THEORY OF SHAPE TRANSITIONS OF 2-DIMENSIONAL DOMAINS

A theory is presented to describe the instability in the circular shape of a two-dimensional domain of particles that experience repulsive and surface tension forces. The treatment is motivated by and extends the work of H. M. McConnell (J. Phys. Chem. 1990, 94, 4728-473 1). We present exact results for the case where the repulsion arises from electrostatic dipole-dipole interaction. We show how to determine the critical radius R(n) at which the circular domain becomes unstable to harmonic perturbations in shape of order n. An analysis is given of the case of general repulsive interactions.