Stern surface

One way of handling this —according to O. Stern —is to divide the aqueous part of the double layer by a hypothetical boundary known as the Stern surface. The Stern surface is situated a distance 6 from the actual surface. Figure 11.9 schematically illustrates the way this surface intersects the double layer potential and how it divides the charge density of the double layer. 

The Stern surface is drawn through the ions that are assumed to be adsorbed on the charged wall. (This surface is also known as the inner Helmholtz plane [IHP], and the surface running parallel to the IHP, through the surface of shear (see Chapter 12) shown in Figure 11.9, is called the outer Helmholtz plane [OHP]. Notice that the diffuse part of the ionic cloud beyond the OHP is the diffuse double layer, which is also known as the Gouy-Chapman... 

Outside the Stern surface the double layer continues to be described by Equation (63) or one of its approximations. The only modifications of the analysis of the diffuse double layer required by the introduction of the Stern surface are that x be measured from 6 rather than from the wall and that 06 be used instead of 0O as the potential at the inner boundary of the diffuse layer. 

In subsequent chapters it will be the potential in the diffuse double layer that concerns us. It can be described relative to its value at the inner limit of the diffuse double layer, which may be either the actual surface or the Stern surface. We continue to use the symbol p0 for the potential at this inner limit. It should be remembered, however, that specific adsorption may make this quantity lower than the concentration of potential-determining ions in the solution would indicate. We see in Chapter 12 how the potential at some (unknown) location close to this inner limit can be measured. It is called the zeta potential. 

Next, let us consider the application of Equation (21) to a particle migrating in an electric field. We recall from Chapter 4 that the layer of liquid immediately adjacent to a particle moves with the same velocity as the surface that is, whatever the relative velocity between the particle and the fluid may be some distance from the surface, it is zero at the surface. What is not clear is the actual distance from the surface at which the relative motion sets in between the immobilized layer and the mobile fluid. This boundary is known as the surface of shear. Although the precise location of the surface of shear is not known, it is presumably within a couple of molecular diameters of the actual particle surface for smooth particles. Ideas about adsorption from solution (e.g., Section 7.7) in general and about the Stern layer (Section 11.8) in particular give a molecular interpretation to the stationary layer and lend plausibility to the statement about its thickness. What is most important here is the realization that the surface of shear occurs well within the double layer, probably at a location roughly equivalent to the Stern surface. Rather than identify the Stern surface as the surface of shear, we define the potential at the surface of shear to be the zeta potential f. It is probably fairly close to the... 

Stem Layer A part of the electric double layer that lies between the surface and a hypothetical boundary—the Stern surface. Ions within the Stern layer are considered to be adsorbed. See also Electric Double Layer. 

According to the space charge model (SC), when a solution is flowing in the porous structure under a pressure gradient, pore wall is reduced to the Stern-surface between the static and the mobile portions of solution. The pore radius equivalent to the Stern-surface is called hydrod5mamic radius Tk with... 

The characteristic model distance des is taken to be zero at coincidence of the Stern surfaces, implying that the actual virus-to-solid separation distance would be approximately I nm on the basis of Smith s work (29). This is quite reasonable, and all solid-virus interaction potentials and free energy differences are matched with a single model distance. 

M. Stern, Surface area relations in polarization and corrosion, Corrosion 14 (1958) 329t-332t. 

Rudnick J and Stern E A 1971 Second-harmonic radiation from metal surfaces Rhys. Rev. B 4 4274-90... 

Fig. 8. Electrical double layer of a sohd particle and placement of the plane of shear and 2eta potential. = Wall potential, = Stern potential (potential at the plane formed by joining the centers of ions of closest approach to the sohd wall), ] = zeta potential (potential at the shearing surface or plane when the particle and surrounding Hquid move against one another). The particle and surrounding ionic medium satisfy the principle of electroneutrafity.

Fig. 2-3. Grand average number (N), surface area (S), and volume (V) distribution of Los Angeles smog. The linear ordinate normalized by total number (NT), area (ST), or volume (VT) is used so that the apparent area under the curves is proportional to the quantity in that size range. Source Corn, M., Properties of non-viable particles in the air. In "Air Pollution," 3rd ed., Vol. I ( A. C. Stern, ed.). Academic Press, New York, 1976, p. 123.

The physical meaning of the g" (ion) potential depends on the accepted model of ionic double layer. The proposed models correspond to the Gouy Chapman diffuse layer, with or without allowance for the Stern modification and/or the penetration of small counterions above the plane of the ionic heads of the adsorbed large ions [17,18]. The presence of adsorbed Langmuir monolayers may induce very high changes of the surface potential of water. For example. A/" shifts attaining ca. —0.9 (hexadecylamine hydrochloride), and ca. -bl.OV (perfluorodecanoic acid) have been observed [68]. 

The adsorption of ions is determined by the potential of the inner Helmholtz plane 0n while the shift of Epzc to more negative values with increasing concentration of adsorbed anions is identical with the shift in 0(m). Thus, the electrocapillary maximum is shifted to more negative values on an increase in the anion concentration more rapidly than would follow from earlier theories based on concepts of a continuously distributed charge of adsorbed anions over the electrode surface (Stern, 1925). Under Stern s assumption, it would hold that 0(m) = 0X (where, of course, 0X no longer has the significance of the potential at the inner Helmholtz plane). 

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. 

Scheme 1 gives a representation of an approximately spherical micelle in water, with ionic head groups at the surface and counterions clustered around the micelle partially neutralizing the charges. Counterions which are closely associated with the micelle can be assumed to be located in a shell, the so-called Stern layer, the thickness of which should be similar to the size of the micellar head groups. Monomeric co-ions will be repelled by the ionic head groups. The hydrophobic alkyl groups pack randomly and parts of the chains are exposed to water at the surface (Section 2). 

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. 

The physical situation is very similar to that of a boat moving on the sea surface, the gravity playing the role of the ponderomotive force in the previous case. The water moves from the immersed volume of the boat towards the stern, where it accumulates in the first crest of a wave produced in the boat... 

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