= Amphiphile packing parameter
{title2=$P=v/(a_0\ell)$}
For an <amphiphile>, let $v$ be its hydrophobic-tail <volume>, $a_0$ its effective head-group <area>, and $\ell$ its maximum tail extension. The dimensionless packing parameter $P=v/(a_0\ell)$ estimates compatible aggregate curvature. For a spherical <micelle> of core radius $r$ containing $n$ molecules, $nv=4\pi r^3/3$ and $na_0=4\pi r^2$, giving $v/a_0=r/3$. Since $r\leq\ell$, spherical packing requires $P\leq1/3$. The analogous long-cylinder calculation gives $v/a_0=r/2$ and the limiting value $1/2$; a planar monolayer has $v/a_0$ equal to its thickness and limiting value one. Thus small $P$ favors spherical <micelles>, intermediate values favor cylindrical aggregates, and values near one favor <lipid bilayers>. This is a geometric guide, not a full thermodynamic prediction of every phase boundary.
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