| 734 |
|
($\mu$).\label{fig:phaseDiagram}} |
| 735 |
|
\end{figure} |
| 736 |
|
|
| 737 |
+ |
We have computed translational diffusion coefficients for lipid |
| 738 |
+ |
molecules from the mean square displacement, |
| 739 |
+ |
\begin{eqnarray} |
| 740 |
+ |
\langle {|\left({\bf r}_{i}(t) - {\bt r}_{i}(0) \right)|}^2 \rangle \\ \\ |
| 741 |
+ |
& = & 6Dt |
| 742 |
+ |
\end{eqnarray} |
| 743 |
+ |
of the lipid bodies. The values of the translational diffusion |
| 744 |
+ |
coefficient for different head-to-tail size ratio are shown in table |
| 745 |
+ |
\ref{tab:relaxation}. |
| 746 |
|
|
| 747 |
|
We have also computed orientational diffusion constants for the head |
| 748 |
|
groups from the relaxation of the second-order Legendre polynomial |
| 766 |
|
\begin{minipage}{\linewidth} |
| 767 |
|
\begin{center} |
| 768 |
|
\caption{Rotational diffusion constants for the head groups |
| 769 |
< |
($\theta_h$) and molecular bodies ($\theta_b$) as a function of the |
| 770 |
< |
head-to-body width ratio. The orientational mobility of the head |
| 769 |
> |
($\theta_h$) and molecular bodies ($\theta_b$) as well as the |
| 770 |
> |
translational diffusion coefficients for the molecule as a function of |
| 771 |
> |
the head-to-body width ratio. The orientational mobility of the head |
| 772 |
|
groups experiences an {\it order of magnitude decrease} upon entering |
| 773 |
|
the rippled phase, which suggests that the rippling is tied to a |
| 774 |
|
freezing out of head group orientational freedom. Uncertainties in |
| 775 |
|
the last digit are indicated by the values in parentheses.} |
| 776 |
< |
\begin{tabular}{lcc} |
| 776 |
> |
\begin{tabular}{lccc} |
| 777 |
|
\hline |
| 778 |
< |
$\sigma_h / d$ & $\theta_h (\mu s^{-1})$ & $\theta_b (1/fs)$ \\ |
| 778 |
> |
$\sigma_h / d$ & $\theta_h (\mu s^{-1})$ & $\theta_b (1/fs)$ & $D ( |
| 779 |
> |
\times 10^{-11} m^2 s^{-1} \\ |
| 780 |
|
\hline |
| 781 |
< |
1.20 & $0.206(1) $ & $0.0175(5) $ \\ |
| 782 |
< |
1.28 & $0.179(2) $ & $0.055(2) $ \\ |
| 783 |
< |
1.35 & $0.025(1) $ & $0.195(3) $ \\ |
| 784 |
< |
1.41 & $0.023(1) $ & $0.024(3) $ \\ |
| 781 |
> |
1.20 & $0.206(1) $ & $0.0175(5) $ & $0.43(1)$ \\ |
| 782 |
> |
1.28 & $0.179(2) $ & $0.055(2) $ & $5.91(3)$ \\ |
| 783 |
> |
1.35 & $0.025(1) $ & $0.195(3) $ & $3.42(1)$ \\ |
| 784 |
> |
1.41 & $0.023(1) $ & $0.024(3) $ & $7.16(1)$ \\ |
| 785 |
|
\end{tabular} |
| 786 |
|
\label{tab:relaxation} |
| 787 |
|
\end{center} |
