| 88 |
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is often unclear what shape of gradient should be imposed at the |
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boundary between materials. |
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|
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< |
% \begin{figure} |
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% \includegraphics[width=\linewidth]{figures/VSS} |
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% \caption{Schematics of periodic (left) and non-periodic (right) |
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% Velocity Shearing and Scaling RNEMD. A kinetic energy or momentum |
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< |
% flux is applied from region B to region A. Thermal gradients are |
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< |
% depicted by a color gradient. Linear or angular velocity gradients |
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< |
% are shown as arrows.} |
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% \label{fig:VSS} |
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< |
% \end{figure} |
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> |
\begin{figure} |
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> |
\includegraphics[width=\linewidth]{figures/npVSS} |
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> |
\caption{Schematics of periodic (left) and non-periodic (right) |
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> |
Velocity Shearing and Scaling RNEMD. A kinetic energy or momentum |
| 95 |
> |
flux is applied from region B to region A. Thermal gradients are |
| 96 |
> |
depicted by a color gradient. Linear or angular velocity gradients |
| 97 |
> |
are shown as arrows.} |
| 98 |
> |
\label{fig:VSS} |
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> |
\end{figure} |
| 100 |
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|
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Reverse Non-Equilibrium Molecular Dynamics (RNEMD) methods impose an |
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unphysical {\it flux} between different regions or ``slabs'' of the |
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We have extended the VSS method for use in {\it non-periodic} |
| 133 |
|
simulations, in which the ``slabs'' have been generalized to two |
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|
separated regions of space. These regions could be defined as |
| 135 |
< |
concentric spheres (as in figure \ref{fig:VSS}), or one of the regions |
| 135 |
> |
concentric spheres (as in figure \ref{fig:npVSS}), or one of the regions |
| 136 |
|
can be defined in terms of a dynamically changing ``hull'' comprising |
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|
the surface atoms of the cluster. This latter definition is identical |
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to the hull used in the Langevin Hull algorithm. |
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|
Table \ref{table:couple} shows the calculated rotational friction coefficients $\Xi^{rr}$ 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 causes the gold structure to rotate about the prescribed axis. |
| 427 |
|
|
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|
\begin{longtable}{lcccc} |
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< |
\caption{Comparison of rotational friction coefficients under ideal ``stick'' conditions ($\Xi^{rr}_{stick}$) calculated via Stokes' and Perrin's laws and effective rotational friction coefficients ($\Xi^{rr}_{\mathit{eff}}$) of gold nanostructures solvated in TraPPE-UA hexane at 230 K. The ellipsoid is oriented with the long axis along the $z$ direction.} |
| 429 |
> |
\caption{Comparison of rotational friction coefficients under ideal ``stick'' conditions ($\Xi^{rr}_{\mathit{stick}}$) calculated via Stokes' and Perrin's laws and effective rotational friction coefficients ($\Xi^{rr}_{\mathit{eff}}$) 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 |
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{Structure} & {Axis of Rotation} & {$\Xi^{rr}_{stick}$} & {$\Xi^{rr}_{\mathit{eff}}$} & {$\Xi^{rr}_{\mathit{eff}}$ / $\Xi^{rr}_{stick}$}\\ |
| 431 |
> |
{Structure} & {Axis of Rotation} & {$\Xi^{rr}_{\mathit{stick}}$} & {$\Xi^{rr}_{\mathit{eff}}$} & {$\Xi^{rr}_{\mathit{eff}}$ / $\Xi^{rr}_{\mathit{stick}}$}\\ |
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{} & {} & {\small(amu A$^2$ fs$^{-1}$)} & {\small(amu A$^2$ fs$^{-1}$)} & \\ \hline |
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Sphere (r = 20 \AA) & {$x = y = z$} & {3314} & {2386} & {0.720}\\ |
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Sphere (r = 30 \AA) & {$x = y = z$} & {11749} & {8415} & {0.716}\\ |
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\label{table:couple} |
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\end{longtable} |
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+ |
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+ |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% **DISCUSSION** |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
