217 |
|
defined. The pressure and temperature bath interacts {\it directly} |
218 |
|
with the atoms on the edge and not with atoms interior to the |
219 |
|
simulation. |
220 |
+ |
|
221 |
+ |
|
222 |
+ |
\begin{figure} |
223 |
+ |
\includegraphics[width=\linewidth]{hullSample} |
224 |
+ |
\caption{The external temperature and pressure bath interacts only |
225 |
+ |
with those atoms on the convex hull (grey surface). The hull is |
226 |
+ |
computed dynamically at each time step, and molecules dynamically |
227 |
+ |
move between the interior (Newtonian) region and the Langevin hull.} |
228 |
+ |
\label{fig:hullSample} |
229 |
+ |
\end{figure} |
230 |
|
|
231 |
+ |
|
232 |
|
Atomic sites in the interior of the point cloud move under standard |
233 |
|
Newtonian dynamics, |
234 |
|
\begin{equation} |
365 |
|
the Langevin Hull on a crystalline system (gold nanoparticles), a |
366 |
|
liquid droplet (SPC/E water), and a heterogeneous mixture (gold |
367 |
|
nanoparticles in a water droplet). In each case, we have computed |
368 |
< |
bulk properties that depend on the external applied pressure. Of |
369 |
< |
particular interest is the bulk modulus, |
368 |
> |
properties that depend on the external applied pressure. Of |
369 |
> |
particular interest for the single-phase systems is the bulk modulus, |
370 |
|
\begin{equation} |
371 |
|
\kappa_{T} = -\frac{1}{V} \left ( \frac{\partial V}{\partial P} \right |
372 |
|
)_{T}. |
386 |
|
\label{eq:BMN} |
387 |
|
\end{equation} |
388 |
|
The region we pick is a spherical volume of 10 \AA radius centered in |
389 |
< |
the middle of the cluster. This radius is arbitrary, and any |
390 |
< |
bulk-like portion of the cluster can be used to compute the bulk |
391 |
< |
modulus. |
389 |
> |
the middle of the cluster. The geometry and size of the region is |
390 |
> |
arbitrary, and any bulk-like portion of the cluster can be used to |
391 |
> |
compute the bulk modulus. |
392 |
|
|
393 |
|
One might also assume that the volume of the convex hull could be |
394 |
|
taken as the system volume in the compressibility expression |
460 |
|
phase, and isolated molecules can detach from the liquid droplet. |
461 |
|
This is expected behavior, but the reported volume of the convex |
462 |
|
hull includes large regions of empty space. For this reason, |
463 |
< |
compressibilities should be computed using local number densities |
464 |
< |
rather than hull volumes.} |
463 |
> |
compressibilities are computed using local number densities rather |
464 |
> |
than hull volumes.} |
465 |
|
\label{fig:coneOfShame} |
466 |
|
\end{figure} |
467 |
|
|