Microemulsion networks: the onset of bicontinuity

We predict theoretically the gradual formation of fluctuating, connected mi croemulsion networks from disconnected cylinders as the spontaneous curvatu re and the radius are varied, in agreement with recent direct measurements of these topological transitions. We discuss the rob of the topological def ects, the network junction and the end-cap of the disconnected cylinders, i n the connectivity transition. The optimal shapes and curvature energies of the junctions and end-caps are calculated numerically and compared with an alytic approximations.