The Critical Micelle Concentration CMC

Almost from the very beginning of the study of the properties of surfactant solutions (actually, soap solutions), it was recognized that their bulk properties were unusual and indicated the presence of colloidal particles in the solution. 

Surfactants and Interfacial Phenomena, Third Edition. Milton J. Rosen ISBN 0-471-47818-0 2004 John Wiley Sons, Inc. 

FIGURE 3-1 Plot of equivalent conductivity versus - /normality of solution for an aqueous solution of surfactant of type Na+R.  

The concentration at which this phenomenon occurs is called the critical micelle concentration (CMC). Similar breaks in almost every measurable physical property that depends on size or number of particles in solution, including micellar solubilization of solvent-insoluble material (Chapter 4) and reduction of surface or interfacial tension (Chapter 5), are shown by all types of surfactants—nonionic, anionic, cationic, and zwitterionic in aquecus media. 

In some cases, particularly where the hydrophobic group is long (e.g., Ci6), a second break in the conductivity-surfactant concentration curve has been observed. It has been suggested (Treiner, 1992) that this indicates change in the micellar structure (Section II, below). 

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At low concentrations surfactant molecules adsorbed at the surface are in equilibrium with other molecules in solution. Above a threshold concentration, called the critical micelle concentration (cmc, for short), another equilibrium must be considered. This additional equilibrium is that between individual molecules in solution and clusters of emulsifier molecules known as micelles. 

Ahphatic amine oxides behave as typical surfactants in aqueous solutions. Below the critical micelle concentration (CMC), dimethyl dodecyl amine oxide exists as single molecules. Above this concentration micellar (spherical) aggregates predorninate in solution. Ahphatic amine oxides are similar to other typical nonionic surfactants in that their CMC decreases with increasing temperature. 

Anionic Surfactants. PVP also interacts with anionic detergents, another class of large anions (108). This interaction has generated considerable interest because addition of PVP results in the formation of micelles at lower concentration than the critical micelle concentration (CMC) of the free surfactant the mechanism is described as a "necklace" of hemimicelles along the polymer chain, the hemimicelles being surrounded to some extent with PVP (109). The effective lowering of the CMC increases the surfactant s apparent activity at interfaces. PVP will increase foaming of anionic surfactants for this reason. 

Surfactant values are at the critical micelle concentration (CMC) in aqueous solution surfactant/defoamer values are at 0.1% concentration in aqueous solution. 

Very large solvent effects arc also observed for systems where the monomers can aggregate either with themselves or another species. For example, the apparent kp for polymerizable surfactants, such as certain vinyl pyridinium salts and alkyl salts of dimethylaminoalkyl methacrylates, in aqueous solution above the critical micelle concentration (cmc) are dramatically higher than they are below the cmc in water or in non-aqueous media.77 This docs not mean that the value for the kp is higher. The heterogeneity of the medium needs to be considered. In the micellar system, the effective concentration of double bonds in the vicinity of the... 

If the coupling component is not ionic, however, more dramatic effects occur, as found by Hashida et al. (1979) and by Tentorio et al. (1985). Hashida used N,N-bis(2-hydroxyethyl)aniline, while Tentorio and coworkers took 1-naphthylamine and l-amino-2-methylnaphthalene as coupling components. With cationic arenediazo-nium salts and addition of sodium dodecyl sulfate (SDS), rate increases up to 1100-fold were measured in cases where the surfactant concentration was higher than the critical micelle concentration (cmc). Under the same conditions the reaction... 

The curve shown in Fig. 6 for sodium dodecyl sulfate is characteristic of ionic surfactants, which present a discontinuous and sharp increase of solubility at a particular temperature [80]. This temperature is known as the Krafft temperature. The Krafft temperature is defined by ISO as the temperature [in practice, a narrow range of temperatures] at which the solubility of ionic surface active agents rises sharply. At this temperature the solubility becomes equal to the critical micelle concentration (cmc). The curve of solubility vs. temperature intersects with the curve of the CMC vs. temperature at the Krafft temperature. 

In addition to their poor solubility in water, alkyl phosphate esters and dialkyl phosphate esters are further characterized by sensitivity to water hardness [37]. A review of the preparation, properties, and uses of surface-active anionic phosphate esters prepared by the reactions of alcohols or ethoxylates with tetra-phosphoric acid or P4O10 is given in Ref. 3. The surfactant properties of alkyl phosphates have been investigated [18,186-188]. The critical micelle concentration (CMC) of the monoalkyl ester salts is only moderate see Table 6 ... 

Surfactants have a unique long-chain molecular structure composed of a hydrophilic head and hydrophobic tail. Based on the nature of the hydrophilic part surfactants are generally categorized as anionic, non-ionic, cationic, and zwitter-ionic. They all have a natural tendency to adsorb at surfaces and interfaces when added in low concentration in water. Surfactant absorption/desorption at the vapor-liquid interface alters the surface tension, which decreases continually with increasing concentrations until the critical micelle concentration (CMC), at which micelles (colloid-sized clusters or aggregates of monomers) start to form is reached (Manglik et al. 2001 Hetsroni et al. 2003c). 

Fig. 13. Relation between the critical micelle concentration (CMC) of self-emulsifying unsaturated polyesters (EUP) and their Mn[119,120].

A similar multiphase complication that should be kept in mind when discussing solutions at finite concentrations is possible micelle formation. It is well known that for many organic solutes in water, when the concentration exceeds a certain solute-dependent value, called the critical micelle concentration (cmc), the solute molecules are not distributed in a random uncorrelated way but rather aggregate into units (micelles) in which their distances of separation and orientations with respect to each other and to solvent molecules have strong correlations. Micelle formation, if it occurs, will clearly have a major effect on the apparent activity coefficient but the observation of the phenomenon requires more sophisticated analytical techniques than observation of, say, liquid-liquid phase separation. 

What characterizes surfactants is their ability to adsorb onto surfaces and to modify the surface properties. At the gas/liquid interface this leads to a reduction in surface tension. Fig. 4.1 shows the dependence of surface tension on the concentration for different surfactant types [39]. It is obvious from this figure that the nonionic surfactants have a lower surface tension for the same alkyl chain length and concentration than the ionic surfactants. The second effect which can be seen from Fig. 4.1 is the discontinuity of the surface tension-concentration curves with a constant value for the surface tension above this point. The breakpoint of the curves can be correlated to the critical micelle concentration (cmc) above which the formation of micellar aggregates can be observed in the bulk phase. These micelles are characteristic for the ability of surfactants to solubilize hydrophobic substances in aqueous solution. So the concentration of surfactant in the washing liquor has at least to be right above the cmc. 

Most studies of micellar systems have been carried out on synthetic surfactants where the polar or ionic head group may be cationic, e.g. an ammonium or pyridinium ion, anionic, e.g. a carboxylate, sulfate or sulfonate ion, non-ionic, e.g. hydroxy-compound, or zwitterionic, e.g. an amine oxide or a carboxylate or sulfonate betaine. Surfactants are often given trivial or trade names, and abbreviations based on either trivial or systematic names are freely used (Fendler and Fendler, 1975). Many commercial surfactants are mixtures so that purity can be a major problem. In addition, some surfactants, e.g. monoalkyl sulfates, decompose slowly in aqueous solution. Some examples of surfactants are given in Table 1, together with values of the critical micelle concentration, cmc. This is the surfactant concentration at the onset of micellization (Mukerjee and Mysels, 1970) and can therefore be taken to be the maximum concentration of monomeric surfactant in a solution (Menger and Portnoy, 1967). Its value is related to the change of free energy on micellization (Fendler and Fendler, 1975 Lindman and Wennerstrom, 1980). 

The concentration of micellized surfactant is that of total surfactant less that of monomer which is assumed to be given by the critical micelle concentration (cmc). The overall first-order rate constant kv is then given by (1). 

The solubility in polyethylene glycol 400 and in aqueous solution of other polyethylene glycols has been described.65-66 The effect of selected surfactants above and below the critical micelle concentration (CMC) on aspirin solubility67 was studied. 

Figure 10.11 As the aggregate number n increases, so the fraction of the added surfactant that goes into the micelle (as y ) varies more steeply with total concentration of surfactant monomer (as V). The critical micelle concentration (CMC) is the midpoint of the region over which the concentration of the micelle changes (Reproduced by permission of Wiley Interscience, from The Colloidal Domain by D. Fennell Evans and Hakan Wennerstrom)...

We call the centre of the concentration range the critical micelle concentration (CMC). As an over-simplification, we say the solution has no colloidal micelles below the CMC, but effectively all the monomer exists as micelles above the CMC. As no micelles exist below the CMC, a solution of monomer is clear - like the solution of dilute soap in the bath. But above the CMC, micelles form in solution and impart a turbid aspect owing to Tyndall light scattering. This latter situation corresponds to washing the face in a sink. 

A wide structural variation is possible within each class of molecules because both the length of the hydrophobic portion and the nature of the hydrophilic head group, as well as its position along the backbone, may be varied. The properties of the aggregates formed from these surfactants and the conditions under which they are formed depends on all these parameters. As the concentration of the surfactant in an aqueous solution is increased, many of the chemical and physical properties of the solution change rather abruptly (but continuously) over a concentration range known as the critical micelle concentration (CMC). 

Choose nonionics as suds stabilizers for use with foaming surfactants that are ionic. Prefer those with higher ability to lower the critical micelle concentration (CMC) of the foaming surfactant. 

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). 

Tokiwa and Ohki (10) have shown that 1) the Ka value of the micellized LDAO is different from the molecular form, viz., 10 2) while the values of Ka are independent of the degree of protonation ( ) below the critical micelle concentration (CMC), they are dependent on 3 at concentrations above the CMC. These authors did not explain why the micellar pKa (5.9) at 3 = 0 is different from the molecular value (pKa = 4.9). 

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