The Stern layer

Stern combined the ideas of Helmholtz and that of a diffuse layer [64], In Stern theory we take a pragmatic, though somewhat artificial, approach and divide the double layer into two parts an inner part, the Stern layer, and an outer part, the Gouy or diffuse layer. Essentially the Stern layer is a layer of ions which is directly adsorbed to the surface and which is immobile. In contrast, the Gouy-Chapman layer consists of mobile ions, which obey Poisson-Boltzmann statistics. The potential at the point where the bound Stern layer ends and the mobile diffuse layer begins is the zeta potential (C potential). The zeta potential will be discussed in detail in Section 5.4. 

Stern layers can be introduced at different levels of sophistication. In the simplest case we only consider the finite size effect of the counterions (Fig. 4.5). Due to their size, which in water might include their hydration shell, they cannot get infinitely close to the surface but always remain at a certain distance. This distance 5 between the surface and the centers of these counterions marks the so-called outer Helmholtz plane. It separates the Stern from the Gouy-Chapman layer. For a positively charged surface this is indicated in Fig. 4.5. 

7 Otto Stern, 1888-1969. German physicist, professor in ffamburg. Nobel Prize in physics in 1943. 

At the next level we also take specific adsorption of ions into account (Fig. 4.6). Specifically adsorbed ions bind tightly at a short distance. This distance characterizes the inner Helmholtz plane. In reality all models can only describe certain aspects of the electric double layer. A good model for the structure of many metallic surfaces in an aqueous medium is shown in Fig. 4.6. The metal itself is negatively charged. This can be due to an applied potential or due to the dissolution of metal cations. Often anions bind relatively strongly, and with a certain specificity, to metal surfaces. Water molecules show a distinct preferential orientation and thus a strongly reduced permittivity. They determine the inner Helmholtz plane. 

Next comes a layer of nonspecifically adsorbed counterions with their hydration shell. Still, the permittivity is significantly reduced because the water molecules are not free to rotate. This layer specifies the outer Helmholtz plane. Finally there is the diffuse layer. A detailed discussion of the structure of the electric double layer at a metal surface is included in Ref. [65], 

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

Let us estimate Cst using the simple equation for a plate capacitor. The two plates are formed by the surface and by the adsorbed ions. Denoting the radius of the hydrated ions by l on, the distance is in the order of Rjon /2 2 A The capacitance per unit area of the Stem layer is Cg, = 2EstEo/rion- The permittivity at the surface is reduced and typically ofthe order of Est w 6-32forwater. Using a value of Esi = lOwe estimate a capacitance for the Stern layer of = 0.44 Fm = 44(iFcm . Experimental values are typically 10-100 p, F cm .  

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The mechanism by which analytes are transported in a non-discriminate manner (i.e. via bulk flow) in an electrophoresis capillary is termed electroosmosis. Eigure 9.1 depicts the inside of a fused silica capillary and illustrates the source that supports electroosmotic flow. Adjacent to the negatively charged capillary wall are specifically adsorbed counterions, which make up the fairly immobile Stern layer. The excess ions just outside the Stern layer form the diffuse layer, which is mobile under the influence of an electric field. The substantial frictional forces between molecules in solution allow for the movement of the diffuse layer to pull the bulk... 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

The solvation dynamics of the three different micelle solutions, TX, CTAB, and SDS, exhibit time constants of 550, 285, 180 ps, respectively. The time constants show that solvent motion in these solutions is significantly slower than bulk water. The authors attribute the observed time constants to water motion in the Stern layer of the micelles. This conclusion is supported by the steady-state fluorescence spectra of the C480 probe in these solutions. The spectra exhibit a significant blue shift with respect the spectrum of the dye in bulk water. This spectral blue shift is attributed to the probe being solvated in the Stern layer and experiencing an environment with a polarity much lower than that of bulk water. 

This work also shows that the time constants for the ionic surfactant micelle solutions are twice as fast as the TX solution time constant. Differences between the Stern layers of the micelles appear to be the charge of the surfactant polar headgroups and the presence of counterions. However, these differences do not account for the observed dynamics. Since the polar headgroups and counterions should interfact more strongly with the water molecules, the water motion at the interface should be slower. This view is supported by recent investigations where systematic variation of surfactant counter-... 

The classical model, as shown in Figure 1, assumes that the micelle adopts a spherical structure [2, 15-17], In aqueous solution the hydrocarbon chains or the hydrophobic part of the surfactants from the core of the micelle, while the ionic or polar groups face toward the exterior of the same, and together with a certain amount of counterions form what is known as the Stern layer. The remainder of the counterions, which are more or less associated with the micelle, make up the Gouy-Chapman layer. For the nonionic polyoxyethylene surfactants the structure is essentially the same except that the external region does not contain counterions but rather rings of hydrated polyoxyethylene chains. A micelle of... 

As can be seen by Reactions 10.1-10.4, the state of the Stern layer depends on the chemistry of the solution it contacts. As pH decreases, the numbers of protonated sites (e.g., >(w)FeOH+) and sites complexed with bivalent anions (e.g., >(w)FeS04) increase. If protonated sites dominate, as is likely under acidic conditions, the surface has a net positive charge. 

Kl Base dissociation constant in a micelle based on molarity in the Stern layer... 

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). 

But this static picture is clearly inadequate, because solutes and surfactant monomers move rapidly from water to micelles, and the surfactant head groups will oscillate about some mean position at the micelle surface (Aniansson, 1978). Non-ionic substrates are not localized within the micelle or its Stern layer and there is no reason to believe that they are distributed uniformly within the Stern layer. 

Calculations based on non-specific coulombic interactions between the micelle and its counterions gave reasonable values of a, which were insensitive to the concentration of added salt (Gunnarsson et al., 1980). Although these calculations do not explain the observed specificity of ion binding, they suggest that such hydrophilic ions as OH- and F- may not in fact enter the Stern layer, as is generally assumed. Instead they may cluster close to the micelle surface in the diffuse layer. 

Similar considerations apply to situations in which substrate and micelle carry like charges. If the ionic substrate carries highly apolar groups, it should be bound at the micellar surface, but if it is hydrophilic so that it does not bind in the Stern layer, it may, nonetheless, be distributed in the diffuse Gouy-Chapman layer close to the micellar surface. In this case the distinction between sharply defined reaction regions would be lost, and there would be some probability of reactions across the micelle-water interface. 

The problem may be a semantic one because OH- does not bind very strongly to cationic micelles (Romsted, 1984) and competes ineffectively with other ions for the Stern layer. But it will populate the diffuse Gouy-Chap-man layer where interactions are assumed to be coulombic and non-specific, and be just as effective as other anions in this respect. Thus the reaction may involve OH- which is in this diffuse layer but adjacent to substrate at the micellar surface. The concentration of OH- in this region will increase with increasing total concentration. This question is considered further in Section 6. 

Based on a molar volume of the Stern layer of 0.14 M 1 litre unless specified b Comicelle with inert surfactant c Micellar molar volume of 0.36 M -1 litre... 

Fig. 17.2. The distribution of charges at the internal wall of a silica capillary. x is the length in cm from the center of charge of the negative wall to a defined distance, 1 = the capillary wall, 2 = the Stern layer or the inner Helmholtz plane, 3 = the outer Helmholtz plane, 4 = the diffuse layer and 5 = the bulk charge distribution within the capillary.

Some colloid chemists often place these specifically bound cations and anions in the Stern layer (see Chapter 3.2). From a coordination chemistry point of view it does not appear very meaningful to assign a surface-coordinating ion to a layer different than H or OH in a =MeOH group. 

The rate constants for the reaction of a pyridinium Ion with cyanide have been measured in both a cationic and nonlonic oil in water microemulsion as a function of water content. There is no effect of added salt on the reaction rate in the cationic system, but a substantial effect of ionic strength on the rate as observed in the nonionic system. Estimates of the ionic strength in the "Stern layer" of the cationic microemulsion have been employed to correct the rate constants in the nonlonic system and calculate effective surface potentials. The ion-exchange (IE) model, which assumes that reaction occurs in the Stern layer and that the nucleophile concentration is determined by an ion-exchange equilibrium with the surfactant counterion, has been applied to the data. The results, although not definitive because of the ionic strength dependence, indicate that the IE model may not provide the best description of this reaction system. 

Schematic diagram Illustrating the attack of an anionic nucleophile on a substrate located In an Interface with a net positive charge, where the attack occurs (a) In the Stern layer...

Fig. 5.5 Distribution of electrical charges and potentials in a double layer according to (a) Gouy-Chapman model and (b) Stern model, where /q and are surface and Stern potentials, respectively, and d is the thickness of the Stern layer...

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