Charge of the micelle

As mentioned above, a substantial part of the electrical charge of the micelle surface has been shown to be neutralized by the association of the counter ions with the micelle. In the calculation based on Equation 12, however, the loss in entropy arising from this counter ion association is not taken into account. This is by no means insignificant in comparison to of Equation 12 (4). A major part of the counter ions are condensed on the ionic micelle surface and counteract the electrical energy assigned to the amphiphilic ions on the micellar surface. The minor part of the counter ions,in the diffuse double layer, are also restricted to the vicinity of the micellar surface. 

The micelle with NCXA+ monomers will have CBr counterions. The positive charge of the micelle will be the sum of positive and negative ions (NCXA+ + CBr ). The actual concentration of each species will vary with the total detergent concentration, as in the case of SDS (Figure 3.9). 

Use Equation (82) to estimate the charge of the micelles. What approximation(s) in the derivation of Equation (82) prevents this expression from applying exactly to this system On the basis of the charges evaluated by Equation (82), calculate the ratio of charge to aggregation number, the effective degree of dissociation, of these micelles. How do these results compare with the numbers given in Table 8.1 ... 

Eqs. (6.14) and (6.13) in combination can be used to compare CMC values for amphiphiles with the same alkyl chain length but with different ionic groups. If it is assumed that the radius i and the charge of the micelle are constant in such a series, the variation in the CMC is due to the variation in rm, i.e., how deeply the amphiphile charge is buried in the micelle. The smaller rm, the larger AGe, and the... 

The aim of most authors (3,11,12) in using Equations 2, 3, 4, or 5 was to predict from a given model the variation of the cmc with solvent composition. To our knowledge, however, except in a few cases (3,4), AGt° was ignored and the electric potentials were calculated with drastic simplifications e.g., the variation of the apparent charge of the micelle with the addition of the organic component was not taken into account. There is no easy way of determining the composition X of the mixed micelle, so we shall focus our discussion on the simplest case, i.e. that described by Equation 5. 

The main goal will be the determination of the apparent charge of the micelle in the binary aqueous solvents. Contradictory findings are found in the literature when the apparent charge is deduced from emf determinations (12,13). We shall discuss these results and compare them with those obtained using a conductivity approach. 

Variation of the Critical Micelle Concentration and Apparent Charge of the Micelles in the Mixed Solvents... 

Table V and Figures 4, 5, and 6 present our essential results. Figures 4 and 5 show the relative magnitude of each term of Equation 5, the electric potential term being represented by the difference between the two curves for AGt° and 2RT In (cmcwf w)/(cmc8f 8). Figure 6 shows that the number of monomers per micelle n decreases rapidly with the addition of acetone for both surfactants as could be expected although the rate of the change of n could not be predicted more important is the very small change of the apparent charge of the micelle Z(mic) with the...

The catalytic effect can be explained by the increased concentrations of both reagents in the neighborhood of the micelles The diazonium ion is attracted by the opposite charge of the micelles and the naphthylamine by solubilization in the micelles. Rufer succeeded in treating these effects not only qualitatively, but also on a quantitative basis. 

At I — 0, the second term approaches unity. Under such conditions, the value of W for a micelle with rm= 17 A (Tanford, 1973) will be W = 0.205. However, the experimentally measured value (W = 0.0674) is much smaller, indicating that only 33% of the adsorbed SDS molecules are not neutralized by counterions (the extent of neutralization by counterion in pure SDS micelle is 85% (Finstein and Rosano, 1967)). The fractional charge of SDS on micelle and the micellar composition allows calculation of the average charge of the micelles. 

The micellar charge was also corroborated by the Guoy—Chapman diffused, double-layer model. At equilibrium, the surface charge of the micelle alters the ionic composition of the interface with respect to the bulk concentration. The difference between the actual proton concentration on the interface and the one measured at the bulk by pH electrode is observed as a pK shift of the indicator and is related with the Gouy-Chapman potential (Goldstein, 1972). 

Similar studies were carried out using photoionization of benzidine derivatives (Narayanaetal., 1982), phenothiazine(Alkaitisetal., 1975), or pyrene (Gratzel and Thomas, 1974) dissolved in the hydrophobic core of charged micelles. A laser pulse ejects an electron which is rapidly hydrated and then decays into hydroxy radicals, or reacts with the excited cation. The charge of the micelle has a dramatic effect on the rate of the latter reaction but the presence of the former reaction forbade a precise kinetic analysis of the overall reaction. 

Tendeloo (25) found that addition of electrolytes decreases the viscosity of 1% gum arabic sols. If a single electrolyte is added, the viscosity decreases as the valence of the anion increases or as the concentration of the electrolyte increases. The effect of equivalent concentrations of mixed electrolytes is additive. The influence seems proportional to the total amount of electrolytes present. Tendeloo (25) postulates that the influence of the electrolytes is of a capillary-electric character ions alter the electric charge of the micelles which corresponds to a diminution of the degree of hydration, and the magnitude of the effect depends upon the valence of the ions adsorbed. 

One way to optimise a separation is by changing the composition of the aqueous mobile phase. For example, the pH of the buffer can be varied. This can have dramatic effects on the EOF and therefore change the zero retention time to. The charge of the micelles might also be altered by a change in pH, resulting in a different tmc- Furthermore, the degree of the ionisation of the analytes and the electrolyte system depends on the pH. This influences both the capacity factor k and the selectivity factor a. 

In 1988, Ohms [90] demonstrated the separation of 16 nucleic acid derivatives by using the MECC technique as the analytical methods enforceable in a clinical practice. In this case, separation of the neutral species, bases, and nucleosides was effected by partitioning the analytes into micelles, which in turn are carried by the dominant electro-osmotic flow, despite the negative charge of the micelles. Without micelles these species co-migrate as a single band at the electro-osmotic velocity. 

If /(, ,j is the micelle aggregation number and the apparent charge of the micelle, the concentrations of the various constituents are ... 

Fig. 5.15 presents the results obtained for sodium octylsulfate. This surfactant has a high cmc (as 0.135M). The agreement between the theory and experiment [57] is satisfactory below the cmc. Above the cmc, experimental and calculated values deviate rapidly. Finally Fig. 5.16 presents the results obtained for sodium octanoate as a function of total monomer concentration. The cmc is very high ( i 0.4M) and there is also a divergence between experiment and theory above the cmc. There is one fitting parameter the charge of the micelle. 

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