![an ordinary spherical micelle is generated. An advantage of this model is that it automatically encompasses a whole range of micellar shapes, which is a desirable feature when analyzing SANS data. Yet, it is evident that the geometrical outline eventually will have to be modified (swollen ends and rims) in order to comply with the shape equation [Eq. (205)].](https://images.tandf.co.uk/common/jackets/crclarge/978036739/9780367394493.jpg "an ordinary spherical micelle is generated. An advantage of this model is that it automatically encompasses a whole range of micellar shapes, which is a desirable feature when analyzing SANS data. Yet, it is evident that the geometrical outline eventually will have to be modified (swollen ends and rims) in order to comply with the shape equation [Eq. (205)].")
ABSTRACT
Among the various options as to aggregate size and shape that are open to a certain surfactant system, those aggregates that have the lowest free energy ∆Ωmic of the respective equilibrium aggregate, and, additionally, the shallowest minimum allowing a multitude of aggregates, but slightly differing in size and shape, will predominate as a result of equilibrium fluctuations. Generally, we can write for the volume fraction of a micellar species:
(206)
where the size fluctuations give rise to the preexponential factor* and the integral in the exponent extends over the dividing surface defining the size
and shape of the fully equilibrated surfactant aggregate (for which the OuYang-Helfrich shape equation is satisfied). The fluctuation factor Sfluct is rather small for ordinary spherical micelles (≈25), but increases rapidly with size and becomes large for rodshaped and disc-shaped micelles.
