= Finite-micelle aggregation-number distribution
{title2=$x_\alpha=\alpha\exp[\alpha(\mu-\mu_\alpha^0)/(k_BT)]$}
Here $\mu$ is the common <equilibrium> <chemical potential> per <amphiphile> and $\mu_\alpha^0$ the standard <free energy> per <amphiphile> in an aggregate of size $\alpha$. A minimum of the aggregate free-energy balance at a finite size produces a micellar population around that size, in addition to monomers. Translational <entropy> leaves a small aggregate population below the nominal <critical micelle concentration>; a preferred finite size is not supplied by the mass-action equation alone.
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