Micellar growth, network formation, and criticality in aqueous solutions of the nonionic surfactant C₁₂E₅

We used cryo-TEM and light scattering to study the micellar growth and subsequent network formation in aqueous solutions of the nonionic surfactant C₁₂E₅. Cryo-TEM shows the first direct evidence for the existence of connected topology in the vicinity of the critical point and the two-phase separation curve of the C₁₂E₅/water micellar system. The coexisting phases within the two-phase region consist of one concentrated and one dilute network of interconnected cylindrical micelles. These findings are consistent with the recent theoretical explanation of criticality and phase separation in certain nonionic surfactant systems as resulting from entropic attraction between network junctions. Away from the two-phase separation curve, we have identified uniaxial micellar growth, with increasing temperature and concentration, into long the threadlike micelles. From the power-law dependence of the radius of gyration, R_G,z, and the hydrodynamic diameter, D_H, on the molecular weight (R_G,z, D̄_H approx. M_w^v), we find that these threadlike micelles have properties resembling those of flexible polymers in a good solvent (v approx. 0.6). Static and dynamic light scattering show that the mean micelle contour length increases as c^0.5 (c is the surfactant concentration) in agreement with theory. Finally, we show that the end-cap energy E_c increases linearly with temperature.