Stem plane

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. 

Figure 5 shows the enhanced concentration of oppositely charged ions near the charged surface, and the depleted concentration of similarly charged ions near the charged surface due to electrostatic attractions and repulsions. Both factors reduce the effective potential, /, as the distance from the surface, X, increases. The distance at which / drops to 1/ (37%) of its value at the Stem plane is called the counterion atmosphere decay distance,... 

Table 5. Angles between the base plane and the bow and stem planes of some thiepin derivatives...

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 ... 

Lyklema(18) considers that the slipping plane may be identified with the Stem plane so that x/ss — f. Thus, since the surface potential xj/o is inaccessible, zeta potentials find practical application in the calculation of Vr from equation 5.16. In practice, electrokinetic measurements must be carried out with considerable care if reliable estimates of f are to... 

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. 

In terms of Equations 7 and 8 the change in adsorption behavior at pH 6 and 10"5M Co (II) shown in Figure 4 can be described as being caused by the operation of a specific adsorption potential (+ cal./mole). Since the hydrolysis products are unlikely to contribute a sufficiently large potential to account for the increased adsorption, it must be concluded that above 10"5M at pH 6, and above pH 6.5-7.5 at 10 4M Co (II), the Co2+ ion is specifically adsorbed and located within the Stem plane. It is probable that these conditions correspond to the fact that an activity ratio of Co2+ and surface O" or OH" sites has been exceeded. 

Region 2 is characterized by a marked change in the slope of the adsorption isotherms. This results from the onset of association of the hydrocarbon chains of the surfactant ions adsorbed in the Stem plane. The mean separation distance of adsorbed ions under these conditions is about 70 A., which approximates the mean separation distance in bulk at the c.m.c. In such adsorption phenomena, there is a relationship between this asociation and the formation of micelles in bulk solution. For example, electrokinetic studies (1) on quartz at neutral pH showed that alkylammonium ions associate in the Stem plane when their bulk concentration is approximately one hundredth of the c.m.c. This association which has been called hemimicelle formation (3), gives rise to a specific adsorption potential which causes the adsorption to increase markedly and brings about a reversal in the sign of the potential at the Stem plane. The hemimicelle concentration, that is the bulk concentration necessary... 

Fig. 3. The structure of the EDL at the mineral-water-electrolyte interface. 1-Layer of charging ions 2j-inner and 2,-outer Helmholtz layer (Grahame and Stem plane, resp.) 3-diffuse layer and 4-slipping or shear plane [after Ref. 16]. V o-phase potential and -Stern s poten-tial.a - H20 dipols, b - hydrated counterions, c - negatively charged ions, d - thickness of the G-S layer o - charge density...

Fuerstenau") was the first who used the Stern-Grahame model of EDL to describe the adsorption of long-chain surfactants for the equilibrium in heterogeneous systems. The adsorption density in the Stem plane is given by the equation... 

The inner part of the double layer may include specifically adsorbed ions. In this case, the center of the specifically adsorbed ions is located between the surface and the Stem plane. Specifically adsorbed ions (e.g., surfactants) either lower or elevate the Stem potential and the zeta potential as shown in Figure 4.31. When the specific adsorption of the surface-active or polyvalent counter ions is strong, the charge sign of the Stem potential will be reversed. The Stem potential can be greater than the surface potential if the surface-active co-ions are adsorbed. The adsorption of nonionic surfactants causes the surface of shear to be moved to a much longer distance from the Stem plane. As a result, the zeta potential will be much lower than the Stem potential. 

The potential in the diffuse layer decreases exponentially with the distance to zero (from the Stem plane). The potential changes are affected by the characteristics of the diffuse layer and particularly by the type and number of ions in the bulk solution. In many systems, the electrical double layer originates from the adsorption of potential-determining ions such as surface-active ions. The addition of an inert electrolyte decreases the thickness of the electrical double layer (i.e., compressing the double layer) and thus the potential decays to zero in a short distance. As the surface potential remains constant upon addition of an inert electrolyte, the zeta potential decreases. When two similarly charged particles approach each other, the two particles are repelled due to their electrostatic interactions. The increase in the electrolyte concentration in a bulk solution helps to lower this repulsive interaction. This principle is widely used to destabilize many colloidal systems. 

Figure 4.38 is a first illustration. The diagrams give some feeling for the quality of the data and of the fit. Regarding the latter, it appeared impossible to account for the data in terms of (4.8.31 and 30] and Du = Du. without Introducing conduction behind the Stem plane. This was done numerically by adjusting not only the fit of fig. 4.38 was obtained but also electro-... 

In fact an inner layer exists because ions are not really point charges and an ion can approach a surface only to the extent allowed by its hydration sphere. The Stern model specifically incorporates a layer of specifically adsorbed ions bounded by a plane, the Stem plane see Figure 13 and refs. 14, 31, and 45). In this case the potential changes from ij/ at the surface, to ilf 8) at the Stern plane, to (/f = 0 in bulk solution. 

Charged surface Stem layer Stem plane Plfflie of share Diffiise layer... 

The nature and the thickness of the electrical donble layer are important becanse the interaction between charged particles is governed by the overlap of their diffnse layers. Unfortunately, it is impossible to measure directly the Stem potential Pg. Instead, the zeta potential, which is the potential at the shear plane close to the Stem plane, can be experimentally measured and is often nsed as a measure of the surface potential. 

In the Stem-Gouy-Chapman (SGC) theory the double layer is divided into a Stem layer, adjacent to the surface with a thickness d, and a diffuse layer of point charges. The diffuse layer begins at the Stem plane in a distance d, from the surface. In the simplest case the Stem layer is free of charges. In real cases the Stem layer is formed by specifically adsorbed ions. The condition of electroneutrality was given by Eq. (2.59) In addition to and Oj, the surface charge can be represented by the Stem potential. It transforms the conditions of electroneutrality into the equation for the determination of the Stem potential. 

A distinction is often made between the plane where the centres of charge of the partially dehydrated specifically adsorbed ions reside, the inner Helmholtz plane, and Stem plane at distance d, which is also called the outer Helmholtz plane. The double layer model consists of an inner and outer Helmholtz layer and a diffuse layer. This is often called the triple layer model. 

In the present treatment we will use the simplified Stem layer model in which the specifically adsorbed ions are located in the Stem plane, i.e., we let the inner and outer Helmholtz plane coincide. Here, however, is a peculiarity caused by the indefiniteness of the location of the charged head of adsorbed surfactant molecules which can be some distance from the interface in direction to the water phase. 

An indirect way to obtain information about the potential at foam lamella interfaces is by bubble electrophoresis, in which an electric field is applied to a sample causing charged bubbles to move toward an oppositely charged electrode. The electrophoretic mobility is the measured electrophoretic velocity divided by the electric field gradient at the location where the velocity was measured. These results can be interpreted in terms of the electric potential at the plane of shear, also known as the zeta potential, using well-known equations available in the literature (29—31). Because the exact location of the shear plane is generally not known, the zeta potential is usually taken to be approximately equal to the potential at the Stem plane (Figure 11) ... 

A schematic representation of the inner region of the double layer model is shown in Fig. 1. Figure lb describes the distribution of counterions and the potential profile /(a ) from a positively charged surface. The potential decay is caused by the presence of counterions in the solution side (mobile phase) of the double layer. The inner Helmholtz plane (IHP) or the inner Stem plane (ISP) is the plane through the centers of ions that are chemically adsorbed (if any) on the solid surface. The outer Helmholtz plane (OHP) or the outer Stem plane (OSP) is the plane of closest approach of hydrated ions (which do not adsorb chemically) in the diffuse layer. Therefore, the plane that corresponds to x = 0 in Eq. (4) coincides with the OHP in the GCSG model. The doublelayer charge and potential are defined in such a way that ao and /o, op and Tp, and <5d and /rf are the charge densities and mean potentials of the surface plane, the Stem layer (IHP), and the diffuse layer, respectively (Fig. 1). 

Zeta potential is the potential of the surface at the plane of shear between the particle and the surrounding medium as the particle and medium move with respect to each other. In the presence of an applied electric field, the charged surface (and the attached material) tends to move in the appropriate direction, while the counterions in the mobile part of the double-layer would have a net migration in the opposite direction. On the other hand, an electric field would be created if the charged surface and the diffuse part of the double-layer were made to move relative to each other. The plane of shear is beyond the Stem plane, and the zeta potential facilitates easy quantification of the surface charge. The pH at which the calculated zeta potential value is zero is known as the isoelectric point (lEP). 

In the dipole expression (equation (10.20)), A y is the change in the number of adsorbed molecules (dipoles), y, fij the dipole moment of y, and the field strength at the Stem plane. For the adsorption of ionic surfactants, only the dipole moment of water needs to be considered. 

Finally, the rear section contains essential hardware components control actuation, propulsion. This section also houses scientific sensors (e.g., digital camera, upward looking acoustic Doppler current profiler (ADCP), 200kHz multi-beam receiver). A rear mounted rudder and stem plane are used to control the vehicles yaw, pitch and depth. 

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