Shapes of lipid monolayer domains: Solutions using elliptic functions

Solid lipid monolayer domains surrounded by a fluid phase at an air-water interface exhibit complex shapes. These intriguing shapes can be understood in terms of a competition between line tension and long-range dipole-dipole interaction. The dipolar energy has recently been relevant to a negative l...

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Bibliographic Details
Published in:The European physical journal. E, Soft matter and biological physics Soft matter and biological physics, 2008-09, Vol.27 (1), p.81-86
Main Authors: Iwamoto, M., Liu, F., Ou-Yang, Z. C.
Format: Article
Language:English
Subjects:
Algorithms
Anisotropy
Biological and Medical Physics
Biophysics
Chemistry
Complex Fluids and Microfluidics
Complex Systems
Exact sciences and technology
Gas-liquid interface and liquid-liquid interface
Gases
General and physical chemistry
Lipid Bilayers - chemistry
Lipids - chemistry
Models, Statistical
Nanotechnology
Physics
Physics - methods
Physics and Astronomy
Polymer Sciences
Pressure
Soft and Granular Matter
Solutions
Surface physical chemistry
Surface Properties
Surfaces and Interfaces
Thermodynamics
Thin Films
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Summary:Solid lipid monolayer domains surrounded by a fluid phase at an air-water interface exhibit complex shapes. These intriguing shapes can be understood in terms of a competition between line tension and long-range dipole-dipole interaction. The dipolar energy has recently been relevant to a negative line tension and a positive curvature energy at the boundary, and a corresponding shape equation was derived by the variation of the approximated domain energy (Phys. Rev. Lett. 93 , 206101 (2004)). Here we further incorporate surface pressure into the shape equation and show that the equation can be analytically solved: the curvature of the domain boundary is exactly obtained as an elliptic function of arc-length. We find that a circular domain can grow into bean-and peach-like domains with pressure, i.e. , dipping and cuspidal transitions of circle by compression. The comparison with the experimental observation shows nice agreement.
ISSN:1292-8941
1292-895X
DOI:10.1140/epje/i2008-10354-y