NOTE ON THE THEORY OF THE SIZES AND SHAPES OF LIPID DOMAINS IN MONOLAYERS

A detailed analysis is given for the application of Green's theorem to the calculation of the dipolar electrostatic energies of lipid domains at the air-water interface. This theorem enables an area integration of a r-3 dipole-dipole interaction to be represented by a double line integral involving r-1, substantially simplifying the calculation of the electrostatic energy. When a cutoff DELTA is introduced in the expression for the dipole-dipole interaction so as to avoid the divergence at r = 0, a multipole collection term needs to be included in the Green's theorem formulation of the electrostatic energy. The present work provides an exact expression for this correction term and shows that it scales like a line tension energy, independent of DELTA when DELTA is small compared to the dimensions of the domain. For two liquid phases this electrostatic contribution to the line tension is simply -mu-2, where mu is the difference in the dipole density in two adjoining phases.