matt_papers/RSA/model.tex

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%% The Model
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\section{Model}
\label{sec:model}

Two different particle types were investigated in this simulation. The 
first was an octopus particle type, and the second, a tilted umbrella
particle. The octopus particle type can be seen in Fig. \ref{fig:octopi}.
This particle was modeled to be a flat circle of fixed radius, $\sigma$,
with eight equally spaced ``legs'' around the perimeter, each of length, 
{\em l}.

The second particle type can be seen in Fig. \ref{fig:t_umbrella}. This
particle type is called the tilted umbrella. The tilted umbrella is
specified by a disc of radius, $\sigma$, a central ``handle'' of length, 
{\em l}, and a surface normal, $\hat{n}$. In the simulation the angle,
 $\theta$,
between the plane of the disc and the handle was fixed to be $104.5^{\circ}$.
Each particle was also assigned a random angle, $\phi$. This corresponded
to the angle between the projection of $\hat{n}$ onto the xy plane and 
the y axis.

For each particle type, two different simulation methods were employed. One
was a continuos RSA simulation, and the other, a RSA simmulation on a lattice.
In the continous case, particles could attach anywhere on the surface. For
the lattice RSA simulation, an underlying gold hexagonal closed packed, hcp,
lattice was employed. This simulation more closely modeled the experimental
research of Lieberman {\em et. al.}\cite{Lieberman01}, where the particles 
were attaced to a gold (100) surface. The sites where the particles were
allowed to attach were taken to be the gaps beteen three gold atoms, as 
illustrated in Fig. \ref{fig:hcp_lattice}.
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#	User	Rev	Content
1	mmeineke	56	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2			%% The Model
3			%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4
5			\section{Model}
6			\label{sec:model}
7
8			Two different particle types were investigated in this simulation. The
9			first was an octopus particle type, and the second, a tilted umbrella
10			particle. The octopus particle type can be seen in Fig. \ref{fig:octopi}.
11			This particle was modeled to be a flat circle of fixed radius, $\sigma$,
12			with eight equally spaced ``legs'' around the perimeter, each of length,
13			{\em l}.
14
15			The second particle type can be seen in Fig. \ref{fig:t_umbrella}. This
16			particle type is called the tilted umbrella. The tilted umbrella is
17			specified by a disc of radius, $\sigma$, a central ``handle'' of length,
18			{\em l}, and a surface normal, $\hat{n}$. In the simulation the angle,
19			$\theta$,
20			between the plane of the disc and the handle was fixed to be $104.5^{\circ}$.
21			Each particle was also assigned a random angle, $\phi$. This corresponded
22			to the angle between the projection of $\hat{n}$ onto the xy plane and
23			the y axis.
24
25			For each particle type, two different simulation methods were employed. One
26			was a continuos RSA simulation, and the other, a RSA simmulation on a lattice.
27			In the continous case, particles could attach anywhere on the surface. For
28			the lattice RSA simulation, an underlying gold hexagonal closed packed, hcp,
29			lattice was employed. This simulation more closely modeled the experimental
30			research of Lieberman {\em et. al.}\cite{Lieberman01}, where the particles
31			were attaced to a gold (100) surface. The sites where the particles were
32			allowed to attach were taken to be the gaps beteen three gold atoms, as
33			illustrated in Fig. \ref{fig:hcp_lattice}.