Counterion binding estimate

This calculation is for spherical micelles, but a similar calculation could be used to obtain estimates of salt concentrations for ionic wormlike micelles. Such salt concentrations for wormlike micelles are expected to be increased in comparison to spherical micelles. In fact, the addition of counterions or a sufficient increase in surfactant concentration often leads to a transition from spherical micelles to wormlike micelles. As the free counterion concentration in solution increases, so does the counterion binding. As a result, electrostatic repulsion between the charged head-groups is increasingly shielded and the mean cross-sectional (effective) headgroup... 

The mass action model (MAM) for binary ionic or nonionic surfactants and the pseudo-phase separation model (PSM) which were developed earlier (I EC Fundamentals 1983, 22, 230 J. Phys. Chem. 1984, 88, 1642) have been extended. The new models include a micelle aggregation number and counterion binding parameter which depend on the mixed micelle composition. Thus, the models can describe mixtures of ionic/nonionic surfactants more realistically. These models generally predict no azeotropic micellization. For the PSM, calculated mixed erne s and especially monomer concentrations can differ significantly from those of the previous models. The results are used to estimate the Redlich-Kister parameters of monomer mixing in the mixed micelles from data on mixed erne s of Lange and Beck (1973), Funasaki and Hada (1979), and others. 

Equilibrium constants for Reactions 4 and 5 were estimated by trial and error to fit the experimental dodecylsulfate adsorption data. No counterion binding reaction, equivalent to Reaction 2, was needed. The experimental data and simulation are compared in Figure 4. 

BAK Bakshi, M.S., Kaur, N., Mahajan, R.K., Singh, J., and Sing, N., Estimation of degree of counterion binding and related parameters of monomeric and dimeric cationic surfactants from cloud point measurements by using triblock polymer as probe. Coll. Polym. Sci., 284, 879, 2006. 

The two-site model leads to the definition of the degree of counterion binding, p, as the ratio of counterions to surfactant ions in a surfactant self-assembly. This is a useful but incomplete characterization of the counterion distribution. The value of p can be obtained directly from self-diffusion data because the self-diffusion coefficients of free ions are easily obtainable. For free counterion diffusion a correction is made for the obstruction effect. The micellar D value is obtained as described above or estimated as Dm free. an exact Dm value is not critical. 

Funasaki [30] has found that as the concentration of CTAB is increased above the CMC, the surface hydroxide ion concentration decreased and bromide counterions were bound to the surface of the micelle in place of carbonate and hydrogen carbonate ions. The rate constant at the micellar surface, which could be estimated by analysis of the results, was found to be proportional to surface OH concentration and to decrease with increasing Br concentration at the surface, as in the bulk phase. This, he suggests, explains the profile for PNPB hydrolysis in CTAB-carbonate buffer systems, shown in Fig. 11.5. Counterion binding was estimated by measurement of bromide ion activities, from which the degree of dissociation of the bromide can be calculated. 

Yoshida et al. [173] estimated the degree of counterion binding from the slope of this relationship (see Section 6.5). Fluorination of the counterion in-... 

The kinetic micellar units include about half of the counterions the mesoaggregates bind counterions even more firmly. It can be estimated from activity measurements, however, that a considerable proportion of... 

Regarding the second point above, we used the slope differences above the CMC to estimate the difference in relative binding of Mg2+ and Ca2+ to the micelle by a method similar to that developed by Evans (24). If the micelle is composed of p long chain ions, X, and q univalent counterions, Me, where Me = Na+, % Mg2+, % Ca2+, etc., the aggregation process can be represented by... 

On the other hand data reported in Fig. 8 Indicate that the higher charge-density of Xanthan compared to PS-10 shows up in a higher heat of Cu ion binding and in a lower activity coefficient of Na counterions. From the initial slope of the Qg against [Cu2tl /N plots of Fig. 6 one estimates for Xanthan in water a differential enthalpy of Cu2+ binding of about 1 Kcal per mole of copper bound. In conclusion, as found with the sulfated polysaccharides (Fig. 4) as well as with different synthetic poly-carboxylates ( ), chelation of Cu2+ ions by polyanions is a process systematically driven by the entropy. 

The same sequences of perturbation are obtained if the specific volumes of polyelectrolytes are measured [18]. These ultrasonic experiments are the best proof of site binding and the importance of water perturbation at the origin of the ion selectivity nevertheless it is a global measurement and only a spectroscopic experiment would be convenient to estimate the number of associated counterions. 

It is probably a good approximation to consider only two binding sites of the counterions, i.e. either they are free or they are bound to the amphiphilic aggregates. The fraction of bound counterions can be estimated from observations by other methods to be in the range 0.6 - 0.9. 

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