| 166 |
|
$\frac{{d^2 }}{4}$ inside the square root of the denominator is |
| 167 |
|
neglected. This is a reasonable approximation in most cases. |
| 168 |
|
Unfortunately, in our headgroup model, the distance of charge |
| 169 |
< |
separation $d$ (4.63 $\AA$ in PC headgroup) may be comparable to |
| 170 |
< |
$r$. Nevertheless, we could still assume $ \cos \theta \approx 0$ |
| 171 |
< |
in the central region of the headgroup. Using Taylor expansion and |
| 169 |
> |
separation $d$ (4.63 \AA in PC headgroup) may be comparable to $r$. |
| 170 |
> |
Nevertheless, we could still assume $ \cos \theta \approx 0$ in |
| 171 |
> |
the central region of the headgroup. Using Taylor expansion and |
| 172 |
|
associating appropriate terms with electric moments will result in a |
| 173 |
|
"split-dipole" approximation: |
| 174 |
|
\[ |
| 238 |
|
\end{equation} |
| 239 |
|
|
| 240 |
|
From Fig.~\ref{lipidFigure:PCFAtom}, we can identify the first |
| 241 |
< |
solvation shell (3.5 $\AA$) and the second solvation shell (5.0 |
| 242 |
< |
$\AA$) from both plots. However, the corresponding orientations are |
| 241 |
> |
solvation shell (3.5 \AA) and the second solvation shell (5.0 \AA) |
| 242 |
> |
from both plots. However, the corresponding orientations are |
| 243 |
|
different. In DLPE, water molecules prefer to sit around $\text{{\sc |
| 244 |
|
NH}}_3$ group due to the hydrogen bonding. In contrast, because of |
| 245 |
|
the hydrophobic effect of the $ {\rm{N(CH}}_{\rm{3}} |
| 360 |
|
electron density is in the hydrocarbon region. As a good |
| 361 |
|
approximation to the thickness of the bilayer, the headgroup spacing |
| 362 |
|
, is defined as the distance between two peaks in the electron |
| 363 |
< |
density profile, calculated from our simulations to be 34.1 $\AA$. |
| 363 |
> |
density profile, calculated from our simulations to be 34.1 \AA. |
| 364 |
|
This value is close to the x-ray diffraction experimental value 34.4 |
| 365 |
< |
$\AA$\cite{Petrache1998}. |
| 365 |
> |
\AA\cite{Petrache1998}. |
| 366 |
|
|
| 367 |
|
\begin{figure} |
| 368 |
|
\centering |
