Ohmic potential drops

It can be seen that the ohmic potential drop (p i,n, differs from the overall potential drop (pp in the electrolyte as given by Eq. (4.25). The dilference between these two values corresponds exactly to the diffusional potential drop (p for the given concentration ratio that was given in Eq. (4.19). 

The trends of behavior described above are found in solutions containing an excess of foreign electrolyte, which by definition is not involved in the electrode reaction. Without this excess of foreign electrolyte, additional effects arise that are most distinct in binary solutions. An appreciable diffusion potential q) arises in the diffusion layer because of the gradient of overall electrolyte concentration that is present there. Moreover, the conductivity of the solution will decrease and an additional ohmic potential drop will arise when an electrolyte ion is the reactant and the overall concentration decreases. Both of these potential differences are associated with the diffusion layer in the solution, and strictly speaking, are not a part of electrode polarization. But in polarization measurements, the potential of the electrode usually is defined relative to a point in the solution which, although not far from the electrode, is outside the diffusion layer. Hence, in addition to the true polarization AE, the overall potential drop across the diffusion layer, 9 = 9 + 9ohm is included in the measured value of polarization, AE. ... 

For measurements involving current flow, three-electrode cells (Fig. ll.lb) are more common they contain both an AE and a RE. No current flows in the circuit of the reference electrode, which therefore is not polarized. However, the OCV value that is measured includes the ohmic potential drop in the electrolyte section between the working and reference electrode. To reduce this undesired contribution from ohmic... 

The ohmic potential drop along the section from x to x + t/x is given by... 

In this example the current density distribution is nonuniform in the vertical, since at all heights x the sums of ohmic potential drops and polarization of the two electrodes must be identical. In the top parts of the electrodes, where the ohmic losses are minor, the current density will be highest, and it decreases toward the bottom. The current distribution will be more uniform the higher the polarization. 

For a cylindrical pore (Fig. 18.4fc), consider the case where concentration gradients arise in the solution but ohmic potential drops can be neglected. With fl as the... 

Porous electrodes are systems with distributed parameters, and any loss of efficiency is dne to the fact that different points within the electrode are not equally accessible to the electrode reaction. Concentration gradients and ohmic potential drops are possible in the electrolyte present in the pores. Hence, the local current density, i (referred to the unit of true surface area), is different at different depths x of the porous electrode. It is largest close to the outer surface (x = 0) and falls with increasing depth inside the electrode. 

We discuss the particular case where only ohmic potential drops are present concentration gradients are absent. The current-density distribution normal to the surface can be found by integrating the differential equation (18.12) with the boundary conditions... 

In the classical version one uses a two-electrode cell with DME and a mercury AE (the pool) at the bottom of the cell (see Fig. 23.2). The latter, which has a large surface area, is practically not polarized. The current at the DME is low and causes no marked ohmic potential drop in the solution and no marked polarization of the AE. Hence, to change the DME potential, it will suffice to vary the external voltage applied to the cell. During the measurements, 7 vs. % rather than 7 vs. E curves are recorded. 

Current flow in a pore of length I and total cross section S produces an ohmic potential drop in the solution, which is the streaming potential ... 

The ohmic potential drop can be compensated by means of positive feedback of the potentiostat or by algebraic subtraction under potentiostatic or galvanostatic conditions, respectively. 

Because of low current densities, the ohmic potential drop can often be neglected and a three-electrode system is not necessary. The same electrode can act as the auxiliary electrode and the reference electrode (sometimes a... 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

The position of a reference electrode for the RHSE is not as crucial as for the rotating disk electrode because of the uniform potential distribution near the surface. To minimize the flow disturbances which might be introduced by a reference capillary, it is advisable to place the reference tip near the equator rather than near the pole of rotation. For a reference electrode located at a large distance from the RHSE, the ohmic potential drop may be estimated from Eq. (57) as (47) ... 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

Alternatively, one may control the electrode potential and monitor the current. This potentiodynamic approach is relatively easy to accomplish by use of a constant-voltage source if the counterelectrode also functions as the reference electrode. As indicated in the previous section, this may lead to various undesirable effects if a sizable ohmic potential drop exists between the electrodes, or if the overpotential of the counterelectrode is strongly dependent on current. The potential of the working electrode can be controlled instead with respect to a separate reference electrode by using a potentiostat. The electrode potential may be varied in small increments or continuously. It is also possible to impose the limiting-current condition instantaneously by applying a potential step. 

In many cases mass transfer is not the sole cause of unsteady-state limiting currents, observed when a fast current ramp is imposed on an elongated electrode. In copper deposition, in particular, as a result of the appreciable surface overpotential (see Section III,C) and the ohmic potential drop between electrodes, the current distribution below the limiting current is very different from that at the true steady-state limiting current. 

Unsuitable position of the reference electrode resulting in inclusion of a high ohmic potential drop between reference and working electrode. Moreover, when extended surfaces are used over which the mass transfer boundary layer thickness depends on position, a suitable number of independent reference electrodes should be used to measure local overpotentials on electrically isolated segments of the working electrode. 

Physically, the sensitivity of reactions to surface curvature can be associated with the space change layer or the resistance of the substrate. For moderately or highly doped materials, this sensitivity is only associated with the space change layer because the ohmic potential drop in the semiconductor substrate is very small. However, for lowly doped material a significant amount of potential can drop in the semiconductor to cause the current flow inside semiconductor to be also sensitive to the curvature of the surface. 

It is the electrode potential

electrochemical experiments it represents a potential difference between two identical metallic contacts of an electrochemical circuit. Such a circuit, whose one element is a semiconductor electrode, is shown schematically in Fig. 2. Besides the semiconductor electrode, it includes a reference electrode whose potential is taken, conventionally, as zero in reckoning the electrode potential (for details, see the book by Glasstone, 1946). The potential q> includes potential drops across the interfaces, i.e., the Galvani potentials at contacts—metal-semiconductor interface, semiconductor-electrolyte interface, etc., and also, if current flows in the circuit, ohmic potential drops in metal, semiconductor, electrolyte, and so on. (These ohmic drops are negligibly small under experimental conditions considered below.)... 

This can be elucidated by a corrosion diagram (Fig. 12), which shows in semilogarithmic coordinates current-voltage characteristics for two conjugated reactions. Using condition (43) and neglecting ohmic potential drop in the system, one can find from the intersection of those characteristics the steady state corrosion current icorr and corrosion potential [Pg.283]

The first term in the right-hand side of (1.61a) is termed the Ohmic potential drop (f [5 2 QjCi] ldx is the dimensionless solution resistance between x and x2) whereas the second term is termed diffusion potential. In the ambipolar case expression (1.61a) reduces to... 

Concentration polarization and overpotential can both occur at the working and auxiliary electrodes. There is an ohmic potential drop between working and auxiliary electrodes. To obtain the best measurement of the working electrode potential, the reference electrode should be placed as close as possible to the working electrode (Figure 17-4). 

The source of ohmic potential drop is the internal resistance of the bulk phases within the cell. If the current distribution is uniform, then for a phase with conductance a (S m" 1), the resistance is R = x/Across-sectional area. Thus for the passage of a current i through a cell with j sequential phases,... 

In most modern practical batteries, a major part of polarization loss at moderately high current densities is due to ohmic potential drop. Considerable attention is therefore given during the design of a battery to ... 

Although being of great fundamental importance, it should not be ignored that practical application of the semi-integral analysis requires separation of the faradaic current density jF, i.e. subtraction of the charging current density jc, from the overall current density, j, as well as perfect instrumental compensation or numerical subtraction of the ohmic potential drop jARn in order to obtain the interfacial potential E. 

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