Helmholtz plane potential

Solvent Static dielectric permittivity, Outer Helmholtz plane potential, zero charge vs. potential of the Foe /Foe electrode (V)... 

Figure 4.12. Apparent electrokinetic potential as a function of the outer Helmholtz plane potential, when the slip process Is determined by the viscoelectrlc effect. J = 10.2 X 10 V m c Is the concentration of the (1-1) electrolyte In M. (Redrawn from J. Lyklema. Colloids Surf. A92 (1994) 41.)...

In the absence of specifically adsorbable ions, the double-layer structure is adequately described in terms of the Gouy-Chapman-Stern theory. The outer Helmholtz plane potential (distinguished by Grahame) is associated with a surface charge density a through the relation... 

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]. 

Fig. 1. The structure of the electrical double layer where Q represents the solvent CD, specifically adsorbed anions 0, anions and (D, cations. The inner Helmholtz plane (IHP) is the center of specifically adsorbed ions. The outer Helmholtz plane (OHP) is the closest point of approach for solvated cations or molecules. O, the corresponding electric potential across the double layer, is also shown.

Grahame introdnced the idea that electrostatic and chemical adsorption of ions are different in character. In the former, the adsorption forces are weak, and the ions are not deformed dnring adsorption and continne to participate in thermal motion. Their distance of closest approach to the electrode surface is called the outer Helmholtz plane (coordinate x, potential /2, charge of the diffuse EDL part When the more intense (and localized) chemical forces are operative, the ions are deformed, undergo partial dehydration, and lose mobility. The centers of the specifically adsorbed ions constituting the charge are at the inner Helmholtz plane with the potential /i and coordinate JCj < Xj. 

Reactant concentrations Cyj in the bulk solution, as well as the Galvani potential between the electrode and the bulk solution (which is a constituent term in electrode potential E), appear in kinetic equations such as (6.8). However, the reacting particles are not those in the bulk solution but those close to the electrode surface, near the outer Helmholtz plane when there is no specific adsorption, and near the inner Helmholtz plane when there is specific adsorption. Both the particle concentrations and the potential differ between these regions and the bulk solution. It was first pointed out by Afexander N. Frumkin in 1933 that for this reason, the kinetics of electrochemical reactions should strongly depend on EDL structure at the electrode surface. 

All factors influencing the potentials of the inner or outer Helmholtz plane will also influence the zeta potential. For instance, when, owing to the adsorption of surface-active anions, a positively charged metal surface will, at constant value of electrode potential, be converted to a negatively charged surface (see Fig. 10.3, curve 2), the zeta potential will also become negative. The zeta potential is zero around the point of zero charge, where an ionic edl is absent. 

FIG. 10 Schematic representation of the proposed surface model (a) the concentration and (b) the electrical potential profiles at the interface of the membrane and aqueous sample solution, x = 0 and 0 are the positions of ions in the planes of closest approach (outer Helmholtz planes) from the aqueous and membrane sides, respectively. (From Ref. 17.)... 

Fig. 4.1 Structure of the electric double layer and electric potential distribution at (A) a metal-electrolyte solution interface, (B) a semiconductor-electrolyte solution interface and (C) an interface of two immiscible electrolyte solutions (ITIES) in the absence of specific adsorption. The region between the electrode and the outer Helmholtz plane (OHP, at the distance jc2 from the electrode) contains a layer of oriented solvent molecules while in the Verwey and Niessen model of ITIES (C) this layer is absent...

A rigorous solution of this problem was attempted, for example, in the hard sphere approximation by D. Henderson, L. Blum, and others. Here the discussion will be limited to the classical Gouy-Chapman theory, describing conditions between the bulk of the solution and the outer Helmholtz plane and considering the ions as point charges and the solvent as a structureless dielectric of permittivity e. The inner electrical potential 0(1) of the bulk of the solution will be taken as zero and the potential in the outer Helmholtz plane will be denoted as 02. The space charge in the diffuse layer is given by the Poisson equation... 

By means of the thermodynamic theory of the double layer and the theory of the diffuse layer it is possible to determine the charge density ox corresponding to the adsorbed ions, i.e. ions in the inner Helmholtz plane, and the potential of the outer Helmholtz plane 2 in the presence of specific adsorption. 

The introduction of the concept of the micropotential permits derivation of various expressions for the potential difference produced by the adsorbed anions, i.e. for the potential difference between the electrode and the solution during specific adsorption of ions. It has been found that, with small coverage of the surface by adsorbed species, the micropotential depends almost linearly on the distance from the surface. The distance between the inner and outer Helmholtz planes is denoted as xx 2 and the distance between the surface of the metal and the outer Helmholtz plane as jc2. The micropotential, i.e. the potential difference between the inner and... 

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). 

According to Ershler, 0X must appear in the expression for the electrochemical potential of ions adsorbed on the inner Helmholtz plane. If their electrochemical potential is expressed by the equation... 

Consider a solid surface in contact with a dilute electrolyte solution. The plane where motion of the liquid can commence is parallel to the outer Helmholtz plane but shifted in the direction into the bulk of the solution. The electric potential in this plane with respect to the solution is termed the electrokinetic potential ( = 02 ). 

The value of the electric potential affecting the activation enthalpy of the electrode reaction is decreased by the difference in the electrical potential between the outer Helmholtz plane and the bulk of the solution, 2, so that the activation energies of the electrode reactions are not given by Eqs (5.2.10) and (5.2.18), but rather by the equations... 

The electric field or ionic term corresponds to an ideal parallel-plate capacitor, with potential drop g (ion) = qMd/4ire. Itincludes a contribution from the polarizability of the electrolyte, since the dielectric constant is included in the expression. The distance d between the layers of charge is often taken to be from the outer Helmholtz plane (distance of closest approach of ions in solution to the metal in the absence of specific adsorption) to the position of the image charge in the metal a model for the metal is required to define this position properly. The capacitance per unit area of the ideal capacitor is a constant, e/Aird, often written as Klon. The contribution to 1/C is 1 /Klon this term is much less important in the sum (larger capacitance) than the other two contributions.2... 

The experimental data bearing on the question of the effect of different metals and different crystal orientations on the properties of the metal-electrolyte interface have been discussed by Hamelin et al.27 The results of capacitance measurements for seven sp metals (Ag, Au, Cu, Zn, Pb, Sn, and Bi) in aqueous electrolytes are reviewed. The potential of zero charge is derived from the maximum of the capacitance. Subtracting the diffuse-layer capacitance, one derives the inner-layer capacitance, which, when plotted against surface charge, shows a maximum close to qM = 0. This maximum, which is almost independent of crystal orientation, is explained in terms of the reorientation of water molecules adjacent to the metal surface. Interaction of different faces of metal with water, ions, and organic molecules inside the outer Helmholtz plane are discussed, as well as adsorption. 

Figure 2.2 (a) The structure of the electrode/electrolyte interface, assuming a single layer of solvated ions adjacent to the electrode. The distance of closest approach of the ions to the electrode is a, and the ion sheet forms the outer Helmholtz plane (OHP). (b) The variation of the potential as a function of the distance from the metal surface for the interface shown in (a). 

There is compelling evidence that reducing agent oxidation and metal ion reduction are, more often than not, interdependent reactions. Nonetheless, virtually all established mechanisms of the electroless deposition fail to take into account this reaction interdependence. An alternative explanation is that the potentials applied in the partial solution cell studies are different to those measured in the full electroless solution studies. Notwithstanding some differences in the actual potentials at the inner Helmholtz plane in the full solution relative to the partial solutions, it is hard to see how this could be a universal reason for the difference in rates of deposition measured in both types of solution. 

The fact that linear CO species are observed at 0.05 V in the absence of C.H.CN (cf. spectrum a) indicates that H.O molecules at the inner Helmholtz plane are not able to displace CO out of its linear configuration at the same potential. This may be due to a re-orientation of the adsorbed HjO as a function of potential, with the positive end of the molecular dipole becoming attracted to the surface as the electrode potential is made more negative. This would reduce the ability of the H O molecule to donate electron density from its oxygen atom, and would also Increase the ability of its hydrogen atoms to compete for accepting electron density from the metal. 

The electrified interface is generally referred to as the electric double layer (EDL). This name originates from the simple parallel plate capacitor model of the interface attributed to Helmholtz.1,9 In this model, the charge on the surface of the electrode is balanced by a plane of charge (in the form of nonspecifically adsorbed ions) equal in magnitude, but opposite in sign, in the solution. These ions have only a coulombic interaction with the electrode surface, and the plane they form is called the outer Helmholtz plane (OHP). Helmholtz s model assumes a linear variation of potential from the electrode to the OHP. The bulk solution begins immediately beyond the OHP and is constant in potential (see Fig. 1). 

Fig. 17.3. Potential difference (i//) at the internal wall of a silica capillary, because of the distribution of charges, x is the length in cm from the center of charge of the negative wall to a defined distance, the zeta potential, 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.

Beyond the surface plane is a layer of ions attracted to the surface by specific chemical interactions. The locus of the center of these ions is known as the inner Helmholtz plane (IHP). The charge in this plane, which results from the specifically adsorbed ions is denoted by a2, and the electrostatic potential at the IHP by The species usually assigned to this plane include... 

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