Counterion concentration

The concentration of free surfactant, counterions, and micelles as a function of overall surfactant concentration is shown in Fig. XIII-13. Above the CMC, the concentration of free surfactant is essentially constant while the counterion concentration increases and... 

If an ionic surfactant is present, the potentials should vary as shown in Fig. XIV-5c, or similarly to the case with nonsurfactant electrolytes. In addition, however, surfactant adsorption decreases the interfacial tension and thus contributes to the stability of the emulsion. As discussed in connection with charged monolayers (see Section XV-6), the mutual repulsion of the charged polar groups tends to make such films expanded and hence of relatively low rr value. Added electrolyte reduces such repulsion by increasing the counterion concentration the film becomes more condensed and its film pressure increases. It thus is possible to explain qualitatively the role of added electrolyte in reducing the interfacial tension and thereby stabilizing emulsions. 

To accomplish any separation of two cations (or two anions) of the same net charge, the stationary phase must show a preference for one more than the other. No variation in the eluant concentration will improve the separation. However, if the exchange involves ions of different net charges, the separation factor does depend on the eluant concentration. The more dilute the counterion concentration in the eluant, the more selective the exchange becomes for polyvalent ions. 

The Gibbs equation allows the amount of surfactant adsorbed at the interface to be calculated from the interfacial tension values measured with different concentrations of surfactant, but at constant counterion concentration. The amount adsorbed can be converted to the area of a surfactant molecule. The co-areas at the air-water interface are in the range of 4.4-5.9 nm2/molecule [56,57]. A comparison of these values with those from molecular models indicates that all four surfactants are oriented normally to the interface with the carbon chain outstretched and closely packed. The co-areas at the oil-water interface are greater (heptane-water, 4.9-6.6 nm2/molecule benzene-water, 5.9-7.5 nm2/molecule). This relatively small increase of about 10% for the heptane-water and about 30% for the benzene-water interface means that the orientation at the oil-water interface is the same as at the air-water interface, but the a-sulfo fatty acid ester films are more expanded [56]. 

In principle, all the curves in Figs. 6.1a, 6.2a, and 6.3a would be expected to have solubility limits imposed by the salt formation. Under conditions of a constant counterion concentration, the effect would be indicated as a point of discontinuity (pA flbbs), followed by a horizontal line of constant solubility. S, -. 

Usually, the solubility of the salt is determined from separate, more concentrated solutions. To conserve on sample, the titration of the salt may be performed with an excess of the counterion concentration [479]. Also, some amount of sample salt may be conserved by titrating in cosolvent mixtures, where salts are often less soluble. 

However in Table IV we see no increase in W at 1%, and only a small increase at 2% of dispersant. The value of W increases rapidly at about the same concentration that the conductivity increases, the counterion concentration increases and the zeta-potential increases. At OLOA-1200 levels of 3.5% and higher the stability ratio exceeds 5x10, with half-times in excess of seven months these stability ratios developed when zeta-potentials were -120 mV or more. 

A stoichiometric model can conveniently be invoked to explain the ion-exchange retention process [43 6]. As discussed in detail in these cited papers on ion-exchange theory, useful information about the involved ion-exchange process can be deduced from plots of log k vs. the log of the counterion concentration [X], which commonly show linear dependencies according to the stoichiometric displacement model (Equation 1.1)... 

This should be illustrated by the counterion concentration dependencies of three different model solutes, namely Af-3,5-dinitrobenzoylated serine (DNB-Ser), aspartic acid (DNB-Asp), and O-phosphoserine (DNB-PSer), which are structural analogs that differ in the number of nominal charges. The solutes have been analyzed in the RP mode with methanol-phosphate buffer (50 50 v/v) (pH 6.5) under variable phosphate concentrations. The results are shown in Figure 1.4. 

From Figure 1.3, it becomes also evident that, while the slopes of the distinct solutes are different, those of the corresponding enantiomers are nearly the same. This means that for both enantiomers an ion-exchange process is at work and both isomers respond almost equally sensitive to the variation of the counterion concentration. In other words, the separation factors are usually almost unaffected by the counterion concentration, which opens up the possibility for a flexible adjustment... 

It largely obeys the trend predicted by Equation 1.4. Maximal retention may be expected when both selector and analyte are dissociated to a high degree (i.e., where the product of and reaches a maximum value). For carboxylic acids, this retention maximum is usually found between pH 5 and 6, where the enantiose-lectivity also adopts its optimum (see Figure 1.5). Above this pH, the retention is decreased because (i) the dissociation of the selector becomes increasingly reduced, (ii) the effective counterion concentration may be increased, and (iii) the superimposed hydrophobic retention increment of the solute on the bonded phase loses its... 

Moreover, in various experiments it was found that at a constant total counterion concentration in the eluent the dependence of the retention factors on the organic modifier content tp largely follows the linear solvent strength theory (LSS) (Equation 1.5)... 

Noticing that the average counterion concentration is Nc for fully ionized polyelectrolytes, we obtain... 

Figure 4. Log cmc vs total counterion concentration in solutions of CjijPyBr and C sPyBr with added NaCl. Broken lines cmc of corresponding chlorides (refs. 35,36). Arrows extrapolated cmc s.

The threshold salt concentration above which the brush contraction sets in is given by the salt concentration which equals the counterion concentration inside the brush. This means that the higher the grafting density (and consequently the higher the internal counterion concentration in the osmotic brush regime), the larger the salt concentration necessary to see any salt effects at all. 

When the added salt is strongly dissociated and the ion pairs slightly dissociated, the counterion concentration is very close to that of the added salt [CZ] ... 

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... 

As the reasons for rate retardations have been discussed for pseudounimolecular probe reactions already, we focus on the reported increased bimolecular rate constants. Two main reasons for increases in bimolecular rate constants come to the fore (1) dehydration of the reactive counterions and (2) charge delocalization during the activation process leading to the transition state. An intriguing third reason (although, admittedly, not strictly equating to an increased bimolecular rate constant) is (3) the increase in local counterion concentration as a result of comoving counterions. We will discuss these three effects in order. 

FIGURE 15.9 The counterion concentration as a function of the distance from a surface according to the G-C theory for three different hulk concentrations of a 1 1 electrolyte 1, 50, and 500mM, respectively. The surface charge density is kept constant to -0.1 C/m. ... 

The activation energies calculated for the two steps of the above reaction are + 160 kJ/mol for the ki step and -l- 78 kJ/mol for the k2 step [15]. The overall enthalpy of reaction is — 78 kJ/mol. It has been found that the half-life for the ki reaction is sensitive to the counterion concentration in case of SDS micelles. The effect of added counterion may be due to the charge neutralisation of the sulphate anion heads in the SDS micellar Stern layer, to facilitate approach and penetration of the CN- ions at the micelle-water interface. Hemin encapsulated in CTAB micelles reacts much faster with cyanide compared to that in SDS presumably because of the cationic Stern layer in CTAB. The... 

After algebraic manipulations, the model reduces to the solution of the following four nonlinear equations for x and the monomer and counterion concentrations Cj, C2, and Cf + ... 

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