Self-assembling networks occur in diverse colloidal systems including cylindrical micelles and microemulsions, ferrofluids, and polymer-colloid assemblies. Although the microscopic nature of these systems can be quite different, the statistical thermodynamics and phase behavior can be quite similar. In particular, we show theoretically that such networks generally exhibit phase coexistence between dilute and dense network phases; these transitions are driven by the competition of the translational entropy (that dominates in the dilute phases) and the configurational entropy (that dominates in the dense network phases). The predictions are in agreement with both structural and thermodynamic studies. Recently, we have focused on the immunity of networks comprising (several) telechelic polymers that connect oil in water microemulsion drops. The dense network phase of this system has higher immunity if it survives a random degradation of polymers, that is, if the network is more likely to maintain a macroscopic connected component. We predict that gel immunity decreases with an increase of the variance of the distribution of the number of polymers that connect a given pair of drops. Repulsive interactions between the polymers decrease the variance, while attractive interactions increase the variance.

*Work done in collaboration with: G. Hed, T. Tlusty, A. Zilman - theory; A. Bernheim, T. Foster, G. Porte, T. Sottmann, R. Strey, Y. Talmon - experiment.