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