Layer, Stem

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.

Figure V-8 illustrates that there can be a pH of zero potential interpreted as the point of zero charge at the shear plane this is called the isoelectric point (iep). Because of specific ion and Stem layer adsorption, the iep is not necessarily the point of zero surface charge (pzc) at the particle surface. An example of this occurs in a recent study of zircon (ZrSi04), where the pzc measured by titration of natural zircon is 5.9 0.1...

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

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... 

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]. 

For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

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. 

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 repeUed from the negative surface and have a lower concentration near that surface. Ions which are very strongly bound (// ds Stem layer, whereas those that can move into and out of the ionic atmosphere < kT) are in the Helmholtz... 

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...

Stem layer, the Gouy-Chapman layer dissipates the surface charge. 

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). 

The electroosmotic pumping is executed when an electric field is applied across the channel. The moving force comes from the ion moves in the double layer at the wall towards the electrode of opposite polarity, which creates motion of the fluid near the walls and transfer of the bulk fluid in convection motion via viscous forces. The potential at the shear plane between the fixed Stem layer and Gouy-Champmon layer is called zeta potential, which is strongly dependent on the chemistry of the two phase system, i.e. the chemical composition of both solution and wall surface. The electroosmotic mobility, xeo, can be defined as follow,... 

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 treatments discussed thus far are based on the assumption that reaction occurs in the micellar Stem layer or in the aqueous medium with no reaction across the boundary between them. The concentration of counter-... 

In a functional micelle in which the reactive group is fully deprotonated there is a 1 1 relationship between the concentrations of reactive nucleophile and micellar head group in the micellar pseudophase. If under these conditions the substrate is fully micellar bound, (5) or (6) take the very simple form (19). This rate constant, kM, can then be converted into the second-order rate constant, k in M 1s 1, estimating the volume element of reaction, VM, which can be assumed to be that of the micelle or of its Stem layer, and these second-order rate constants can be compared with reaction in water of a chemically similar, non-micellized, nucleophile. 

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. 

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