matt_papers/RSA/model.tex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% The Model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}.
Revision:	57
Committed:	Tue Jul 30 18:47:17 2002 UTC (23 years, 3 months ago) by mmeineke
Content type:	application/x-tex
File size:	1734 byte(s)
Log Message:	This commit was generated by cvs2svn to compensate for changes in r56, which included commits to RCS files with non-trunk default branches.
#	Content
1	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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}.