| 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 |
|
|
