Stern layer thickness

Figure 1. Phase volume corrected rate constant (ko ) phase volume ((f)) for the N-dodecylnicotinamide-cyanide reaction in (a) Brlj yE and (b) CTAB yE, Curves (c) and (d) are the ionic strength corrected Brij rate constants for Stern layer thicknesses of 4A and 2A, respectively (vide text).

The above attempts to apply the Stern model to five sets of charging curves of silica were rather unsuccessful. On the other hand, Sonnefeld [37] reports successful application of the Stern model to the surface charging of silica at five concentrations (0.005-0.3 mol dm ) of five alkali chlorides. Two adjustable parameters and the acidity constant) were independent of the nature of alkali metal cation and one parameter, C was dependent on the nature of the alkali metal cation. This result was explained in terms of the correlation between the Stern layer thickness and the size of the counterions. 

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). 

In order to understand this Interaction, we have calculated the electrostatic potential field of plastocyanin. For our calculations, we chose the Del-Phi program of Klapper et al. (5) because It allows us to vary parameters such as dielectric constant, solvent Ionic strength and Stern layer thickness. In addition, we were able to vary oxidation state of PC and the pH. 

Fig. 2. Schematic diagram of a suspended colloidal particle, showing relative locations of the Stern layer (thickness, S) that consists of adsorbed ions and the Gouy-Chapman layer (1/k), which dissipates the excess charge, not screened by the Stem layer, to zero in the bulk solution (67). In the absence of a Stern layer, the Gouy-Chapman layer dissipates the surface charge.

Fig. 1 Schematic representation of the electric double layer at a solid-liquid interface and variation of potential with the distance from the solid surface iJjq, surface potential potential at the Stern plane potential at the plane of share (zeta potential) 8, distance of the Stern plane from the surface (thickness of the Stern layer) /< thickness of the diffuse region of the double layer.

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). 

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...

The zeta potential is also modified by the ionic strength. When ionic strength increases, the absolute value of Zeta potential reduces. This observed phenomenon can be explained by both the presence of more counterions in the shear layer due to the decreasing double-layer thickness and to the increasing counterion adsorption into the stern layer. 

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... 

Treating the Stern layer as a molecular condenser of thickness 5 and with a permittivity c, ... 

The surface volume is, expressed in dm3, the surface area in dm2 times the thickness of the Stern layer. We assume it to be 1 nm or 10 8 dm. In every clay suspension that we have investigated the proflavine concentration was 2.5 1(T6 M. The surface concentration is then 2.5 10 6 M/surface volume or 250/ surface area (dm2). 

The adsorption of the growth unit(s) into the surface adsorption layer. This step is likely to involve the partial dehydration of the growth unit(s). The adsorption layer is a region immediately adjacent to the surface of thickness < 1000 nm. It is that part of the electrical double layer of ionic crystals, termed the Stern layer, in which specific adsorption occurs. 

Stem layers can be introduced In categories of proficiency of which three are drawn in fig. 3.20a, b and c, and one in fig. 3.21. Figure 3.20a is the most simple picture only ion size is accounted for. and only in the first layer. We shall refer to this picture as the zeroth-order Stern layer. Even in this simple case the double layer is actually a triple layer. The charge distribution remains ideal, meaning that all the relevant equations of sec. 3.5 remain valid after replacing x by (x-d). The borderline between the Stem layer of thickness d and the diffuse layer is called the outer Helmholtz plane (oHp). The charge balance is simply... 

The Helmholtz-von Smoluchowski equation indicates that under constant composition of the electrolyte solution, the electro-osmotic flow depends on the magnitude of the zeta potential which is determined by many different factors, the most important being the dissociation of the silanol groups on the capillary wall, the charge density in the Stern layer, and the thickness of the diffuse layer. Each of these factors depends on several variables, such as pH, specific adsorption of ionic species in the compact region of the electric double layer, ionic strength, viscosity, and temperature. 

The outer surface of the Stern layer is the shear surface of the micelle. The core and the Stern layer together constitute what is termed the kinetic micelle. Surrounding the Stern layer is a diffuse layer called the Gouy-Chapman electrical double layer, which contains the aN counterions required to neutralise the charge on the kinetic micelle. The thickness of the double layer is dependent on the ionic strength of the solution and is greatly compressed in the presence of electrolyte. 

In the Stern-Gouy-Chapman (SGC) theory the double layer is divided into a Stern layer, adjacent to the surface with a thickness dj and a diffuse (GC) layer of point charges. The diffuse layer starts at the Stern plane at distance d] from the surface. In the most simple case the Stern layer is free of, charges. The presence of a Stern layer has considerable consequences for the potential distribution across the Stern layer the potential drops linearly from the surface potential V s to the potential at the Stern plane, V>d- Often is considerably lower than especially in the case of specific adsorption (s.a.). 

Surface potential Stern potential Zeta potential Double>layer thickness (reciprocal Debye length)... 

The establishment of an exact quantitative relationship between the thermodynamic potential, (p0, or the potential of the adsorption layer (the Stern layer) potential, (pd, and the electrokinetic potential, , is an important and at present unsolved problem. Depending on the thickness of the layer with increased viscosity near the solid surface, the electrokinetic potential may either approach the value of the Stem layer potential or be lower than the latter. In some cases (e.g. for quartz), as shown in studies by D.A. Fridrikhsberg and M.P. Sidorova [10,11], the difference between the electrokinetic and thermodynamic potentials may be related to the hydration (swelling) of the solid surface and the formation of a gel-like layer resistant to deformation, within which a partial potential drop takes place. The difference between (pdand C, may also be related to microscopic surface roughness of the solids, i.e. to the presence of growth steps, dislocations and other defects (see Chapter IV). 

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