LYOTROPIC MESOPHASE (LIQUID CRYSTAL) 675 (Smectic) Middle (Nemotic) To, k Viscous 'l'sotropic Figure 14. Intermicellar equilibrium and associated phase changes shown by nafoxidine hydrochloride shown as an amphiphile ,• with W hydrophilic section ofmicelle • amphiphilic section ofmicelle 6 oleophilic section ofmicelle as described in Figure 1 This scheme is described by Winsor (2) to include conjugate solutions at equilibrium mixtures between the phase changes. Anisotropic gel phase may be considered as a lamellar intermediate between the microemul- sions of oil-in-water and water-in-oil forms. renders a fluid nature to this region characteristic of an organic layer. The model shown in Figure 14 may be reversed to show a spherical micelle formed from an amphiphile in an oil or organic hydrocarbon environment. In such a case, the core of the micelle would be aT layer. This is shown as a viscous isotropic aggregate in Figure 14. The micelles are thus, in the case shown, formed when the energy released by aggre- gating the hydrocarbon portions of the amphiphilic nafoxidine monomer is great enough to overcome the electrical repulsion among the ionic groups and balance the entropy decrease associated with micelle formation. Micelle formation and stability are dependent on temperature and concentration as well as the influence of additives. Micelles can be formed by several classes of amphiphiles, typically cationic, anionic and nonionic surfactants. Each will be capable of forming a liquid crystal phase in sub- sequent binary or ternary (i.e., emulsion) systems. A theory of micelle stability based on hydrophobic bonding has been described by Scheraga and co-workers (8) who viewed the physical picture of a micelle as a spherical aggregate of hydrocarbon tails, the polar heads on the surface with entangled tails in- side. Using a free valence approach and also considering a micelle as a lattice, they con- clude that stable micelles require not only that the free energy per molecule be a minimum at some large degree of aggregation, but also that this minimum free energy should be smaller than that of the monodispersed amphiphile. The theory is related to

676 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS the excess turbidity which results with increased concentration of the amphilile above the cmc. This would explain the changes observed in Figure 8. Poland and Seheraga in- terpret this as evidence of an increase in the most probable micelle size. The thermodynamics of micelle formation have been reviewed by Hall and Pethica (9). Their treatment is a refinement of the standard treatment of mass action vs. phase- separation models inasmuch as they introduce the small-system thermodynamic ap- proach as applied to mixed micelies. The mass-action model has often been used suc- cessfully to predict cmc values. However at higher surfactant concentrations and in multicomponent or solubilized systems this model becomes limited in application. Since micelles are not arranged in a fixed stoichiometry, a multi-species approach to miceliar equilibria has also been used in the treatment of micelles as reaction products of surfactants and water. The occurrence of lyotropic mesophase domains in amphi- phile-water systems is not readily explained by the mass action model. The phase separation model for micelle formation considers the cmc as the maximum concentration of molecular dispersion of the surfactant. Micelles are treated as a separate phase, often the justification based on ultra-filtration studies and the fact that the concentration of the surfactant monomer appears constant above the cmc. However apparent phase heterogeneity and electro-inequality (especially for surface layers of charged micelies, ionic surfactants) make a strict thermodynamic treatment of micelles as a phase somewhat difficult. This criticism of the phase model, which altogether is much better for concentrated surfactant systems than the mass-action model, has been the limiting reason for a strict thermodynamic approach to micelliza- tion through an entire concentration profile. The treatment of micelle formation by small-system thermodynamics considers a general macroscopic system of multicomponent solutions and multicomponent micelies. Hall and Pethica (9) also consider the thermodynamics of mixed small systems and regard their overall treatment as chiefly speculative, awaiting experimental verification. In general, this small-system approach to micellization is very similar to the phase-separation model except that the solvent is considered to be in excess and therefore ignored. The assumption is therefore made that the small systems are so dilute in the solvent that they do not interact. For assimilation of this treatment into systems where lyotropic mesophases occur, however, several difficulties arise. Micelles are in kinetic as well as thermodynamic equilibrium with the molecularly dis- persed surfactant. It is generally accepted that micelles can occur well below the cmc and also that micelles cannot exist alone as a phase above the cmc without the presence of monomers in solution. The lamellar micelle in particular (shown as a McBain micelle in part of the neat phase of Figure 14), though often represented to the contrary, de- pends very critically on the presence of a solution phase for its "sandwich" or bimolecular leaflet structure. Micellization and demicellization occur throughout a surfactant solvent system at all concentration levels. Thus, depending on the overall concentration of the amphiphile in the entire system, it is best to refer to the most probable micellar size as the best representation of the structure. Most probably a statistical concentration of many micelles and micellar fragments (trimer, tetramers, etc.) occur in equilibrium with the recognized miceliar size and structure. The existence of a liquid crystal mesophase in these micellar systems helps in under- standing the various anomalous phase characteristics. Being a mesophase thermody- namically, its structure is found to be uniform and homogeneous throughout its