Cylindrical micelle geometry ($R=2v/a_0$)

For a long cylindrical micelle with negligible end caps, incompressible tail volume $v$ and head-group area $a_0$ give $v/a_0=R/2$. The geometric requirement $R\le {\ell }_c$ bounds the amphiphile packing parameter by $1/2$. The conventional cylindrical range is approximately $1/3\lesssim v/(a_0{\ell }_c)\lesssim 1/2$; aggregate transitions also depend on interactions and chain conformations.