= Spherical micelle geometry
{title2=$R=3v/a_0,\quad n=36\pi v^2/a_0^3$}
In a sharp-core spherical <micelle> of aggregation number $n$, incompressible tail <volume> $v$ per molecule and effective head-group <area> $a_0$ give $nv=4\pi R^3/3$ and $na_0=4\pi R^2$. Division gives the displayed radius and aggregation number. If the maximum tail extension is $l_c$, the model requires $R\leq l_c$, equivalently the <amphiphile packing parameter> $v/(a_0l_c)\leq1/3$. Input dimensions violating that inequality cannot describe an exact spherical filled core without modifying the molecular geometry assumptions.
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