ($\kappa$) and friction factors ($f$) of gold nanostructures solvated in TraPPE-UA hexane at 230 K. The ellipsoid is oriented with the long axis along the $z$ direction.} |
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\\ \hline \hline |
323 |
< |
{Structure} & {Axis of rotation} & {$\kappa_{VSS}$} & {$\kappa_{calc}$} & {$f_{VSS}$} & {$f_{calc}$}\\ |
323 |
> |
{Structure} & {Axis of Rotation} & {$\kappa_{VSS}$} & {$\kappa_{calc}$} & {$f_{VSS}$} & {$f_{calc}$}\\ |
324 |
|
{} & {} & {\small($10^{-29}$ Pa s m$^{3}$)} & {\small($10^{-29}$ Pa s m$^{3}$)} & {} & {}\\ \hline |
325 |
< |
{Sphere} & {$x = y = z$} & {} & {5.37237} & {1} & {1}\\ |
326 |
< |
{Prolate Ellipsoid} & {$x = y$} & {} & {3.59881} & {} & {0.768726}\\ |
327 |
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{Prolate Ellipsoid} & {$z$} & {} & {9.01084} & {} & {1.92477}\\ \hline \hline |
325 |
> |
{Sphere (r = 20 \AA)} & {$x = y = z$} & {} & {6.13239} & {1} & {1}\\ |
326 |
> |
{Sphere (r = 30 \AA)} & {$x = y = z$} & {} & {20.6968} & {1} & {1}\\ |
327 |
> |
{Sphere (r = 40 \AA)} & {$x = y = z$} & {} & {49.0591} & {1} & {1}\\ |
328 |
> |
{Prolate Ellipsoid} & {$x = y$} & {} & {8.22846} & {} & {1.92477}\\ |
329 |
> |
{Prolate Ellipsoid} & {$z$} & {} & {3.28634} & {} & {0.768726}\\ |
330 |
> |
\hline \hline |
331 |
|
\label{table:interfacialfrictionstick} |
332 |
|
\end{longtable} |
333 |
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|