| 95 |
|
|
| 96 |
|
In a recent paper, we presented a simple ``web of dipoles'' spin |
| 97 |
|
lattice model which provides some physical insight into relationship |
| 98 |
< |
between dipolar ordering and membrane buckling.\cite{Sun2007} We found |
| 99 |
< |
that dipolar elastic membranes can spontaneously buckle, forming |
| 98 |
> |
between dipolar ordering and membrane buckling.\cite{sun:031602} We |
| 99 |
> |
found that dipolar elastic membranes can spontaneously buckle, forming |
| 100 |
|
ripple-like topologies. The driving force for the buckling of dipolar |
| 101 |
|
elastic membranes is the anti-ferroelectric ordering of the dipoles. |
| 102 |
|
This was evident in the ordering of the dipole director axis |
| 156 |
|
modeling large length-scale properties of lipid |
| 157 |
|
bilayers.\cite{Ayton01} In its original form, the Gay-Berne potential |
| 158 |
|
was a single site model for the interactions of rigid ellipsoidal |
| 159 |
< |
molecules.\cite{Gay81} It can be thought of as a modification of the |
| 159 |
> |
molecules.\cite{Gay1981} It can be thought of as a modification of the |
| 160 |
|
Gaussian overlap model originally described by Berne and |
| 161 |
|
Pechukas.\cite{Berne72} The potential is constructed in the familiar |
| 162 |
|
form of the Lennard-Jones function using orientation-dependent |
| 270 |
|
\end{figure} |
| 271 |
|
|
| 272 |
|
To take into account the permanent dipolar interactions of the |
| 273 |
< |
zwitterionic head groups, we have placed fixed dipole moments $\mu_{i}$ at |
| 274 |
< |
one end of the Gay-Berne particles. The dipoles are oriented at an |
| 275 |
< |
angle $\theta = \pi / 2$ relative to the major axis. These dipoles |
| 276 |
< |
are protected by a head ``bead'' with a range parameter ($\sigma_h$) which we have |
| 277 |
< |
varied between $1.20 d$ and $1.41 d$. The head groups interact with |
| 278 |
< |
each other using a combination of Lennard-Jones, |
| 273 |
> |
zwitterionic head groups, we have placed fixed dipole moments |
| 274 |
> |
$\mu_{i}$ at one end of the Gay-Berne particles. The dipoles are |
| 275 |
> |
oriented at an angle $\theta = \pi / 2$ relative to the major axis. |
| 276 |
> |
These dipoles are protected by a head ``bead'' with a range parameter |
| 277 |
> |
($\sigma_h$) which we have varied between $1.20 d$ and $1.41 d$. The |
| 278 |
> |
head groups interact with each other using a combination of |
| 279 |
> |
Lennard-Jones, |
| 280 |
|
\begin{equation} |
| 281 |
|
V_{ij}(r_{ij}) = 4\epsilon_h \left[\left(\frac{\sigma_h}{r_{ij}}\right)^{12} - |
| 282 |
|
\left(\frac{\sigma_h}{r_{ij}}\right)^6\right], |
| 325 |
|
|
| 326 |
|
The solvent model in our simulations is similar to the one used by |
| 327 |
|
Marrink {\it et al.} in their coarse grained simulations of lipid |
| 328 |
< |
bilayers.\cite{Marrink04} The solvent bead is a single site that |
| 328 |
> |
bilayers.\cite{Marrink2004} The solvent bead is a single site that |
| 329 |
|
represents four water molecules (m = 72 amu) and has comparable |
| 330 |
|
density and diffusive behavior to liquid water. However, since there |
| 331 |
|
are no electrostatic sites on these beads, this solvent model cannot |
| 332 |
|
replicate the dielectric properties of water. Note that although we |
| 333 |
|
are using larger cutoff and switching radii than Marrink {\it et al.}, |
| 334 |
|
our solvent density at 300 K remains at 0.944 g cm$^{-3}$, and the |
| 335 |
< |
solvent diffuses at 0.43 $\AA^2 ps^{-1}$ (only twice as fast as liquid |
| 335 |
> |
solvent diffuses at 0.43 \AA$^2 ps^{-1}$ (only twice as fast as liquid |
| 336 |
|
water). |
| 337 |
|
|
| 338 |
|
\begin{table*} |
| 403 |
|
molecular dynamics runs was 25 fs. No appreciable changes in phase |
| 404 |
|
structure were noticed upon switching to a microcanonical ensemble. |
| 405 |
|
All simulations were performed using the {\sc oopse} molecular |
| 406 |
< |
modeling program.\cite{Meineke05} |
| 406 |
> |
modeling program.\cite{Meineke2005} |
| 407 |
|
|
| 408 |
|
A switching function was applied to all potentials to smoothly turn |
| 409 |
|
off the interactions between a range of $22$ and $25$ \AA. The |
| 593 |
|
arrangement of the dipoles is always observed in a direction |
| 594 |
|
perpendicular to the wave vector for the surface corrugation. This is |
| 595 |
|
a similar finding to what we observed in our earlier work on the |
| 596 |
< |
elastic dipolar membranes.\cite{Sun2007} |
| 596 |
> |
elastic dipolar membranes.\cite{sun:031602} |
| 597 |
|
|
| 598 |
|
The $P_2$ order parameters (for both the molecular bodies and the head |
| 599 |
|
group dipoles) have been calculated to quantify the ordering in these |
