Stem layer, counterions

Surface active electrolytes produce charged micelles whose effective charge can be measured by electrophoretic mobility [117,156]. The net charge is lower than the degree of aggregation, however, since some of the counterions remain associated with the micelle, presumably as part of a Stem layer (see Section V-3) [157]. Combination of self-diffusion with electrophoretic mobility measurements indicates that a typical micelle of a univalent surfactant contains about 1(X) monomer units and carries a net charge of 50-70. Additional colloidal characterization techniques are applicable to micelles such as ultrafiltration [158]. 

The layer of solution immediately adjacent to the surface that contains counterions not part of the soHd stmcture, but bound so tightly to the surface that they never exchange with the solution, is the Stem layer. The plane separating this layer from the next is the Stem plane. The potential at the Stem plane is smaller than that at the surface. 

As the pH is iacreased or decreased from the isoelectric point, the particles acquire a charge (surface potential) that can enhance repulsion. Surface charge on the particle can be approximated by measuring 2eta potential, which is the electrostatic potential at the Stem layer surrounding a particle. The Stem layer is the thickness of the rigid or nondiffiise layer of counterions at a distance (5) from the particle surface, which corresponds to the electrostatic potential at the surface divided by e (2.718...). 

Certain counterions may be held in the compact region of the donble layer by forces additional to those of purely electrostatic origin, resulting in their adsorption in the Stem layer. Specifically... 

Figure 2 Conventional representation of micelles formed by an ionic surfactant, such as sodium dodecyl sulfate. The inner core region consists of the methylene tails of the surfactants. The Stem layer consists of surfactant headgroups and bound counterion species. The diffuse double layer consists of unbound counterions and coions which preserve the electrical neutrality of the overall solution. Also pictured are the transition moment vectors for the S-O stretching modes of sodium dodecyl sulfate.

For the Tar—Tar kissing loops, the P—B calculations are unable to discern their propensity to accumulate counterions accumulation at the loop—loop interface (data not shown). This is because the fully hydrated ions as defined by the Stem layer cannot penetrate into the central cation binding pocket (data not shown). Similarly, the axial spine of counterion density observed in the A-RNA helix (Fig. 20.5) is not captured by the P—B calculation (Fig. 20.7). No noticeable sequence specificity is observed in the counterion accumulation patterns in the P—B calculations, even though the sequence effects are explicitly represented in the P—B calculation through the appropriate geometry and assignment of point-charges. This is because the sequence specificity observed in the molecular dynamics simulations usually involves first shell interactions of base moieties with partially dehydrated ions, which cannot be accurately represented in the P—B framework. 

We first used isotope substitution in diffuse neutron scattering measurements to determine the distribution of water molecules and counterions (n-butylammonium ions) around the clay layers in the gel state, and obtained a unique picture of a dressed macroion in solution. We obtained a structure in which the naked clay plate of 10 A thickness was extended out to about 35 A by layers of water molecules and counterions. The dressed macroion has exactly two layers of water molecules coating the clay layers these layers are 6 A thick on both sides, extending the effective clay plate out to 22 A, before any counterions at all are found. This is in direct contradiction to the Stem layer picture, widely held in colloid science, that... 

The adsorbed Stem layer is compensated by a compact and essentially fixed layer of hydrated counterions and water molecules which takes the form of a molecular capacitor between the inner and outer Helmholtz planes shown in Figure 9.14. The solid surface adsorbs the Stem layer ions and gives a potential of the inner Helmholtz plane, which is partially compensated by the hydrated counterions and water molecviles of the outer Helmholtz plane. The diffuse double layer of (jOuy-Chapman starts at the OHP and extends further into the liquid. 

Here is the radius of particle a. The hard wall repulsion is equivalent to the introduction of a distance of closest approach for the counterions in order to define a Stem layer thickness. In a more restricted primitive model the radius a is set identical for all ionic species. The Coulomb term in 3.6.3] represents the interaction of an ion with a charge q at jc, with the surface charge and its image. According to Coulomb s law. 

Panel (b) pictures the case corresponding to that of double layers with a chcU ge-free Stem layer, considered in sec. 11.3.6c. To indicate that the counterions, say Na ions, retain their hydration shells they are given a bigger volume. For the diffuse part y = Fy /RT is obtainable from... 

The purely electrostatic diffuse layer model often underestimates the affinity of the counterions to the surface. In the Stem model, the surface charge is partially balanced by chemisorbed counterions (the Stem layer), and the rest of the surface charge is balanced by a diffuse layer. In the Stern model, the interface is modeled as two capacitors in series. One capacitor has a constant capacitance (independent of pH and ionic strength), which represents the affinity of the surface to chemisorbed counterions, and which is an adjustable parameter the relationship between a, and Vd in the other capacitor (the diffuse layer) is expressed by Equation 2.18. A version of the Stern model with two different values of C (below and above pHg) has also been used. The capacitance of the Stem layer reflects the size of the hydrated counterion and varies from one salt to another. The correlation between cation size and Stern layer thickness was studied for a silica-alkali chloride system in [733]. Ion specificity of adsorption on titania was discussed in terms of differential capacity as a function of pH in [545]. The Stern model with the shear plane set at the end of the diffuse layer overestimated the absolute values of the potential of titania [734]. A better fit was obtained with the location of the shear plane as an additional adjustable parameter (fitted separately for each ionic strength). Chemisorption of counterions can also be quantified within the chemical model in terms of expressions similar to the mass law (Section 2.9.3.3). 

FIGURE 5.1 Electric double layer in the vicinity of an adsorption layer of ionic surfactant, (a) The diffuse layer contains free ions involved in Brownian motion, whereas the Stem layer consists of adsorbed (bonnd) counterions, (b) Near the charged snrface there is an accnmnlation of counterions and a depletion of coions. 

The adsorption of the coions of the nonamphiphilic salt is expected to be equal to zero, Fj = 0, because they are repelled by the similarly charged interface. However, the adsorption of surfactant at the interface, Fj, and the binding of counterions in the Stem layer, F2, are different from zero (Figure 5.1). For this system the Gouy Equation 5.33 acquires the form ... 

In general, the total adsorption F of an ionic species include contributions from both the adsorption layer (surfactant adsorption layer + adsorbed counterions in the Stem layer), F , and the diffuse layer,... 

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. 

FIGURE 2-4 Stem model of the electrical double layer, showing reversal of the sign of the charged surface caused by adsorption of counterions in the Stem layer. 

Surrounding the core is the Stem layer where the charged head groups (SO3) of the surfactant 2 are located together with the counterions (Na+) in a compact region a few angstroms wide. The rhodium atom of the catalyst is probably located... 

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