FIG. 12.

(A) An assembly state phase diagram for the amphiphillic aggregate model in eq. (44) for dimensionless stiffness $\overline{k}=1$ and $v_0^2/a_0^3=10$, where ϕ_* is the nominal CMC for cylinders. Solid lines mark the boundaries between the most populous aggregate type, and dashed lines indicate the boundaries in the infinite Φ limit. The inset shows a zoom in near the boundary between cylinders and bilayers, illustrating an extremely narrow window of secondary CMC behavior due to the large mean (finite) size of cylinders. (B) Summarizes the polymorphic assembly of the amphiphile model in the plane of stiffness $\overline{k}$ and inverse packing parameter P⁻¹, for $v_0^2/a_0^3=10$. Regimes of single CMC behavior are shown as solid red, white, and blue for bilayers, cylinders, and spheres, respectively. The regime of polymorphic concentration-driven sphere-to-spherocylinder transitions is colored on a blue-green scale according to the ratio of second CMC (spheres to spherocylinders) to the first CMC (monomers to spheres). (C-F) show cryo-transmission electron micrographs of micelles formed by dimeric (gemini) surfactancts, at 25° C at increasing weight percent: (C) 0.26%; (D) 0.5%; (E) 0.62%; and (F) 0.74% (scale bars equal 100 nm). The coexistence of cylindrical micelles of increasing total length for (D-F), and absence of lengths intermediate to spheres and the shortest cylinders is consistent with a concentration-dependent second-CMC. The inset of (F) shows the bulbous ends of a cylindrical micelle (scale bar, 25 nm), consistent with an energy barrier between spherical and (long) cylinders due to a mismatch in preferred radius. (C-F) are adapted from (Bernheim-Groswasser et al., 2000).