The Stem Layer

Fig. V-3. Schematic representation of (a) the Stem layer (b) the potential-determining ions at an oxide interface (c) the potential-determining and Stem layers together.

The adsorption appears to be into the Stem layer, as was illustrated in Fig. V-3. That is, the adsorption itself reduces the f potential of such minerals in fact, at higher surface coverages of surfactant, the potential can be reversed, indicating that chemical forces are at least comparable to electrostatic ones. The rather sudden drop in potential beyond a certain concentration suggested to... 

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. 

Fig. 2. Schematic diagram of a suspended colloidal particle, showing relative locations of the Stem layer (thickness, 5) that consists of adsorbed ions and the Gouy-Chapman layer (1 /k) which dissipates the excess charge, not screened by the Stem layer, to 2ero ia the bulk solution (108). In the absence of a...

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...). 

Not all of the ions in the diffuse layer are necessarily mobile. Sometimes the distinction is made between the location of the tme interface, an intermediate interface called the Stem layer (5) where there are immobilized diffuse layer ions, and a surface of shear where the bulk fluid begins to move freely. The potential at the surface of shear is called the zeta potential. The only methods available to measure the zeta potential involve moving the surface relative to the bulk. Because the zeta potential is defined as the potential at the surface where the bulk fluid may move under shear, this is by definition the potential that is measured by these techniques (3). 

Kinetic treatments are usually based on the assumption that reaction does not occur across the micelle-water interface. In other words a bimolecular reaction occurs between reactants in the Stern layer, or in the bulk aqueous medium. Thus the properties of the Stem layer are of key importance to the kineticist, and various probes have been devised for their study. Unfortunately, many of the probes are themselves kinetic, so it is hard to avoid circular arguments. However, the charge transfer and fluorescence spectra of micellar-bound indicators suggest that the micellar surface is less polar than water (Cordes and Gitler, 1973 Fernandez and Fromherz, 1977 Ramachan-dran et al., 1982). 

It seems possible that a very hydrophilic anion such as OH- might not in fact penetrate the micellar surface (Scheme 1) so that its interaction with a cationic micelle would be non-specific, and it would exist in the diffuse, Gouy-Chapman layer adjacent to the micelle. In other words, OH" would not be bound in the Stem layer, although other less hydrophilic anions such as Br, CN or N 3 probably would bind specifically in this layer. In fact the distinction between micellar and aqueous pseudophases is partially lost for reactions of very hydrophilic anions. The distinction is, however, appropriate for micellar reactions of less hydrophilic ions. 

The protonation of the triplet jtjt state of 3-bromonitrobenzene is shown to be responsible for the acid-catalysed promotion of halogen exchange which follows a S y23Ar mechanism26 (equation 23). Cationic micellar effects on the nucleophilic aromatic substitution of nitroaryl ethers by bromide and hydroxide ions have also been studied27. The quantum efficiency is dependent on the chain length of the micelle. The involvement of counter ion exchanges at the surface of ionic micelles is proposed to influence the composition of the Stem-layer. 

For present purposes, the electrical double-layer is represented in terms of Stem s model (Figure 5.8) wherein the double-layer is divided into two parts separated by a plane (Stem plane) located at a distance of about one hydrated-ion radius from the surface. The potential changes from xj/o (surface) to x/s8 (Stem potential) in the Stem layer and decays to zero in the diffuse double-layer quantitative treatment of the diffuse double-layer follows the Gouy-Chapman theory(16,17 ... 

The diffuse layer of excess electrons and holes in solids is called the space charge layer and the diffuse layer of excess hydrated ions in aqueous solution is simply called the diffuse layer and occasionally called the Gouy layer [Gouy, 1917]. The middle layer of adsorbed water moleciiles, between the diffuse layer on the aqueous solution side and the space charge layer on the soUd side, is called the compact or the inner layer. This compact or inner layer is also called the Helmholtz layer [Helmholtz, 1879] or the Stem layer [Stem, 1924] the plane of the closest approach of hydrated ions to the solid surface is called the outer Helmholtz plane (OHP) [Graham, 1947]. 

In the Stem model, the surface charge is balanced by the charge in solution, which is distributed between the Stem layer at a distance d from the surface and a diffuse layer having an ionic Boltzman-type distribution. The total charge a is therefore due to the charge in the two layers ... 

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... 

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

The changes in pKa between the aqueous solutions and the micelles must therefore arise from the hydrophobic interactions inside the micelle [27, 31]. In general, the pKa in the micelle is lower than that in its absence, implying that the water molecule inside the micelle is more acidic than that outside. The effect of the hydrophobic interaction of the micellar cavity is further evident in the trend of variation of the pKa with micelle (see Table 1). For all the complexes, the pKa increases in the order anionic SDS > neutral TX-lOO > cationic CTAB. The trend is consistent with the expectation based on consideration of the electrostatic charges in the Stem layer. The anionic SDS micelle, in comparison with CTAB and TX-lOO, stabilizes positive charge on the cationic aqua (pyridinato) ferric heme complexes, and therefore exhibits higher pKa. 

Further evidence for three distinct modes of adsorption can be seen in the electrophoretic behavior of alumina in the presence of sodium dodecyl sulfonate. Below 6 X 10 5M, the electrophoretic mobility is nearly independent of concentration, but at this concentration the slope of the mobility-us.-concentration curve abruptly changes. At 3 X 10"4M dodecyl sulfonate concentration, the electrophoretic mobility reverses its sign, indicating that the charge in the Stem layer now exceeds the surface charge in absolute magnitude. 

Inorganic Ions. Because of electrostatic attraction, positive ions are attracted to negatively charged surfaces and have a higher concentration near the surface than in the bulk. Negative ions are repelled from the negative surface and have a lower concentration near that surface. Ions which are very strongly bound (/zADS > kT) are in the Stem layer, whereas those that can move into and out of the ionic atmosphere (nADS < kT) are in the Helmholtz layer. The effect of ionic attraction or repulsion from the surface is to enhance or reduce the nonionic adsorption coefficient ... 

An important quantity with respect to experimental verification is the differential capacitance of the total electric double layer. In the Stern picture it is composed of two capacitors in series the capacity of the Stem layer, Cgt, and the capacitance of the diffuse Gouy-Chapman layer. The total capacitance per unit area is given by... 

Double layer Two layers of ions associated with a charged particle in an aqueous solution. The Stem layer is attached onto the surface of the particle. The diffuse Gouy layer surrounds particle and its Stem layer. 

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. 

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