--- trunk/nanoglass/experimental.tex	2007/09/25 19:23:21	3230
+++ trunk/nanoglass/experimental.tex	2007/09/27 18:45:55	3233
@@ -7,10 +7,10 @@ $\mathrm{Ag}_6\mathrm{Cu}_4$.  All three compositions 
 
 Cu-core / Ag-shell and random alloy structures were constructed on an
 underlying FCC lattice (4.09 {\AA}) at the bulk eutectic composition
-$\mathrm{Ag}_6\mathrm{Cu}_4$.  All three compositions were considered
+$\mathrm{Ag}_6\mathrm{Cu}_4$.  Both initial geometries were considered
 although experimental results suggest that the random structure is the
-most likely composition after
-synthesis.\cite{Jiang:2005lr,gonzalo:5163}  Three different sizes of
+most likely structure to be found following
+synthesis.\cite{Jiang:2005lr,gonzalo:5163} Three different sizes of
 nanoparticles corresponding to a 20 \AA radius (1961 atoms), 30 {\AA}
 radius (6603 atoms) and 40 {\AA} radius (15683 atoms) were
 constructed.  These initial structures were relaxed to their
@@ -34,25 +34,33 @@ the nanoparticle evolved under Langevin Dynamics with 
 To approximate the effects of rapid heat transfer to the solvent
 following a heating at the plasmon resonance, we utilized a
 methodology in which atoms contained in the outer $4$ {\AA} radius of
-the nanoparticle evolved under Langevin Dynamics with a solvent
-friction approximating the contribution from the solvent and capping
-agent.  Atoms located in the interior of the nanoparticle evolved
-under Newtonian dynamics.  The set-up of our simulations is nearly
-identical with the ``stochastic boundary molecular dynamics'' ({\sc
-sbmd}) method that has seen wide use in the protein simulation
+the nanoparticle evolved under Langevin Dynamics,
+\begin{equation}
+m \frac{\partial^2 \vec{x}}{\partial t^2} = F_\textrm{sys}(\vec{x}(t))
+- 6 \pi a \eta \vec{v}(t)  + F_\textrm{ran}
+\label{eq:langevin}
+\end{equation}
+with a solvent friction ($\eta$) approximating the contribution from
+the solvent and capping agent.  Atoms located in the interior of the
+nanoparticle evolved under Newtonian dynamics.  The set-up of our
+simulations is nearly identical with the ``stochastic boundary
+molecular dynamics'' ({\sc sbmd}) method that has seen wide use in the
+protein simulation
 community.\cite{BROOKS:1985kx,BROOKS:1983uq,BRUNGER:1984fj} A sketch
-of this setup can be found in Fig. \ref{fig:langevinSketch}.  For a
-spherical atom of radius $a$, the Langevin frictional forces can be
-determined by Stokes' law
-\begin{equation} 
-\mathbf{F}_{\mathrm{frictional}}=6\pi a \eta \mathbf{v}
+of this setup can be found in Fig. \ref{fig:langevinSketch}.  In
+equation \ref{eq:langevin} the frictional forces of a spherical atom
+of radius $a$ depend on the solvent viscosity.  The random forces are
+usually taken as gaussian random variables with zero mean and a
+variance tied to the solvent viscosity and temperature,
+\begin{equation}
+\langle F_\textrm{ran}(t) \cdot F_\textrm{ran} (t')
+\rangle = 2 k_B T (6 \pi \eta a) \delta(t - t')
+\label{eq:stochastic}
 \end{equation}
-where $\eta$ is the effective viscosity of the solvent in which the
-particle is embedded.  Due to the presence of the capping agent and
-the lack of details about the atomic-scale interactions between the
-metallic atoms and the solvent, the effective viscosity is a
-essentially a free parameter that must be tuned to give experimentally
-relevant simulations.
+Due to the presence of the capping agent and the lack of details about
+the atomic-scale interactions between the metallic atoms and the
+solvent, the effective viscosity is a essentially a free parameter
+that must be tuned to give experimentally relevant simulations.
 \begin{figure}[htbp]
 \centering
 \includegraphics[width=\linewidth]{images/stochbound.pdf}
@@ -246,3 +254,12 @@ structural features associated with bulk glass formati
 \end{figure}
 
 
+\begin{figure}[htbp]
+\centering
+\includegraphics[width=\linewidth]{images/cross_section_array.jpg}
+\caption{Cutaway views of 30 \AA\ Ag-Cu nanoparticle structures for
+random alloy (top) and Cu (core) / Ag (shell) initial conditions
+(bottom).  Shown from left to right are the crystalline, liquid
+droplet, and final glassy bead configurations.}
+\label{fig:q6}
+\end{figure}
