Stability analysis of three-dimensional colloidal domains: quadratic fluctuations

Three-dimensional domain patterns can self-assemble in a charged colloidal suspension with competing short-range attraction and long-range Yukawa repulsion. Following the investigation of the ground-state domain shapes in our previous paper, we study the stability of isolated spherical, cylindrical, and lamellar domains with respect to shape fluctuations on boundaries. In the framework of the continuum model, we expand the free energy variation to quadratic terms under the constraint of constant volume. For the three shapes (sphere, cylinder, and lamella) discussed, domains with equilibrium sizes are stable with respect to shape fluctuations, and the stability of domains decreases as the spatial symmetry decreases.