Micelle number

N JVagg Ni Ns n nc P Po Aggregation number of surfactant micelles Number of molecules of a certain species i (dimensionless or mol) Surfactant parameter Refractive index, integer number Number of carbon atoms in an alkyl chain Pressure (Pa), probability Equilibrium vapor pressure of a vapor in contact with a liquid having a planar surface (Pa)... 

Fig. VI-9. The micelle number concentration, mic, as a function of the total surfactant concentration in the system, c0...

A number of control experiments were performed to establish that the copurification observed between HOS and HAS was not the result of nonspecific interactions (30). In the first experiment, HOS and HAS were expressed in different cells, and the detergent-solubilized cell lysates were then combined and incubated together prior to protein purification. Again, HOS and HAS were found to copurify. In a second experiment, / -dodecyl p-D-maltoside was used to solubilize HOS and HAS instead of the detergent Triton X-100, and this change was found to have no effect on the interaction between HOS and HAS. Because -dodecyl P-D-maltoside has a lower micelle number as well as a lower critical micelle concentration (cmc), it seems unlikely that the copurification observed is an artifact of the two enzymes being trapped in the same micelle. 

The aggregation number of the micelle (number of molecules of bile salt per micelle) as a function of the concentration of NaCl is given for free bile salts (Fig. 42), taurine conjugates (Fig. 43), and glycine conjugates (Fig. 44), respectively, at 20 °C and pH values from 8 to 9. 

Temperature Micellar weight ( X 10- ) Number of surfactant molecules per micelle Number of solubilizate molecules per micelle... 

Hence, the depletion effect due to ionic micelles is greater than that of nonionic micelles at the same micelle number concentration and is strongly dependent on the electrolyte concentration. 

Emerson, M.F., Holtzer, A. The ionic strength dependence of micelle number. J. Phys. Chem. 1965, 69(11), 3718-3721. 

The examples in the preceding section, of the flotation of lead and copper ores by xanthates, was one in which chemical forces predominated in the adsorption of the collector. Flotation processes have been applied to a number of other minerals that are either ionic in type, such as potassium chloride, or are insoluble oxides such as quartz and iron oxide, or ink pigments [needed to be removed in waste paper processing [92]]. In the case of quartz, surfactants such as alkyl amines are used, and the situation is complicated by micelle formation (see next section), which can also occur in the adsorbed layer [93, 94]. 

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. 

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 binding behaviour of benzene can be extrapolated to many other aromatic compounds such as naphthalene and benzene derivativesInterestingly, a large number of probe molecules contain aromatic rings and many of them will prefer the outer regions of micelles, whereas in bilayer systems, the same molecules prefer the interior of the aggregate ". Qearly these probes cannot be used to determine polarity of the micellar interior or the extent of water penetration therein . 

Analogously, the effect of micelles on the rate of the unimolecular retro Diels-Alder reaction has been studied. Also here only a modest retardation" or acceleration" is observed. Likewise, the presence of micelles has been reported to have a modest influence on an intramolecular Diels-Alder reaction . Studies on the endo-exo selectivity of a number of different Diels-Alder reactions in micellar media lead to comparable conclusions. Endo-exo selectivities tend to be somewhat smaller in micellar solutions than in pure water, but still are appreciably larger than those in organic media In contrast, in microemulsions the endo-exo selectivity is reduced significantly" ... 

It turned out that the dodecylsulfate surfactants Co(DS)i Ni(DS)2, Cu(DS)2 and Zn(DS)2 containing catalytically active counterions are extremely potent catalysts for the Diels-Alder reaction between 5.1 and 5.2 (see Scheme 5.1). The physical properties of these micelles have been described in the literature and a small number of catalytic studies have been reported. The influence of Cu(DS)2 micelles on the kinetics of quenching of a photoexcited species has been investigated. Interestingly, Kobayashi recently employed surfactants in scandium triflate catalysed aldol reactions". Robinson et al. have demonshuted that the interaction between metal ions and ligand at the surface of dodecylsulfate micelles can be extremely efficient. ... 

Chapter 5, may provide a rationale. Conclusions derived from a number of H-MVIR measurements indicate that cyclopentadiene has a high affinity for the interior of the micelles that were investigated, whereas the dienophile prefers the outer regions. In view of the structures of most dienes and dienophiles such a spatial separation can be expected for the majority of Diels-Alder reactions. This arrangement accounts for the unexpectedly small influence of micelles on the rates of Diels-Alder reactions as reported in the literature. 

Detergents are substances including soaps that cleanse by micellar action A large number of synthetic detergents are known One example is sodium lauryl sulfate Sodium lauryl sulfate has a long hydrocarbon chain terminating m a polar sulfate ion and forms soap like micelles m water... 

In an emulsion polymerization experiment at 60°C the number of micelles per unit volume is 5.0 X 10 hter and the monomer concentration in the micelle... 

In this example the number of micelles per unit volume is exactly twice the stationary-state free-radical concentration hence the rates are identical. Although the numbers were chosen in this example to produce this result, neither N nor M are unreasonable values in actual emulsion polymerizations. 

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