Degree of counterion binding

Here (log cmc) is tire log cmc in tire absence of added electrolyte, is related to tire degree of counterion binding and electrostatic screening and c- is tire ionic strengtli (concentration) of inert electrolyte. Effects of added salt on cmc are illustrated in table C2.3.7. 

In Figure 3, the curves for the ionic/ionic systems are all below the curve for the nonionic/nonionic case. As the degree of counterion binding increases, i.e. as y9j and increase, the value of c /c2 decreases for a given value of a. The bottom curve in Figure 3 corresponds to the ionic/ionic system with Pi = 0.6, P2 = 0.0, and P = 1.0. This case is probably physically unrealistic, inasmuch as these parameters correspond to a system in which both surfactants 1 and 2 are ionic and contribute counterions to the system but surfactant 2 in the micelles acts as a nonionic surfactant and therefore has a zero degree of counterion binding. 

The effect of methanol on micellar solutions is slight at the low concentration used (5% v/v = 1.3 mol/L = 0.022 mole fraction). The effect of NaCl however, is more significant the CMC is greatly decreased, the degree of counterion binding and the aggregation number are increased. 

Solution behavior of ionomers can be divided into two types, primarily depending on the polarity of the solvent [46,47], One is polyelectrolyte behavior due to the dissociation of counterions in polar solvents (e.g., DMF), and another is association behavior due to the formation of ion pairs and even higher order aggregates in less polar solvents (e.g., THF). Table 2 shows the solvents frequently used for the study of ionomer solutions, as well as their dielectric constants. As the dielectric constant decreases, the degree of counterion binding and also ion pair formation changes (increases) gradually, and so does the solution behavior. In this chapter, only the polyelectrolyte behavior of ionomers in a polar solvent is described. Some brief... 

For non-ionic/ionic mixed micelles the degree of counterion binding must be proportional to the mole fraction of ionic component, in contrast to experimental observations. 

Theories, considering changes of the micellar electrical potential and degree of counterion binding form a third group [29, 30, 47, 48]. 

If the adsorption values are the same in both relations (5.143), an expression for the degree of counterion binding from experimental surface tensions can be easily obtained... 

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. 

Figure 19.13. Concentrations of micellar and free unimeric surfactant ions (-F) and counterions (—) as a function of the total surfactant (decylammonium dichloroacetate) concentration p is the degree of counterion binding. (Redrawn from P. Stilbs and B. Lindman, J. Phys. Chem., 85 (1981) 2587)...

The self-diffusion coefficient method was developed originally by Lindman and co-workers [42], This method is by far the most powerful and successful application of NMR in the study of surfactant systems. The self-diffusion method permits a full characterization of the system under investigation, since it can yield the values of the free monomeric surfactant concentration, the degree of counterion binding, and the amount of water bound (hydration). Moreover, these data can help one deduce the information on micelle size, shape, and composition from the monomer surfactant concentration in a surfactant mixture ... 

A Degree of Counterion Binding (fi) Discussion has concentrated on the degree of counterion binding (fi) [38,55,59]. The ratio of the slopes of the conductivity versus concentration curve above and below the CMC gives the degree of coimterion... 

Many theoretical discussions have centered on the degree of counterion binding to micelles, because an understanding of the specific binding of counterions to micelles is a prerequisite for an understanding not only... 

Table 4.2. Degree of Counterion Binding to Micelles (m/n) of Sodium Dodecyl Sulfate"...

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