COMPOSITION FLUCTUATIONS PROMOTING THE FORMATION OF LONG ROD-SHAPED MICELLES

Because of composition fluctuations, the number of accessible states is generally much larger for a mixed surfactant aggregate than for the corresponding pure aggregate. In particular, for a rod-shaped, ionic surfactant micelle, the number of additional states due to adding a long-chain alcohol increases notably with the length of the micelle. By means of model calculations for sodium dodecyl sulfate/dodecanol/salt systems we demonstrate this circumstance to have interesting consequences as to the genesis and size distribution of rod-shaped micelles. For pure rod-shaped micelles, the size distribution is exponential and it broadens significantly when the salt concentration is increased, but the position of the maximum remains essentially unaffected. However, when both the long-chain alcohol and salt concentrations are comparatively high, the size distribution becomes distinctly nonexponential, and the maximum is shifted to well above the minimum aggregation number. A rod-shaped micelle is a small thermodynamic system, and the ratio between the composition fluctuation entropy contribution to the free energy and the average excess free energy is 0.15-0.25 at low aggregation numbers N and decreases slowly at higher N. For very large N, i.e., for macroscopically long, rod-shaped micelles, the composition fluctuation contribution eventually becomes negligible compared with the average free energy of a micelle.