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%% The Model |
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\section{Model} |
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\label{sec:model} |
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Two different particle types were investigated in this simulation. The |
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first was an octopus particle type, and the second, a tilted umbrella |
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particle. The octopus particle type can be seen in Fig. \ref{fig:octopi}. |
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This particle was modeled to be a flat circle of fixed radius, $\sigma$, |
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with eight equally spaced ``legs'' around the perimeter, each of length, |
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{\em l}. |
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The second particle type can be seen in Fig. \ref{fig:t_umbrella}. This |
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particle type is called the tilted umbrella. The tilted umbrella is |
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specified by a disc of radius, $\sigma$, a central ``handle'' of length, |
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{\em l}, and a surface normal, $\hat{n}$. In the simulation the angle, |
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$\theta$, |
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between the plane of the disc and the handle was fixed to be $104.5^{\circ}$. |
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Each particle was also assigned a random angle, $\phi$. This corresponded |
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to the angle between the projection of $\hat{n}$ onto the xy plane and |
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the y axis. |
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For each particle type, two different simulation methods were employed. One |
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was a continuos RSA simulation, and the other, a RSA simmulation on a lattice. |
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In the continous case, particles could attach anywhere on the surface. For |
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the lattice RSA simulation, an underlying gold hexagonal closed packed, hcp, |
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lattice was employed. This simulation more closely modeled the experimental |
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research of Lieberman {\em et. al.}\cite{Lieberman01}, where the particles |
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were attaced to a gold (100) surface. The sites where the particles were |
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allowed to attach were taken to be the gaps beteen three gold atoms, as |
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illustrated in Fig. \ref{fig:hcp_lattice}. |
