Double layer Stem potential

Inner Potential (Stern) In the diffuse electric double layer extending outward from a charged interface, the electrical potential at the boundary between the Stern and the diffuse layer is termed the inner electrical potential. Synonyms include the Stern layer potential or Stem potential. See also Electric Double Layer, Zeta Potential. 

Zeta potential is defined as the electric double layer (EDL) potential located at the shear plane between the Stem layer and the diffuse layer of the EDL that is formed in the neighborhood of a charged solid-liquid interface. Zeta potential is an experimentally measurable electrical potential that characterizes the strength and polarity of the EDL of the charged solid-liquid interface. Depending on the solid surface and the solution, zeta potentials values are within a range of —100 mV to - -100 mV for most solid-liquid interfaces in aqueous solutions. 

The evolution of the potential, when we move away from the particle surface, is calculated by expressing the electrochemical potential difference between the particle surface and the solution. In the structured part of the double layer (Stem layer), the ions are supposed to be located on distinct planes. The decreases in the potential between the surface and the IHP, and between the IHP and the OHP are therefore as linear as inside a condenser. The potential decreases exponentially with the distance in the diffuse layer starting from the OHP. The electrically disturbed zone extends to about 100 angstroms. Its thickness depends highly on the concentration and the charge of the electrolyte ions. The greater the charge and the concentration, the more the diffuse layer is compressed. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

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... 

Much use has been made of micellar systems in the study of photophysical processes, such as in excited-state quenching by energy transfer or electron transfer (see Refs. 214-218 for examples). In the latter case, ions are involved, and their selective exclusion from the Stem and electrical double layer of charged micelles (see Ref. 219) can have dramatic effects, and ones of potential imfKntance in solar energy conversion systems. 

The physical meaning of the g (ion) potential depends on the accepted model of an ionic double layer. The proposed models correspond to the Gouy-Chapman diffuse layer, with or without allowance for the Stem modification and/or the penetration of small counter-ions above the plane of the ionic heads of the adsorbed large ions. " The experimental data obtained for the adsorption of dodecyl trimethylammonium bromide and sodium dodecyl sulfate strongly support the Haydon and Taylor mode According to this model, there is a considerable space between the ionic heads and the surface boundary between, for instance, water and heptane. The presence in this space of small inorganic ions forms an additional diffuse layer that partly compensates for the diffuse layer potential between the ionic heads and the bulk solution. Thus, the Eq. (31) may be considered as a linear combination of two linear functions, one of which [A% - g (dip)] crosses the zero point of the coordinates (A% and 1/A are equal to zero), and the other has an intercept on the potential axis. This, of course, implies that the orientation of the apparent dipole moments of the long-chain ions is independent of A. 

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,... 

At this point, the combination of Equation 12 to 14 represents a solution to the problem. It is possible, however, to simplify this solution further by introducing a few approximations. First, it is well-known in electrochemistry that the relation between charge and potential in the double layer is dominated by the Stem capacitance at high electrolyte concentrations. The relation of Equation 14 is then nearly linear the linearization of the sinh-1 function around the point [Pg.83]

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 ... 

For a long time, the electric double layer was compared to a capacitor with two plates, one of which was the charged metal and the other, the ions in the solution. In the absence of specific adsorption, the two plates were viewed as separated only by a layer of solvent. This model was later modified by Stem, who took into account the existence of the diffuse layer. He combined both concepts, postulating that the double layer consists of a rigid part called the inner—or Helmholtz—layer, and a diffuse layer of ions extending from the outer Helmholtz plane into the bulk of the solution. Accordingly, the potential drop between the metal and the bulk consists of two parts ... 

We show that the electric field in the metal-solution interphase is very high (e.g., 10 or lO V/cm). The importance of understanding the structure of the metal-solution interphase stems from the fact that the electrodepKJsition processes occur in this very thin region, where there is a very high electric field. Thus, the basic characteristics of the electrodeposition processes are that they proceed in a region of high electric field and that this field can be controlled by an external power source. In Chapter 6 we show how the rate of deposition varies with the potential and structure of the double layer. 

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. 

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. 

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

FIGURE 9,14 Schematic representation of molecular arrangement dose to a solid surface showing the inner (IHP) and outer (OHP) Helmholtz planes, the stem layer, difAise double layer, also called the Gouy layer, and the slip plane where the zeta potential is measured. Also shown is the potential for various distances from the surface. 

The surface after adsorption will be chained with a potential, as in Figure 9.14, so that primary adsorption can be treated in terms of a capacitor model called the Stem model [43]. The other type of adsorption that can occur involves an exchange of ions in the diffuse layer with those of the surface. In the case of ion exchange, the primary ions are chemically bound to the structure of the solid and exchanged between ions in the diffuse double layer. 

The adsorbed Stem layer is compensated by a compact and essentially fixed layer of hydrated counterions and water molecules which takes the form of a molecular capacitor between the inner and outer Helmholtz planes shown in Figure 9.14. The solid surface adsorbs the Stem layer ions and gives a potential of the inner Helmholtz plane, which is partially compensated by the hydrated counterions and water molecviles of the outer Helmholtz plane. The diffuse double layer of (jOuy-Chapman starts at the OHP and extends further into the liquid. 

Stem s Theory of the Double Layer.—The variations of capacity of the double layer with the conditions, the influence of electrolytes on the zeta-potential, and other considerations led Stern to propose a model for the double layer which combines the essential characteristics of the Helmholtz and the Gouy theories. According to Stern the double layer consists of two parts one, which is approximately of a molecular diame r in thickness, Is supposed to remain fixed to the surface, while ihe other is anlttfuse layer extending for me distance into tlie solution The fall of potential in the fixed layer is sharp while that in the diffuse layer is gradual, the decrease being exponential in nature, as required by equation (5). 

Carlo simulations a random walk through the phase space of the model stem Is made. In this way a sequence of microscopic states are generated which are either or not accepted based on some criterion. Usually, in double layer problems the chemical potential is kept constant so that the thermodynamic parameters are obtained grand canonically, see Lapp. 6. 

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