Molecular packing parameter and surfactant self-assembly: The neglected role of the surfactant tail

The concept of molecular packing parameter is widely invoked in the literature to explain, rationalize and even predict molecular self-assembly in surfactant solutions. The molecular packing parameter is defined as nu(o)/a(e)l(o) where nu(o) is the surfactant tail volume, l(o) is the tail length, and a, is the equilibrium area per molecule at the aggregate surface. A particular value of the molecular packing parameter can be translated via simple geometrical relations into specific shape and size, of the equilibrium aggregate. This is the predictive application of the concept of molecular packing parameter, as discussed in the literature. In calculating the packing parameter, the dominant notion in the literature is that the surfactant headgroup determines the surface area per molecule of equilibrium aggregates a(e). It follows that, given a headgroup, the molecular packing parameter v(o)/a(e)l(o), is fixed, because the volume-to-length ratio (v(o)/l(o)) of the tail is a constant independent of the tail length for common surfactants. Therefore, in this view, the surfactant tail has no role in determining the size and shape of equilibrium aggregates. We show that this is contrary to fact, by focusing on the neglected role of the surfactant tail. Illustrative calculations are presented in this paper to demonstrate that the surfactant tail does also control equilibrium aggregate structures. It is shown that the role of the tail can be either explicit via modification of the area a(e), and thus of the packing parameter, or implicit via other means, without modifying a(e) or the packing parameter.