We present a molecular-level theory for amphiphile packing in linear micelles, focusing on the early stages I Iof lnicellar elongation, i.e., on small and "intermediate-size" micelles, whose endcaps are not yet molded I into a final sha~.. The internal free energy of a micelle of given size and shape is expressed as an integral : over local molecular packing free energies in different regions of the micelle. The free energy per molecule I is expressed as a sum of interfacial ("opposing forces") and chain conformational contlibutions, both depending i on the local geometry; The equilibrium shape and energy of the micelle is determined by functional Imiriiinization of the total free energy.. For amphiphiles exhibiting strong preference for packing in the cylindrical geometry, we show that the early stages of growth involve an energetic barrier, resulting in a ?gap" in the micellar size distribution: That is, at low total aInphiphile concentrations only small (globular) micelles appear ins~lution. Their concentration reaches awell-definedsaturatioffvalue, beyond which, all added amphiphiles are incorporated in long micelles, whose "non-interacting" endcaps are well separated by the cylindrical , middle part. This, "second CMC" behavior is demonstrated by numerical calculations of micellar size disu.ibutions and average aggI:egation numbers as a function of the total concentration. The conditions necessary for the appearance of a second CMC are 'analyzed theoretically, with explicit reference to the underlying molecul3.rpackingcharacteristics. In particular, it is shown that a necessary condition for the appearance of a sharply defined second CMC is that the endcap energies (of at least some) of the smallQr intermediate-size micelles must be considerably lower than the asymptotic (long micelle) value of this quantity. The diameter of the .'minimal, spherical micelles, as well as that of the final endcaps, is found to be larger than the diameser of the cylindrical body of the very long micelles. Our results are in good., qualitative agreement with regent cryo- TEM imaging studies of micellar shape and growth, as well as with previous (less direct) experiments revealing second CMCbehavior.
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