Shampoo and Conditioner Science 80 The shapes of surfactant molecules and the way they can be packed also plays an important role in determining micelle shape. Although thermodynamics and packing geometries are inextricably linked, by considering the limits of possible packing arrangements one can obtain insight into the shapes of micelles and the transformation from one shape to another as physical and chemical conditions are changed. In this context, the many shapes of micelles, arising from the principle of opposing forces, can be appreciated by considering Packing Factor Theory (see Figure 2).13 First, consider a spherical micelle. In this instance the micelle radius, R, the volume of the hydrophobic core, v, and the surface area of the amphipathic molecule at the hydrophobe/water interface, a, are related by: (Eq. 1) The radius of a micelle, R, cannot exceed the fully extended length, l, of the hydrophobe chain of the surfactant molecule. This gives the critical condition for the formation of spherical micelles: (Eq. 2) Figure 2. The packing factor of a surfactant molecule is the volume of the tail group divided by the volume of the cylinder subtended by the head group to the length of the tail group.