Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / Section D / 25 / c / i

The amphiphile packing parameter is $p=v/(a\ell )$: hydrocarbon volume divided by the product of effective head-group area and maximal tail length. For a spherical core of radius $R$, $v/a=R/3$; requiring $R\le \ell$ gives spheres for $p\lesssim 1/3$. Cylindrical cores instead have $v/a=R/2$, favouring cylinders or rods for roughly $1/3<p\lesssim 1/2$. Lower-curvature bilayer structures are favoured towards $p\simeq 1$; intermediate ranges can include flexible or closed bilayer morphologies.

The charged sulfate head groups make the effective area sensitive to electrostatic repulsion, salt and counterion binding. Screening can reduce that area, increasing $p$ and favouring growth from spheres towards elongated micelles. These are geometric selection rules, not exact phase boundaries or a claim that every morphology is stable at any concentration.