The critical micelle concentration

Micelles are formed by association of molecules in a selective solvent above a critical micelle concentration (one). Since micelles are a thermodynamically stable system at equilibrium, it has been suggested (Chu and Zhou 1996) that association is a more appropriate term than aggregation, which usually refers to the non-equilibrium growth of colloidal particles into clusters. There are two possible models for the association of molecules into micelles (Elias 1972,1973 Tuzar and Kratochvil 1976). In the first, termed open association, there is a continuous distribution of micelles containing 1,2,3. n molecules, with an associated continuous series of equilibrium constants. However, the model of open association does not lead to a cmc. Since a cmc is observed for block copolymer micelles, the model of closed association is applicable. However, as pointed out by Elias (1973), the cmc does not correspond to a thermodynamic property of the system, it can simply be defined phenomenologically as the concentration at which a sufficient number of micelles is formed to be detected by a given method. Thermodynamically, closed association corresponds to an equilibrium between molecules (unimers), A, and micelles, Ap, containingp molecules  

For an advancement of the equilibrium from left to right by a fractional extent a, K is given by (Yang ct al. 1995) 

Under this condition, for molecules and micelles in equilibrium just above the critical concentration (Attwood and Florence 1983) 

Otherwise eqn 3.4 must be used to obtain K. For a small association number, say p = 10, the error in approximating K by 1/cmc is large calculation of AmicG° via eqn 3.6 requires p a 50 (Hall 1987). For example, for a = 0.1 and ernes of 10 1 and HT6 mol dm 3, the error in AraicG° is 30 and 15% respectively. For a large association number, the standard enthalpy of micelle formation is then 

Because there are many factors that have been shown to affect the observed critical micelle concentration strongly, the following discussion has been divided so as to isolate (as much as possible) the various important factors. 

Any discussion of cmc data must be tempered with the knowledge that the reported values cannot be taken to be absolute but reflect certain variable factors inherent in the procedures employed for their determination. The variations in cmc found in the literature for nominally identical materials under supposedly identical conditions must be accepted as minor noise that should not significantly affect the overall picture (assuming, of course, that good experimental technique has been employed). 

The relationship between the hydrocarbon chain length and cmc for ionic surfactants generally fits the Klevens equation 

For nonionic surfactants, in which the mechanism of solubihzation of the surfactant molecule is basically hydrogen bonding, the relative importance of the tail and head groups to the overall process changes. An empirical relation- 

TABLE 15.4. Elevens Constants [Eq. (15.20)] for Connnon Snrfactant Classes 

One characteristic property of surfactants is that they spontaneously aggregate in water and form well-defined structures such as spherical micelles, cylinders, bilayers, etc. (review Ref. [524]). These structures are sometimes called association colloids. The simplest and best understood of these is the micelle. To illustrate this we take one example, sodium dode-cylsulfate (SDS), and see what happens when more and more SDS is added to water. At low concentration the anionic dodecylsulfate molecules are dissolved as individual ions. Due to their hydrocarbon chains they tend to adsorb at the air-water interface, with their hydrocarbon chains oriented towards the vapor phase. The surface tension decreases strongly with increasing concentration (Fig. 3.7). At a certain concentration, the critical micelle concentration or 

Similar dependencies on concentration are observed for the osmotic pressure or the electrical conductance of the solution. If we look at the optical turbidity of the solution the trend is opposite. At low concentration the solution is transparent. When the concentration reaches the CMC many solutions become opaque. In parallel, a property, which is of great practical relevance, changes the capacity to solubilize another hydrophobic substance. At concentrations below the CMC of the surfactant, hydrophobic substances are poorly dissolved. At the CMC they start being soluble in aqueous solution. This capability increases with increasing surfactant concentration. There may be small systematic differences in the concentration at which the specific property abruptly changes and the CMC determined by different methods may be different. However, the general trend and the dependency on external parameters such as temperature or salt concentration is always the same. 

The situation is more complex. With increasing concentration the mean aggregation number is not strictly constant. It increases slightly with increasing total concentration. 

A micelle is a dynamic structure. Surfactants leave the micelle and go into solution while other surfactants enter the micelle from solution. The timescales involved depend critically on the specific structure of the surfactant, in particular on the length of the hydrocarbon chain. For example, the residence time of a single dodecylsulfate (CH3(CH2)h0S03 ) in a SDS micelle at 25° C is 6 /xs [525], If we reduce the chain length by two methylene units to decyl sulfate (CH3(CH2)g0S03 ) the residence time decreases to roughly 0.5 /us. Tetradecyl sulfate (CH3(CH2)i30S03 ), which has two methylene units more than dodecylsulfate, typically remains 83 /its in a micelle. 

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The concentration at which micellization commences is called the critical micelle concentration, erne. Any experimental teclmique sensitive to a solution property modified by micellization or sensitive to some probe (molecule or ion) property modified by micellization is generally adequate to quantitatively estimate the onset of micellization. The detennination of erne is usually done by plotting the experimentally measured property or response as a hmction of the logarithm of the surfactant concentration. The intersection of asymptotes fitted to the experimental data or as a breakpoint in the experimental data denotes the erne. A partial listing of experimental... 

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. 

MeutralSoluble Salts. So dium sulfate [7757-82-6] and, to a considerably lesser extent, sodium chloride [7647-14-5] are the principal neutral soluble salts used in laundering compositions. They are often considered to be fillers although they perform an important standardizing function enabling the formulator to manufacture powders of a desired, controlled density. Sodium sulfate, in addition, lowers the critical micelle concentration of organic surfactants and thus the concentration at which effective washing can be achieved. 

Surfactants lower the surface tension of water, typically from 72 to ca 30—35 mN/m (= dyn/cm), and many surfactants have a strong effect on the contact angle when used at low concentrations. Both changes help dewatering. Too much surfactant, near or above the critical micelle concentration... 

Finally, some general rules for the amount of surfactant appear to be vaHd (13). For anionic surfactants the average size of droplets is reduced for an increase of surfactant concentration up to the critical micellization concentration, whereas for nonionic surfactants a reduction occurs also for concentrations in excess of this value. The latter case may reflect the solubiHty of the nonionic surfactant in both phases, causing a reduction of interfacial tension at higher concentrations, or may reflect the stabilizing action of the micelles per se. 

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

One of the most important characteristics of the emulsifier is its CMC, which is defined as the critical concentration value below which no micelle formation occurs. The critical micelle concentration of an emulsifier is determined by the structure and the number of hydrophilic and hydrophobic groups included in the emulsifier molecule. The hydrophile-lipophile balance (HLB) number is a good criterion for the selection of proper emulsifier. The HLB scale was developed by W. C. Griffin [46,47]. Based on his approach, the HLB number of an emulsifier can be calculated by dividing... 

For an a-helical fraction fH = 0,5 30% methanol, 20% ethanol, 15% i-propanol or 10% trifluoroethanol are necessary. Trifluoroethanol like perfluorinated alcohols, e.g. hexafluoroisopropanol is characterised on the hand by a strong acidic proton at the OG-group due to the —1-effect of the fluor atoms. On the other hand fluorocarbons are more hydrophobic than the hydrocarbons which is mainly due to the larger surface of the F compared with H. For this reason the critical micelle concentration of perfluorinated detergents is much lower than that of the corresponding hydrocarbon compounds. It was found that C4F7-derivatives act as detergents... 

In the latter function, the reagent behaves as a surfactant and forms a cationic micelle at a concentration above the critical micelle concentration (1 x 10 4M for CTMB). The complexation reactions occurring on the surface of the micelles differ from those in simple aqueous solution and result in the formation of a complex of higher ligand to metal ratio than in the simple aqueous system this effect is usually accompanied by a substantial increase in molar absorptivity of the metal complex. 

The pioneering work on amphiphilic polyelectrolytes goes back to 1951, when Strauss et al. [25] first synthesized amphiphilic polycations by quaternization of poly(2-vinylpyridine) with n-dodecyl bromide. They revealed that the long alkyl side chains attached to partially quaternized poly(vinylpyridine)s tended to aggregate in aqueous solution so that the polymers assumed a compact conformation when the mole fraction of the hydrophobic side chains exceeded a certain critical value. Thus, Strauss et al. became the first to show experimentally the intramolecular micellation of amphiphilic polymers and the existence of a critical content of hydrophobic residues which may be compared to the critical micelle concentration of ordinary surfactants. They called such amphiphilic polyelectrolytes polysoaps [25],... 

An interesting change of the UV-absorbances with electrolyte concentration was observed for A18 and T18, as shown in Fig. 5. The molar extinction coefficient of A18 decreased by about 7% at 0.09 mM, and that of T18 about 10% at 0.16 mM. These concentrations may correspond to the critical micelle concentration, since the cmc observed from the surface tension measurements were about 0.1 mM for both A18 and T18. 

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... 

Figure 20 shows the plot of the surface tension vs. the logarithm of the concentration (or-lg c-isotherms) of sodium alkanesulfonates C,0-C15 at 45°C. In accordance with the general behavior of surfactants, the interfacial activity increases with growing chain length. The critical micelle concentration (cM) is shifted to lower concentration values. The typical surface tension at cM is between 38 and 33 mN/m. The ammonium alkanesulfonates show similar behavior, though their solubility is much better. The impact of the counterions is twofold First, a more polarizable counterion lowers the cM value (Fig. 21), while the aggregation number of the micelles rises. Second, polarizable and hydrophobic counterions, such as n-propyl- or isopropylammonium and n-butylammonium ions, enhance the interfacial activity as well (Fig. 22). Hydrophilic counterions such as 2-hydroxyethylammonium have the opposite effect. Table 14 summarizes some data for the dodecane 1-sulfonates.

The poor solubility of higher sodium alkanesulfonates cited above is reflected in the surface tension vs. concentration plots of sodium pentadecane 4-sulfonate (Fig. 26). Because below the critical micelle concentration the solubility limit is reached, a break in the a-c plot occurs. The problem of solubility properties of alkanesulfonates below the point at which the hydrated crystals or solid... 

If the property evaluated, for instance, the critical micelle concentration, can be approximated by a suitable plot, it is depicted in the ternary system as a concave area (e.g., cM area) located in the space above the Gibbs triangle as the basis for the distinct concentrations. The property axis describing the cM data stands vertically on the base triangle. 

In the homologous series of alkane 1-sulfonates, micellization in aqueous solutions begins with the pentanesulfonate at cM = 1 mol/L. The critical micelle concentrations of the technical alkanesulfonates are cM = 0.002 mol/L (sulfo-chlorination route) and cM = 0.44 g/L (sulfoxidation route). 

The Stauff-Klevens equation is valid for the critical micelle concentration of homologous surfactants with the same ionic head group ... 

A positive value of ME means that the insertion of a hetero atom or group makes the molecule more lipophilic. If ME is negative, the hetero surfactant is more hydrophilic. In general, hetero atom insertion hydrophilizes the surfactant molecule as does the shift of the hetero group to the middle of the carbon chain [71]. ME values are temperature-dependent. / and ME values can also be useful to take into account the influence of various cations on the critical micelle concentration. 

Sanchez et al. [61,62] studied the stability of sodium decyl, dodecyl, and tetradecyl sulfates and sodium lauryl ether (3 EO) sulfate in acid media (pH 1) at different temperatures and concentrations above and below the critical micelle concentration. Sodium decyl sulfate was shown to be relatively stable for several hours at temperatures up to 90°C. Sodium dodecyl and tetradecyl sulfates were only stable for short periods of time at temperatures above 40-50°C. As expected, sodium lauryl ether sulfate was less stable to hydrolysis than the corresponding lauryl sulfate. 

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. 

Table 17 shows the CMCs of sodium alcohol propoxysulfates at 20°C determined from surface tension measurements by the maximum bubble pressure [127] and Table 18 shows the critical micelle concentrations of sodium pro-poxylated octylphenol and propoxylated nonylphenol sulfates. Surface tension... 

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). 

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