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 tails and core radius , the volume and area relations are and . Dividing gives , so a sphere fits without overextending a tail if . Here and
Thus 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.
Figure 1.
An original cross-section of spherical micelle packing
. Hydrophilic heads face the water and hydrophobic tails fill the core; the drawing illustrates packing geometry rather than a measured aggregation number. Details.