Theoretical and numerical investigations on shapes of planar lipid monolayer domains

Shapes of planar lipid monolayer domains at the air-water interface are theoretically and
Shapes of planar lipid monolayer domains at the air-water interface are theoretically and numerically investigated by minimizing the formation energy of the domains, which consist of
the surface energy, line tension energy, and dipole electrostatic energy. The shape
equation, which describes boundary curves of the domains at equilibrium state, is derived
from the first order variation of the formation energy. A relaxation method is proposed to find
the numerical solutions of the shape equation. The theoretical and numerical results are in
good agreement with previous experimental observation. Some new shapes not observed in
previous experiments are also obtained, which awaits experimental confirmation in the
future.