PHYSICAL CHEMISTRY AND PRODUCT DEVELOPMENT 905 Figure 7. Micelle structure CRITICAL MICELLE CONCENTRATION The critical micelie concentration (cmc) is that point or range at which the constitution of the surfactant solute changes from a disperse state to an equilibrium between molecules (or ions) and aggregates (mi- celies) (Fig. 7). Below this concentration, surfactant molecules are unas- sociated above it, almost all additional solute forms micelies. These micelles may comprise from tens to thousands of units and vary in shape from lamellar to spherical to "log boom" (Figs. 8-11). This change in solution character is reflected in a number of physical properties, many of which are important to the product development chemist. Some of the properties that show an abrupt change at the cmc include surface tension, interfacial tension, degree of foaming, conductivity, turbid- ity, refractive index, viscosity, flocculation rate, and solubilization. All of these changes have been used to determine cmc. Figure 8. Lameliar micelie

906 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Figure 9. Spherical micelle Two general factors determine what the cmc will be for a specific surfactant in solution. The first is the structure of the surfactant mole- cule and the second is the nature and amount of additives in solution. Concerning the surfactant molecule, as molecule weight increases for a given ionic species the cmc decreases. As branching increases (for a given molecular weight) cmc increases (Table I). Concerning addi- tives, salts generally lower the cmc, probably increasing the size of the aggregates. Table I Effect of Anionic Surfactant Molecular Weight and Structure on Critical Micelie Concentration Surfactant Cmc (m/l.) Ref. Sodium decyl (1) sulfate 3.4 X 10 -2 Sodium dodecyl (1) sulfate 8.5 X 10-a Sodium tetradecyl (1) sulfate 2.2 X 10 -a Sodium hexadecyl (1) sulfate 5.2 X 10-4 Sodium decanoate 9.4 X 10 -2 Sodium dodecanoate 2.3 X 10 -2 Sodium tetradecanoate 6.9 X 10 -a Sodium hexadecanoate 2.1 X 10-a Sodium tetradecyl (1) sulfate 2.2 X 10 -3 Sodium tetradecyl (2)sulfate 3.3 X 10 -3 Sodium tetradecyl (3) sulfate 4.3 X 10-a Sodium tetradecyl (4) sulfate 5.2 X 10 -a Sodium tetradecyl (7) sulfate 9.7 X 10 -3 (9) (9) lo) lo) 11) 11) 11) 12) 10) 13) (13) (lo) (13)