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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 $n{a}_0=4\pi r^2$, giving $v/a_0=r/3$. Since $r\le \ell$, spherical packing requires $P\le 1/3$. 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.

A cationic surfactant with a sixteen-carbon hydrocarbon tail and a positively charged trimethylammonium head group, accompanied by a ${\mathrm{Br}}^{-}$ counterion. It is an amphiphile that can form aqueous micelles. Its head-group charge has the opposite sign to that of sodium dodecyl sulfate.

The critical micelle concentration is the approximate surfactant concentration above which additional dissolved amphiphile predominantly enters micelles rather than remaining as isolated molecules. It is a concentration crossover governed by equality of the molecular chemical potential in the two environments, not a claim that absolutely no aggregates exist below a sharp threshold. Temperature, ionic conditions and molecular structure affect its value.

Two examples are sodium dodecyl sulfate, with a negatively charged sulfate head and a hydrocarbon tail, and cetrimonium bromide, with a positively charged ammonium head and a hydrocarbon tail. Both are amphiphiles: one region is hydrophilic and another is hydrophobic.

In water, the hydrophobic effect favors association of the tails into a core, reducing their exposed area while the hydrated heads remain outside. This can lower the total Gibbs free energy despite loss of translational entropy. Head-group repulsion, interfacial cost and chain-packing constraints oppose unlimited growth, so finite micelles are favored under suitable conditions above the critical micelle concentration.

The appropriate geometric measure is the amphiphile packing parameter:For a spherical micelle with $n$ tails and core radius $r_c$, the volume and area relations are $nv=4\pi r_c^3/3$ and $n{a}_0=4\pi r_c^2$. Dividing gives $r_c=3v/a_0$, so a sphere fits without overextending a tail if $P\le 1/3$. Here $P<1/3$ andThus the packing model predicts spherical micelles. This is a preferred aggregate geometry, not a claim that concentration, temperature or ionic conditions can never alter the morphology.

An anionic surfactant with a twelve-carbon hydrocarbon tail and a negatively charged sulfate head group, accompanied by a sodium counterion. This separation of hydrophobic and hydrophilic regions makes it an amphiphile. It forms aqueous micelles under suitable concentration and temperature conditions and is used in sodium dodecyl sulfate polyacrylamide gel electrophoresis.