| 389 |
|
P_2(\cos(\theta)) = \left < \frac{1}{2} \left (3\cos^2(\theta) - 1 \right ) \right > |
| 390 |
|
\end{equation} |
| 391 |
|
|
| 392 |
< |
A ligand chain that is perpendicular to the particle surface has a P$_2$ value of 1, while a ligand chain lying flat on the nanoparticle surface has a P$_2$ value of $-0.25$. Disordered ligand layers will exhibit a mean P$_2$ value of 0. As shown in Figure \ref{fig:NPthiols_combo} the ligand P$_2$ value approaches 0 as ligand chain length -- and ligand flexibility -- increases. |
| 392 |
> |
A ligand chain that is perpendicular to the particle surface has a P$_2$ value of 1, while a ligand chain lying flat on the nanoparticle surface has a P$_2$ value of $-0.5$. Disordered ligand layers will exhibit a mean P$_2$ value of 0. As shown in Figure \ref{fig:NPthiols_combo} the ligand P$_2$ value approaches 0 as ligand chain length -- and ligand flexibility -- increases. |
| 393 |
|
|
| 394 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 395 |
|
% ORIENTATION OF INTERFACIAL SOLVENT |
