Critical pure micelle concentration

Fig. 10.4 (a) Polymer concentration (solid lines) at the sol-gel transition, and the critical pure micelle... 

When apphed to a nonionic surfactant in pure water at concentrations below the critical micelle concentration, Eq. (22-42) simplifies into Eq. (22-43)... 

For pure nonionic EO adducts, increase in the number of oxyethylene groups in the molecule results in a decrease in the tendency to form micelles and an increase in the surface tension of the solution at the critical micelle concentration (1 ) (l. ) This change in surface activity is due to the greater surface area of the molecules in the adsorption layer and at the micellar surface as a result of the presence there of the highly hydrated polyoxyethylene chain. The reduction in the tendency to form micelles is due to the increase in the free energy of micelle formation as a result of partial dehydration of the polyoxyethylene chain during incorporation into the micelle ( 1 6) (17). 

In recent studies, Friberg and co-workers (J, 2) showed that the 21 carbon dicarboxylic acid 5(6)-carboxyl-4-hexyl-2-cyclohexene-1-yl octanoic acid (C21-DA, see Figure 1) exhibited hydrotropic or solubilizing properties in the multicomponent system(s) sodium octanoate (decanoate)/n-octanol/C2i-DA aqueous disodium salt solutions. Hydrotropic action was observed in dilute solutions even at concentrations below the critical micelle concentration (CMC) of the alkanoate. Such action was also observed in concentrates containing pure nonionic and anionic surfactants and C21-DA salt. The function of the hydrotrope was to retard formation of a more ordered structure or mesophase (liquid crystalline phase). 

The formation of mixed micelles in surfactant solutions which contain two or more surfactant components can be significantly affected by the structures of the surfactants involved. The observed critical micelle concentration (cmc) is often significantly lower than would be expected based on the erne s of the pure surfactants. This clearly demonstrates that interactions between different surfactant components in the mixed micelles are taking place. 

In mixed surfactant systems, physical properties such as the critical micelle concentration (cmc) and interfacial tensions are often substantially lower than would be expected based on the properties of the pure components. Such nonideal behavior is of both theoretical interest and industrial importance. For example, mixtures of different classes of surfactants often exhibit synergism (1-3) and this behavior can be utilized in practical applications ( ).In addition, commercial surfactant preparations usually contain mixtures of various species (e.g. different isomers and chain lengths) and often include surface active impurities which affect the critical micelle concentration and other properties. 

Above the critical micelle concentration (C ) in a pure surfactant solution the chemical potential of the monomer is given by... 

Synergism in mixed micelle formation. Synergism in this respect is present when the critical micelle concentration of any mixture is lower than that of either pure surfactant. This is illustrated in Figure 2. 

Figure 3.8 shows the dynamic surface tension of a pure anionic and a non-ionic surfactant dependent on the absorption time after the creation of new surface for different concentrations [9]. For both surfactants, the time dependence of the surface tension is greatly reduced when the concentration increases and this effect is especially pronounced when the critical micelle concentration is reached. The reason for this dependence is the diffusion of surfactant molecules and micellar aggregates to the surface which influences the surface tension on newly generated surfaces. This dynamic effect of surface tension can probably be attributed to the observation that an optimum of the washing efficiency usually occurs well above the critical micelle concentration. The effect is an important factor for cleaning and institutional washing where short process times are common. 

The industrial pro cess is b ased on the Fischer synthesis and commercial development work started some 25 years ago. Once a route using coconut-based alcohols had been established, full-scale plants became viable and alcohol blends are now used to control hydrophobicity of the molecules produced. Thus, products based on C8 alcohols are water soluble and those based on C18 are virtually insoluble. The critical micelle concentration (CMC) values of pure alkyl glucosides and CulCu alkyl polyglucoside (APG) are comparable with those of a typical non-ionic surfactant and decrease with increasing alkyl chain length. 

Surfactant surface activity is most completely presented in the form of the Gibbs adsorption isotherm, the plot of solution surface tension versus the logarithm of surfactant concentration. For many pure surfactants, the critical micelle concentration (CMC) defines the limit above which surface tension does not change with concentration, because at this stage, the surface is saturated with surfactant molecules. The CMC is a measure of surfactant efficiency, and the surface tension at or above the CMC (the low-surface-tension plateau) is an index of surfactant effectiveness (Table XIII). A surfactant concentration of 1% was chosen where possible from these various dissimilar studies to ensure a surface tension value above the CMC. Surfactants with hydrophobes based on methylsiloxanes can achieve a low surface tension plateau for aqueous solutions of —21-22 mN/m. There is ample confirmation of this fact in the literature (86, 87). 

The surface tension of a solution of a surfactant is lower than that of the pure solvent. Surface tension is roughly a linear function of ln(surfactant concentration) up to the critical micelle concentration (CMC) (Figure 3). Above the CMC the thermodynamic activity of the surfactant does not increase with the addition of more surfactant, and the surface tension remains constant. Interfacial tension also decreases with the concentration of an emulsifier dissolved in one of the phases. In Figure 4 the decrease in y does not level off, because the emulsifier (PGMS) does not form micelles in the organic solvent phase (heptane). The changes in the slope of the plot are attributed to changes in orientation of emulsifier molecules at the interface (7). 

This study is a continuation of our previous investigations, in which the aggregation phenomena of surfactant molecules (amphiphiles) in aqueous media to form micelles above the critical micelle concentration (c.m.c.) has been described based on different physical methods (11-15). In the current literature, the number of studies where mixed micelles have been investigated is scarcer than for pure micelles (i.e., mono-component). Further, in this study we report various themodynamlc data on the mixed micelle system, e.g., ci H25soi4Na (NaDDS) and sodium deoxycholate (NaDOC), enthalpy of micelle formation (by calorimetry), and aggregation number and second virial coefficient (by membrane osmometry) (1 6). 

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