| 103 |
|
(4\%) initial rise in $\theta_{J}$ as a function of particle |
| 104 |
|
anisotropy. However, the jamming limit {\it decreases} with |
| 105 |
|
increasing particle anisotropy once the length-to-breadth ratio rises |
| 106 |
< |
above 2. I.e. ellipsoids landing randomly on a surface will, in |
| 106 |
> |
above 2, \emph{i.e.}~ellipsoids landing randomly on a surface will, in |
| 107 |
|
general, cover a smaller surface area than disks. Randomly thrown thin |
| 108 |
|
lines cover an even smaller area.\cite{Viot1992b} |
| 109 |
|
|
| 110 |
|
How, then, can one explain a near-monolayer coverage by the umbrella |
| 111 |
< |
molecules? There are really two approaches, one static and one |
| 112 |
< |
dynamic. In this paper, we present a static RSA model with {\em |
| 111 |
> |
molecules? In this paper, we present a static RSA model with {\em |
| 112 |
|
tilted} disks that allows near-monolayer coverage and which can |
| 113 |
|
explain the differences in coverage between the octopus and umbrella. |
| 114 |
|
In section \ref{rsaSec:model} we outline the model for the two adsorbing |
| 218 |
|
was then checked for intersection with both of the umbrella tops. If |
| 219 |
|
the line did indeed intersect the tops, then the points of |
| 220 |
|
intersection along the line were checked to insure sequential |
| 221 |
< |
intersection of the two tops. ie. The line most enter then leave the |
| 221 |
> |
intersection of the two tops. ie. The line must enter then leave the |
| 222 |
|
first top before it can enter and leave the second top. These series |
| 223 |
|
of tests were demanding of computational resources, and were therefore |
| 224 |
|
only attempted if the original handle - projection overlap test had |
| 231 |
|
|
| 232 |
|
For the on-lattice simulations, the initially chosen location on the |
| 233 |
|
plane was used to pick an attachment point from the underlying |
| 234 |
< |
lattice. I.e. if the initial position and orientation placed one of |
| 234 |
> |
lattice. Meaning, if the initial position and orientation placed one of |
| 235 |
|
the thiol legs within a small distance ($\epsilon = 0.1 \mbox{\AA}$) |
| 236 |
|
of one of the interstitial attachment points, the lander was moved so |
| 237 |
|
that the thiol leg was directly over the lattice point before checking |
| 273 |
|
larger gold surface. |
| 274 |
|
|
| 275 |
|
Once the system is constrained by the underlying lattice, $\theta_{J}$ |
| 276 |
< |
drops to 0.5378, showing that the lattice has an almost |
| 276 |
> |
drops to 0.5378, showing that the lattice has an |
| 277 |
|
inconsequential effect on the jamming limit. If the spacing between |
| 278 |
|
the interstitial sites were closer to the radius of the landing |
| 279 |
|
particles, we would expect a larger effect, but in this case, the |
