Micellar aggregation number

NMR self-diffusion coefficients (Lindman, 1983), small-angle neutron scattering (SANS) (Cebula, 1982 Triolo, 1983 Corti, 1984), freezing point and vapor pressure methods (Herrington, 1986) and fluorescent probes (Atik, 1979) have been used to calculate aggregation numbers of several different types of surfactants (Zana, 1980 Lianos, 1980, 1981, 1982, 1983). Some aggregation numbers of surfactants are listed in Table 3-1. 

TABLE 3-1 Aggregation Numbers of Some Surfactant Micelles 

Compound Solvent Temp. (°C) Aggregation Number Reference 

Ionic surfactants with two long (six or more carbons) alkyl chains have high VH values relative to lc, and probably do not form spherical micelles. They have values of n that increase with surfactant concentration, the increase becoming more pronounced with increase in the length of the chains. Some of these micellar solutions are in equilibrium with lamellar liquid crystal structures (Lianos, 1983). 

The addition of neutral electrolyte to solutions of ionic surfactants in aqueous solution causes an increase in the aggregation number, presumably because of compression of the electrical double layer surrounding the ionic heads. The resulting reduction of their mutual repulsion in the micelle permits closer packing of the head groups (a0 is reduced), with a consequent increase in n. 

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Other solubilization and partitioning phenomena are important, both within the context of microemulsions and in the absence of added immiscible solvent. In regular micellar solutions, micelles promote the solubility of many compounds otherwise insoluble in water. The amount of chemical component solubilized in a micellar solution will, typically, be much smaller than can be accommodated in microemulsion fonnation, such as when only a few molecules per micelle are solubilized. Such limited solubilization is nevertheless quite useful. The incoriDoration of minor quantities of pyrene and related optical probes into micelles are a key to the use of fluorescence depolarization in quantifying micellar aggregation numbers and micellar microviscosities [48]. Micellar solubilization makes it possible to measure acid-base or electrochemical properties of compounds otherwise insoluble in aqueous solution. Micellar solubilization facilitates micellar catalysis (see section C2.3.10) and emulsion polymerization (see section C2.3.12). On the other hand, there are untoward effects of micellar solubilization in practical applications of surfactants. Wlren one has a multiphase... 

An interesting application of static quenching is the determination of micellar aggregation numbers (see Box 4.2). 

Box 4.2 Determination of micellar aggregation numbers by means of fluorescence quenching3 ... 

Quenching of pyrene by excimer formation (Py + Py —> (PyPy) —> 2Py) (see Section 4.4.1) is widely used for the determination of micellar aggregation numbers for new surfactant systems. An example is given in Figure B4.2.1. 

This approach proves that a phase diagram can be modeled when the solution microstructure is known (i.e., aggregation number and micellar aggregate number per unit volume) together with an experimental determination of the potential between aggregates. If the variation of the potential versus various parameters (metal salt in the organic phase) can be obtained experimentally, the limits of the phase separation can be reliably correlated with theory. 

T. M. Herrington and S. S. Sahi, Temperature dependence of the micellar aggregation number of aqueous solutions of sucrose monolaurate and sucrose monooleate, Colloids Surf, 17 (1986) 103-113. 

The methods mentioned above do not measure the micellar aggregation number itself but rather some micellar size. A direct determination of aggregation numbers can be performed by analysing some physico-chemical parameter in terms of the equilibria involved equilibrium analyses on the basis of potentiometric data have been pioneered by Danielsson and co-workers who studied short-chain, not typically micelle-forming, amphiphiles in the presence of added electrolyte (see above). 

A similar case is mentioned by Heilweil89 who investigated sodium 2,6-di-n-octyl-and sodium 2,6-di-n-dodecylnaphthalene sulfonates in n-decane, n-heptane and benzene. In n-decane the apparent micellar aggregation numbers were essentially independent of C8- and C j 2-chain lengths. 

Drug R R2 R3 Critical micellar concentration (mol kg- ) Micellar aggregation number... 

The mass action model describes micelle formation as an equilibrium process. The micellar aggregation number becomes an important parameter. The solubilization process can be treated as a stepwise addition of solute molecules to the micelles. However, the partition coefficient based on this model requires the aggregation number, which makes it difficult to use in practice. There are several methods of simplification. One is to define the partition coefficient as ... 

The work done by Thompson [153] has shown that sodium laureth-2 sulfate (SLES-2) is superior to ammonium lauryl sulfate (ALS) in cleaning sebum, results that are consistent with those of Clarke and co-workers [152,154], One reason for this finding is that SLES-2 has a lower CMC and a larger micellar aggregation number than ALS under the same conditions [155,156]. Thus, at a given concentration above the CMC, a solution of SLES-2 is likely to solubilize more sebum than ALS simply because more of its molecules are involved in micelle formation... 

For zwitterionics of the betaine and sulfobetaine types, Ci2H25N+(CH3)2(CH2)m COO- and C12H25N+(CH3)2(CH2)3S03-, respectively, the micellar aggregation number varies very little with change in surfactant concentration or electrolyte content (Kamenka, 1995a). 

Explain why the data on micellar aggregation numbers in Table 3-1 for ionic surfactants often include the surfactant concentration at which the value was determined (the value in parentheses in the table), while the data for nonionics and zwitterionics do not include the concentration. 

Bivalent metal alkyl sulfates appear to show greater solubilizing power than the corresponding sodium salts for hydrocarbons, probably reflecting the greater micellar aggregation numbers, asymmetry, and volumes of the former compared to the latter (Satake, 1963). 

From surface tension studies of bola-surfactants, it is concluded that they exhibit wicket-like conformations at the gas-water interface [239,428,430,431], In micelles and liquid crystals however, a stretched conformation is preferred [436,437] this implies that surface tension data and interfacial tension data do no more describe the micellar interface with all the implications for solubilization (compare Sect. 3.4). In fact, some reports stress the extremely low solubilization capacity of bola-surfactants [431,432, 437,438], although others obtain capacities comparable to the ones of the monomers [430]. Also noteworthy, solubilized fluorescence probes indicate a more polar environment for the solubilizates than in micelles of the monomers [430-432], but micellar aggregation numbers of the bola-surfactants are comparable or only slightly lower [429,432, 438, 439]. In exceptional cases, very high aggregation numbers and the existence of an additional pre-CMC are observed [440]. 

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