18 |
|
|
19 |
|
\begin{document} |
20 |
|
|
21 |
< |
\title{Ripple Phase of the Lipid Bilayers: A Monte Carlo Simulation} |
21 |
> |
\title{Symmetry breaking and the Ripple phase} |
22 |
|
\author{Xiuquan Sun and J. Daniel Gezelter\footnote{Corresponding author. Email: gezelter@nd.edu} \\ |
23 |
|
Department of Chemistry and Biochemistry \\ |
24 |
|
University of Notre Dame \\ |
29 |
|
\maketitle |
30 |
|
|
31 |
|
\begin{abstract} |
32 |
< |
The molecular explanation for the origin and properties of the ripple |
33 |
< |
phase is addressed in this paper. A model which contains the surface |
34 |
< |
tension and dipole-dipole interactions is used to describe the |
35 |
< |
potential for a monolayer of simple point dipoles. The simulations are |
36 |
< |
carried out using Monte Carlo method. It is shown asymmetry of the |
37 |
< |
translational freedom of the dipoles breaks the symmetry of the |
38 |
< |
hexagonal lattice and allow antiferroelectric ordering of the |
39 |
< |
dipoles. The existence of the ripples only depends on the dipolar |
40 |
< |
property of the system. The structure of the ripples is affected by |
41 |
< |
surface tension. Only close to the hexagonal lattice, can the ripple |
42 |
< |
phase be reached. Surface has the lowest transition temperature on |
43 |
< |
hexagonal lattice elucidates the reason of the existence of the ripple |
44 |
< |
phase in organism. A mechanism for the phase transition of the lipid |
45 |
< |
bilayer is proposed. |
32 |
> |
The ripple phase in phosphatidylcholine (PC) bilayers has never been |
33 |
> |
explained. Our group has developed some simple (XYZ) spin-lattice |
34 |
> |
models that allow spins to vary their elevation as well as their |
35 |
> |
orientation. The extra degree of freedom allows hexagonal lattices of |
36 |
> |
spins to find states that break out of the normally frustrated |
37 |
> |
randomized states and are stabilized by long-range anti-ferroelectric |
38 |
> |
ordering. To break out of the frustrated states, the spins must form |
39 |
> |
``rippled'' phases that make the lattices effectively non-hexagonal. Our |
40 |
> |
XYZ models contain surface tension and dipole-dipole interactions to |
41 |
> |
describe the interaction potential for monolayers and bilayers of |
42 |
> |
model lipid molecules. The existence of the ripples depends primarily |
43 |
> |
on the strength and lattice spacing of the dipoles, while the shape |
44 |
> |
(wavelength and amplitude) of the ripples is only weakly sensitive to |
45 |
> |
the applied surface tension. Additionally, the wave vector for the |
46 |
> |
ripple is always perpendicular to the director axis for the |
47 |
> |
dipoles. Non-hexagonal lattices of dipoles are not inherently |
48 |
> |
frustrated, and are therefore less likely to form ripple phases |
49 |
> |
because they can easily form low-energy anti-ferroelectric states. |
50 |
> |
Indeed, we see that the dipolar order-disorder transition is |
51 |
> |
substantially lower for hexagonal lattices and the ordered phase for |
52 |
> |
this lattice is clearly rippled. |
53 |
|
\end{abstract} |
54 |
|
|
55 |
|
\section{Introduction} |