Double layer potential across

The electrokinetic effect is one of the few experimental methods for estimating double-layer potentials. If two electrodes are placed in a coUoidal suspension, and a voltage is impressed across them, the particles move toward the electrode of opposite charge. For nonconducting soHd spherical particles, the equation controlling this motion is presented below, where u = velocity of particles Tf = viscosity of medium V = applied field, F/cm ... 

The potential x as the difference of electrical potential across the interface between the phase and gas, is not measurable. But its relative changes caused by the change of solution composition can be determined using the proper voltaic cells (see Section IV). The name surface potential is unfortunately also often used for the description the ionic double layer potential (i.e., the ionic part of the Galvani potential) at the interfaces of membranes, microemulsion droplets and micelles, measured usually by the acid-base indicator technique (Section V). 

The vertical shift has arisen from the application of an absolute potential difference of d to a hypothetical interface, initially with zero potential difference across it, i.e., zhj) = 0. But the argument is valid for any change of potential across the interface. Thus, if the double-layer potential is initially Atye (i.e., the interface is at equilibrium) and then the potential is change to zf< ), the Morse curve for the initial state is shifted vertically through an energy F(Aty — Atye), or Ft],... 

A double-layer potential is continuous on R3 T but exhibits a discontinuity across the interface T. The density p is a solution to the integral equation... 

FIGURE 5.8 Theoretical analysis of an amphifunctionally electrified interface (a) effect of pH and externally applied potential on the interfacial double-layer potential and (b) potential necessary to apply across the interface to reach the isoelectric point as a function of pH. Electrolyte concentration, 0.01 M protolytic site density, 3 x 1018/m2 point of zero charge, pHPZC = 4.5 inner-layer capacitance, 0.05 F/m2 outer-layer capacitance, 0.30 F/m2. (Adapted from Duval, J., et al., Langmuir, 17, 7573, 2001.)... 

In short, DL is termed below also double layer potential. It is related to the electrode potential, potential drop across the double layer at the reference electrode, DL RE

/8t) = (d[Pg.95]

A general mathematical formulation and a detailed analysis of the dynamic behavior of this mass-transport induced N-NDR oscillations were given by Koper and Sluyters [8, 65]. The concentration of the electroactive species at the electrode decreases owing to the electron-transfer reaction and increases due to diffusion. For the mathematical description of diffusion, Koper and Sluyters [65] invoke a linear diffusion layer approximation, that is, it is assumed that there is a diffusion layer of constant thickness, and the concentration profile across the diffusion layer adjusts instantaneously to a linear profile. Thus, they arrive at the following dimensionless set of equations for the double layer potential, [Pg.117]

Alternatively, we can also determine and C from the potential decay following current switch-off at the time t = t. At open circuit, the double layer discharges across the resistance while a faradaic reaction takes place. 

According to Verwey [47], the Galvani potential difference across the oil/water interface may be divided into a surface potential jump (the chi potential) caused by orientation of dipoles etc. and a double layer potential related to ionic displacement. Verwey and Niessen [47] investigated the distribution of this double layer potential over the two phases, assuming that the double layer charge is situated in two diffuse double layers on both sides of the interface and calculating the electric potential... 

The exchange current is directiy related to the reaction rate constant, to the activities of reactants and products, and to the potential drop across the double layer. The larger the more reversible the reaction and, hence, the lower the polarization for a given net current flow. Electrode reactions having high exchange currents are favored for use in battery apphcations. 

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.

The potential difference across the electric double layer A. This cannot be determined in absolute terms but must be defined with reference to another charged interface, i.e. a reference electrode. In the case of a corroding metal the potential is the corrosion potential which arises from the mutual polarisation of the anodic and cathodic reactions constituting the overall corrosion reaction see Section 1.4). 

Fig. 20.17 Potential energy-distance curves for a cathodic reaction showing how the potential energy barrier is lowered by when E < p,z.c. The barrier is assumed to be symmetrical so that /S => yi, where 5 is the distance of the O.H.P. from the surface of the electrode. Full curve—no field across double layer dashed curve-potential diflcrence is E and is negative...

If an electrolyte AB is distributed between two solvents, a and f3, there will in general be a difference of potential established across the boundary, due to the existence of a double layer ( 198). 

If we add the two equations of (10) we obtain the potential difference across the double layer ... 

FIGURE 1-12 Variation of the potential across the electrical double layer. 

The charging of the double layer is responsible for the background (residual) current known as the charging current, which limits die detectability of controlled-potential techniques. Such a charging process is nonfaradaic because electrons are not transferred across the electrode-solution interface. It occurs when a potential is applied across the double layer, or when die electrode area or capacitances are changing. Note that the current is the tune derivative of die charge. Hence, when such processes occur, a residual current flows based on die differential equation... 

The application of the overpotential t] can be considered to be equivalent to the displacement of the potential energy curves by the amount 7]F with respect to each other. The high field is now applied across the double layer between the electrode and the ions at the plane of closest approach. It is apparent from Fig. 12 that the energy of activation in the favoured direction will be diminished by etrjF while that in the reverse direction will be increased by (1 — ac)r]F where the simplest interpretation of a is in terms of the slopes of the potential energy curves (a = mi/ mi+m )) at the points of intersection electrode processes indeed are the classical example of linear free energy relations. 

An electric potential drop across the boundary between two dissimiliar phases as well as at their surfaces exposed to a neutral gas phase is the most characteristic feature of every interface and surface electrified due to ion separation and dipole orientation. This charge separation is usually described as an ionic double layer. 

Ohmic potential gradients are established practically instantaneously across conductors, certainly within times shorter than the response time of the fastest measuring devices, which is about 1 ns. They are caused by formation of a double layer, the charge of which is located on the opposite faces of the conductor in question. 

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