The energetics of highly charged spherical micelles as applied to sodium lauryl sulphate

The electrical free energy of micelle formation is treated for spherical micelles with a Gouy type double layer, allowing for high surface charge. Use is made of double layer computations carried out by Hoskin for spherical particles with high surface potential. A procedure is developed for interpolating between Hoskin's results. A correction is applied for the difference between the smeared out surface charge as in the model calculations and the actual assembly of discrete charges. From the equilibrium equation for micellization in which this electrical free energy occurs together with terms depending on the concentrations of free ions and of micelles the non‐electrical part of the standard free energy of micelle formation (W‐TΔSo) can be calculated. The method is applied to micelles of sodium lauryl sulphate in aqueous sodium chloride solutions. In this system W‐TΔSo is found to be nearly independent of micelle size and slightly above 1 kT per carbon atom in the chain. Comparison with other data on the free energy change in the transfer of aliphatic chains from water to non‐polar surroundings shows excellent agreement.