| 322 |
|
$P_2$ order paramter of the dipoles on head group rising with |
| 323 |
|
increasing head group size. When the heads of the lipid molecules are |
| 324 |
|
small, the membrane is flat. The dipolar ordering is essentially |
| 325 |
< |
frustrated on orientational ordering in this circumstance. Another |
| 326 |
< |
reason is that the lipids can move independently in each monolayer, it |
| 327 |
< |
is not nessasory for the direction of dipoles on one leaf is |
| 328 |
< |
consistant to another layer, which makes total order parameter is |
| 329 |
< |
relatively low. With increasing head group size, the surface is |
| 330 |
< |
corrugated, and dipoles do not move as freely on the |
| 325 |
> |
frustrated on orientational ordering in this circumstance. Figure |
| 326 |
> |
\ref{} shows the snapshots of the top view for the flat system |
| 327 |
> |
($\sigma_h=1.20\sigma$) and rippled system |
| 328 |
> |
($\sigma_h=1.41\sigma$). The pointing direction of the dipoles on the |
| 329 |
> |
head groups are represented by two colored half spheres from blue to |
| 330 |
> |
yellow. For flat surfaces, the system obviously shows frustration on |
| 331 |
> |
the dipolar ordering, there are kinks on the edge of defferent |
| 332 |
> |
domains. Another reason is that the lipids can move independently in |
| 333 |
> |
each monolayer, it is not nessasory for the direction of dipoles on |
| 334 |
> |
one leaf is consistant to another layer, which makes total order |
| 335 |
> |
parameter is relatively low. With increasing head group size, the |
| 336 |
> |
surface is corrugated, and dipoles do not move as freely on the |
| 337 |
|
surface. Therefore, the translational freedom of lipids in one layer |
| 338 |
|
is dependent upon the position of lipids in another layer, as a |
| 339 |
|
result, the symmetry of the dipoles on head group in one layer is tied |
| 344 |
|
and the order parameter increases dramaticaly. However, the total |
| 345 |
|
polarization of the system is still close to zero. This is strong |
| 346 |
|
evidence that the corrugated structure is an antiferroelectric |
| 347 |
< |
state. The orientation of the dipolar is always perpendicular to the |
| 348 |
< |
ripple wave vector. These results are consistent with our previous |
| 349 |
< |
study on dipolar membranes. |
| 347 |
> |
state. From the snapshot in Figure \ref{}, the dipoles arrange as |
| 348 |
> |
arrays along $Y$ axis and fall into head-to-tail configuration in each |
| 349 |
> |
line, but every $3$ or $4$ lines of dipoles change their direction |
| 350 |
> |
from neighbour lines. The system shows antiferroelectric |
| 351 |
> |
charactoristic as a whole. The orientation of the dipolar is always |
| 352 |
> |
perpendicular to the ripple wave vector. These results are consistent |
| 353 |
> |
with our previous study on dipolar membranes. |
| 354 |
|
|
| 355 |
|
The ordering of the tails is essentially opposite to the ordering of |
| 356 |
|
the dipoles on head group. The $P_2$ order parameter decreases with |
