Micellar solution aggregation number

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

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... 

The logarithm of the micellar molecular weight (M) and consequently the aggregation number of sodium dodecyl sulfate at 25°C in aqueous sodium chloride solutions is linearly related to the logarithm of the CMC plus the concentration of salt (Cs), both expressed in molar units, through two equations [116]. Below 0.45 M NaCl micelles are spherical or globular, and Eq. (18) applies ... 

Molecular micellar weights can be calculated from the aggregation number. In the case of sodium dodecyl sulfate it is around 15,000 (aggregation number = 52) and it increases to 30,000 (aggregation number = 104) in diluted NaCl solutions. 

Little is known about the structures of these kinetically effective complexes, or even about the aggregates of the amphiphile. Both hydrophobic and coulombic interactions are important because these aggregates are much less effective than micelles at assisting reactions of hydrophilic nucleophilic anions. These observations are consistent with the view that the aggregates are much smaller than micelles. It is probable that the structures and aggregation numbers of these aggregates depend on the nature of the solutes which bind to them and Piszkiewicz (1977) has suggested that such interactions play a role in micellar kinetics. 

Fluorescence quenching studies in micellar systems provide quantitative information not only on the aggregation number but also on counterion binding and on the effect of additives on the micellization process. The solubilizing process (partition coefficients between the aqueous phase and the micellar pseudo-phase, entry and exit rates of solutes) can also be characterized by fluorescence quenching. 

When micellar aggregates are formed in solutions and their aggregation numbers are not very large, they are randomly dispersed, owing to thermal motion. Weak indications of anisotropy are found at very high concentrations only. 

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. 

Consider a micellar solution at equilibrium that is subject to a sudden temperature change (T-jump). At the new temperature the equilibrium aggregate size distribution will be somewhat different and a redistribution of micellar sizes will occur. Aniansson and Wall now made the important observation that when scheme (5.1) represents the kinetic elementary step, and when there is a strong minimum in the micelle size distribution as in Fig. 2.23(a) the redistribution of micelle sizes is a two-step process. In the first and faster step relaxation occurs to a quasi-equilibrium state which is formed under the constraint that the total number of micelles remains constant. Thus the fast process involves reactions in scheme (5.1) for aggregates of sizes close to the maximum in the distribution. This process is characterized by an exponential relaxation with a time constant Tj equal to... 

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