Counterion adsorption

The controhing effect of various ions can be expressed in terms of thermodynamic equhibria [Karger and DeVivo, Sep. Sci., 3, 393 1968)]. Similarities with ion exchange have been noted. The selectivity of counterionic adsorption increases with ionic charge and decreases with hydration number [Jorne and Rubin, Sep. Sci., 4, 313 (1969) and Kato and Nakamori, y. Chem. Eng. Japan, 9, 378 (1976)]. 

The parameter n increases exponentially with increasing surface charge further approximated as follows ... 

Co/pH and V o/pH results are sensitive to different aspects of the surface chemistry of oxides. Surface charge data allow the determination of the parameters which describe counterion complexation. Surface potential data allow the determination of the ratio /3 —< slaDL- Given assumptions about the magnitude of the site density Ns and the Stern capacitance C t, this quantity can be combined with the pHp2C to yield values of Ka and Ka2. Surface charge/pH data contain direct information about the counterion adsorption capacitances in their slope. To find the equilibrium constants for adsorption, a plot such as those in Figures 7 and 8 can be used, provided that Ka and Kai are independently known from V o/pH curves. 

Figure 9. The V o/pH response of AI2O3 presented in a reduced fashion, to remove the dominant linear response Vo = Vo + 48(pi — 8) (mV). The various electrolytes at 0.1M concentration are 0 NaCl, A NaH2P04/Na2HP04, Merck buffer. Line a is the site-dissociation theory without counterion adsorption, and the other lines include various amounts of counterion adsorption. Reproduced with permission from Ref. (14). Copyright 1983, North Holland.

The zeta potential is also modified by the ionic strength. When ionic strength increases, the absolute value of Zeta potential reduces. This observed phenomenon can be explained by both the presence of more counterions in the shear layer due to the decreasing double-layer thickness and to the increasing counterion adsorption into the stern layer. 

In Eq. 38, the partial surface coverage, 0i, of the surfactant is defined as 01 = ri/Foo, where Ao is the surface excess of surfactant at saturation. K is the adsorption constant, which is a function of the surfactant and counterion adsorptions. The dependence is usually linear, yielding K = Ki + K20.1, where Ki and A are the equilibrium adsorption constants of the surfactant ions and their counterions. 

Table II shows that morpholinium laurate is markedly less effective in enhancing mechanical stability than are the other laurates which have been investigated. This is attributed to specific counterion adsorption, with a consequent reduction of the effective surface potential at the rubber-water interface.

Another prediction of the model is the decrease in the size of the polymer as the salt concentration is increased [48]. If counterion adsorption is dominant, the interactions between the ion pairs are attractive in nature, and leads to the radius of gyration being less than that of a Gaussian chain [48],... 

Although electrokinetlc potentials belong to the most common characteristics of charged surfaces, their interpretation In terms of double layer potentials Is not yet straightforward. Rarely is identical to mostly it is lower, if not much lower. When superequivalent counterion adsorption occurs even the signs of f and 1//° differ. In these respects f rather resembles a correspondence that is supported by the frequently observed correlation between electrokinetlc potentials and the stability of electrocratlc colloids. 

In the acidic route (with pH < 2), both kinetic and thermodynamic controlling factors need to be considered. First, the acid catalysis speeds up the hydrolysis of silicon alkoxides. Second, the silica species in solution are positively charged as =SiOH2 (denoted as I+). Finally, the siloxane bond condensation rate is kinetically promoted near the micelle surface. The surfactant (S+)-silica interaction in S+X 11 is mediated by the counterion X-. The micelle-counterion interaction is in thermodynamic equilibrium. Thus the factors involved in determining the total rate of nanostructure formation are the counterion adsorption equilibrium of X on the micellar surface, surface-enhanced concentration of I+, and proton-catalysed silica condensation near the micellar surface. From consideration of the surfactant, the surfactants first form micelles as a combination of the S+X assemblies, which then form a liquid crystal with molecular silicate species, and finally the mesoporous material is formed through inorganic polymerization and condensation of the silicate species. In the S+X I+ model, the surfactant-to-counteranion... 

A surfactant adsorption isotherm, E, = E,(a,j,fl2j), and a counterion adsorption isotherm, Ej = E2(fljj,fl2s), are thermodynamically compatible only if they satisfy Equation 5.46. The counterion adsorption isotherm is usually taken in the form ... 

For the solution without NaCl the occupancy of the Stem layer, r2/Ti rises from 0.15 to 0.73 and then exhibits a tendency to level off. The latter value is consonant with data of other authors, who have obtained values of r2/Fi up to 0.70 to 0.90 for various ionic surfactants pronounced evidences for counterion binding have been obtained also in experiments with solutions containing surfactant micelles." ° As could be expected, both Fj and F2 are higher for the solution with NaCl. These results imply that the counterion adsorption (binding) should be always taken into account. 

The above discussion by no means implies that other contributions to nei, such as counterion adsorption or discrete ion effects, are not oper-... 

The interfacial mass balance, interrelating the change of the surfactant or counterion adsorptions Tj with time and the respective electro-diffusion influx from the bulk, reads... 

Figure 6 Ionic surfactant solution relaxation times of interfacial tension, x j, of surfactant adsorption, x j, and of counterion adsorption (binding), X2, calculated in Ref. 36 as functions of surfactant (SDS) concentration, cj q, using parameters values determined from the best fit of experimental data in Ref. 17. (a) SDS solutions with 115 mM added NaCl (b) SDS solutions without added NaCl.

Counterion adsorption For a metal cation in the presence of two different anions, the anion with the highest potential to form surface complexes controls the metal s adsorption potential. For example, Ni " in the presence of Ca(N03) exhibits greater adsorption potential than Ni " in the presence of CaS04 because of the sulfate s potential to react with the surface and produce sites with higher specificity for Ca +. 

As illustration, we consider the interpretation of experimental isotherms by Tajima et al. [40,42,43] for the surface tension o versus SDS concentrations at 11 fixed concentrations of NaCl, see Figure 4.2. Processing the set of data for the interfacial tension o = o(Ci , C2J as a function of the bulk concentrations of surfactant (DS ) ions and Na" counterions, and C2 , we can determine the surfactant adsorption, Fi(ci , C2J, the counterion adsorption, F2(Ci , C2J), the surface potential, Vs(Ci< . Czo=)> and the Gibbs elasticity gCcioo, C2J for every desirable surfactant and salt concentrations. 

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