Lipid membranes with free edges
arXiv:cond-mat/0305700 · doi:10.1103/PhysRevE.68.061915
Abstract
Lipid membrane with freely exposed edge is regarded as smooth surface with curved boundary. Exterior differential forms are introduced to describe the surface and the boundary curve. The total free energy is defined as the sum of Helfrich's free energy and the surface and line tension energy. The equilibrium equation and boundary conditions of the membrane are derived by taking the variation of the total free energy. These equations can also be applied to the membrane with several freely exposed edges. Analytical and numerical solutions to these equations are obtained under the axisymmetric condition. The numerical results can be used to explain recent experimental results obtained by Saitoh \emph{et al}. [Proc. Natl. Acad. Sci. \textbf{95}, 1026 (1998)].
15 pages, 6 figures
References in corpus (2)
Cited by in corpus (24)
- Geometric theory on the elasticity of bio-membranes
- Cylindrical equilibrium shapes of fluid membranes
- Environmental bias and elastic curves on surfaces
- Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model
- Dynamics of Vesicle Formation from Lipid Droplet: Mechanism and Controllability
- Concise theory of chiral lipid membranes
- Compatibility between shape equation and boundary conditions of lipid membranes with free edges
- Challenges in theoretical investigations on configurations of lipid membranes
- Convergence of an approximation for rotationally symmetric two-phase lipid bilayer membranes
- Kinks in two-phase lipid bilayer membranes
- Free energy of the edge of an open lipid bilayer based on the interactions of its constituent molecules
- Stable approximations for axisymmetric Willmore flow for closed and open surfaces
- Elasticity of polymer vesicles by osmotic pressure: an intermediate theory between fluid membranes and solid shells
- General neck condition for the limit shape of budding vesicles
- mKdV Surfaces
- Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries
- Periodic-cylinder vesicle with minimal energy
- Deformation and orientational order of chiral membranes with free edges
- Moving frames applied to shell elasticity
- Shapes of fluid membranes with chiral edges
- Boundary behaviours of open vesicles in axisymmetric case
- Functionals on Closed 2-Surfaces
- On p-Willmore Disks with Boundary Energies
- Modelling and Simulations of Multi-component Lipid Membranes and Open Membranes via Diffusive Interface Approaches