| 7 |
|
|
| 8 |
|
Cu-core / Ag-shell and random alloy structures were constructed on an |
| 9 |
|
underlying FCC lattice (4.09 {\AA}) at the bulk eutectic composition |
| 10 |
< |
$\mathrm{Ag}_6\mathrm{Cu}_4$. All three compositions were considered |
| 10 |
> |
$\mathrm{Ag}_6\mathrm{Cu}_4$. Both initial geometries were considered |
| 11 |
|
although experimental results suggest that the random structure is the |
| 12 |
< |
most likely composition after |
| 13 |
< |
synthesis.\cite{Jiang:2005lr,gonzalo:5163} Three different sizes of |
| 12 |
> |
most likely structure to be found following |
| 13 |
> |
synthesis.\cite{Jiang:2005lr,gonzalo:5163} Three different sizes of |
| 14 |
|
nanoparticles corresponding to a 20 \AA radius (1961 atoms), 30 {\AA} |
| 15 |
|
radius (6603 atoms) and 40 {\AA} radius (15683 atoms) were |
| 16 |
|
constructed. These initial structures were relaxed to their |
| 34 |
|
To approximate the effects of rapid heat transfer to the solvent |
| 35 |
|
following a heating at the plasmon resonance, we utilized a |
| 36 |
|
methodology in which atoms contained in the outer $4$ {\AA} radius of |
| 37 |
< |
the nanoparticle evolved under Langevin Dynamics with a solvent |
| 38 |
< |
friction approximating the contribution from the solvent and capping |
| 39 |
< |
agent. Atoms located in the interior of the nanoparticle evolved |
| 40 |
< |
under Newtonian dynamics. The set-up of our simulations is nearly |
| 41 |
< |
identical with the ``stochastic boundary molecular dynamics'' ({\sc |
| 42 |
< |
sbmd}) method that has seen wide use in the protein simulation |
| 37 |
> |
the nanoparticle evolved under Langevin Dynamics, |
| 38 |
> |
\begin{equation} |
| 39 |
> |
m \frac{\partial^2 \vec{x}}{\partial t^2} = F_\textrm{sys}(\vec{x}(t)) |
| 40 |
> |
- 6 \pi a \eta \vec{v}(t) + F_\textrm{ran} |
| 41 |
> |
\label{eq:langevin} |
| 42 |
> |
\end{equation} |
| 43 |
> |
with a solvent friction ($\eta$) approximating the contribution from |
| 44 |
> |
the solvent and capping agent. Atoms located in the interior of the |
| 45 |
> |
nanoparticle evolved under Newtonian dynamics. The set-up of our |
| 46 |
> |
simulations is nearly identical with the ``stochastic boundary |
| 47 |
> |
molecular dynamics'' ({\sc sbmd}) method that has seen wide use in the |
| 48 |
> |
protein simulation |
| 49 |
|
community.\cite{BROOKS:1985kx,BROOKS:1983uq,BRUNGER:1984fj} A sketch |
| 50 |
< |
of this setup can be found in Fig. \ref{fig:langevinSketch}. For a |
| 51 |
< |
spherical atom of radius $a$, the Langevin frictional forces can be |
| 52 |
< |
determined by Stokes' law |
| 53 |
< |
\begin{equation} |
| 54 |
< |
\mathbf{F}_{\mathrm{frictional}}=6\pi a \eta \mathbf{v} |
| 50 |
> |
of this setup can be found in Fig. \ref{fig:langevinSketch}. In |
| 51 |
> |
equation \ref{eq:langevin} the frictional forces of a spherical atom |
| 52 |
> |
of radius $a$ depend on the solvent viscosity. The random forces are |
| 53 |
> |
usually taken as gaussian random variables with zero mean and a |
| 54 |
> |
variance tied to the solvent viscosity and temperature, |
| 55 |
> |
\begin{equation} |
| 56 |
> |
\langle F_\textrm{ran}(t) \cdot F_\textrm{ran} (t') |
| 57 |
> |
\rangle = 2 k_B T (6 \pi \eta a) \delta(t - t') |
| 58 |
> |
\label{eq:stochastic} |
| 59 |
|
\end{equation} |
| 60 |
< |
where $\eta$ is the effective viscosity of the solvent in which the |
| 61 |
< |
particle is embedded. Due to the presence of the capping agent and |
| 62 |
< |
the lack of details about the atomic-scale interactions between the |
| 63 |
< |
metallic atoms and the solvent, the effective viscosity is a |
| 54 |
< |
essentially a free parameter that must be tuned to give experimentally |
| 55 |
< |
relevant simulations. |
| 60 |
> |
Due to the presence of the capping agent and the lack of details about |
| 61 |
> |
the atomic-scale interactions between the metallic atoms and the |
| 62 |
> |
solvent, the effective viscosity is a essentially a free parameter |
| 63 |
> |
that must be tuned to give experimentally relevant simulations. |
| 64 |
|
\begin{figure}[htbp] |
| 65 |
|
\centering |
| 66 |
|
\includegraphics[width=\linewidth]{images/stochbound.pdf} |
| 254 |
|
\end{figure} |
| 255 |
|
|
| 256 |
|
|
| 257 |
+ |
\begin{figure}[htbp] |
| 258 |
+ |
\centering |
| 259 |
+ |
\includegraphics[width=\linewidth]{images/cross_section_array.jpg} |
| 260 |
+ |
\caption{Cutaway views of 30 \AA\ Ag-Cu nanoparticle structures for |
| 261 |
+ |
random alloy (top) and Cu (core) / Ag (shell) initial conditions |
| 262 |
+ |
(bottom). Shown from left to right are the crystalline, liquid |
| 263 |
+ |
droplet, and final glassy bead configurations.} |
| 264 |
+ |
\label{fig:q6} |
| 265 |
+ |
\end{figure} |
