Resistive electrodes

In some applications, the electric resistivity of electrodes cannot be neglected, for instance in thin wire or strip electrodes carrying important currents [ 4 ] [ 5], [122]. The new boundary conditions on elec- 

In general the potential distribution in the electrode is also governed by the Laplace equation. But, in two-dimensional and axisymmetrical problems with thin electrodes (e.g. fig. 1.13) the Laplace equation can be replaced by 

Remark The treatment of porous electrodes is beyond the scope of this work. 

When an electrode is coated with a bad conducting substance (paints, plastics.), and when the thickness of that coating is small compared to the size of the system, it is convenient to take its effect in the boundary conditions. The new boundary conditions are 

This type of condition can be useful when coated metals are protected by cathodic protection. 

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Since the energy required to strip the electrons from plutonium metal at the anode is exactly matched by the energy returned at the cathode, the potential required by the process is only that required to overcome time invariant (i2r) losses in the cell circuit, and time dependent resistance (electrode polarization). 

The pH meter is a specialized voltmeter that measures the potential difference (in mV) between the sensing and reference electrode and converts it to a display of pH. To provide an accurate measurement of the voltage of an extremely high resistance electrode (108 Q) [5], this specialized voltmeter must be designed with high input resistance or impedance characteristics (100 times that of the electrode used). Since the measurement potential difference per pH change is very small (59.16 mV/pH unit at 25°C), a reliable amplifier in the pH meter is also essential. It should be sufficiently sensitive to detect changes of at least 0.05 pH unit (or 3 mV). 

In addition to solution resistance, electrodes may have appreciable resistance in themselves. The common example is the mercury in a dropping mercury electrode (DME) capillary. Such resistances are summed with solution resistances since they are in series and the treatment that follows is unchanged. 

Two general approaches have been used in low-temperature studies. In the first, the uncompensated resistance, electrode capacitance, diffusion coefficient, and kinetic and thermodynamic parameters describing the electrode reaction are incorporated in a master model, which is treated (usually by some form of digital simulation) to calculate the expected voltammetric response for comparison with experiment [7,49]. 

Steward et al. [73] preferred the Co(III)/HN03 system. These authors utilized the cell of Fig. 18 with a separator (which permits concentration of the waste in the anolyte reservoir) and corrosion-resistant electrodes such as Pt. The suggested concentrations are 0.5 M for Co(II) and 4-12 M for HN03. This process appears to be able to destroy the vast majority of organic materials. Double bond, alcohol, and carboxylic acid groups greatly facilitate the oxidation process. However, aliphatic hydrocarbons exhibit slow oxidation. Only the CF bond, such as that contained in PTFE, polyvinylidenefluoride, and fluoroelastomers (Viton), is not oxidized. Thus, these polymers are excellent materials for the construction of mediated... 

The pH meter is a specialized voltmeter that measnres the potential difference (in mV) between the sensing and reference electrode and converts it to a display of pH. To provide an accnrate measnrement of the voltage of an extremely high resistance electrode (10 [5], this speciahzed voltmeter mnst be designed with... 

Having thus examined how the various polarizations affect the behavior of an electrochemical cell, we can state that a low solution resistance, electrode processes characterized by a high exchange constant, and a high concentration of electroactive species are fundamental requisites for batteries with high efficiency in converting chemical into electric energy. 

Although it has been reported that an external DC electric field can induce an electrophoretic back transport that can significantly enhance flux in crossflow membrane filtration, its commercial implementation appears to be restricted by several factors. These include lack of suitably inexpensive corrosion-resistant electrode materials, concerns about energy consumption, and the complexity of module manufacture. 

In early attempts to oxidize hydrocarbons electrochemically, organic solvents and corrosion-resistant electrodes (PbO, C, Pt) were used to overcome low reactant solubility and anode dissolution at extreme potentials, -I-1.8 V and up to 4.5 V (326, 327). The primary anodic reaction was usually oxygen evolution or solvent decomposition. The electrode material, nonetheless, affected the product even at the small attainable yields. Thus, toluene oxidized to traces of aldehydes on PbO2 (333), while on Pt it yielded up to 19% benzaldehyde (326). The catalytic efifect of the anode, however, on rate and selectivity was not realized. 

Figure 1 is a cross-section of an electrolytic cell with a resistive electrode and a terminal for contact at one end of the electrode. The current lines in the cell are shown along with the corresponding potential drop. Within the electrolyte (point C-D) the potential drop is linear at the electrolyte/seed layer interface there is a sudden drop in potential, on one side there is the charge transfer and concentration overpotential while on the other side is the metal potential. Finally there is a non-linear drop through the seed layer (A-B). The current lines are closely spaced near the contact terminal both on the electrolyte side and within the seed layer. This effectively means that the local current density will be high next to the contact terminal where the current lines are closely spaced. 

Kawamoto (2) developed a two-dimensional model that is based on a double iterative boundary element method. The numerical method calculates the secondary current distribution and the current distribution within anisotropic resistive electrodes. However, the model assumes only the initial current distribution and does not take into account the effect of the growing deposit. Matlosz et al. (3) developed a theoretical model that predicts the current distribution in the presence of Butler-Volmer kinetics, the current distribution within a resistive electrode and the effect of the growing metal. Vallotton et al. (4) compared their numerical simulations with experimental data taken during lead electrodeposition on a Ni-P substrate and found limitations to the applicability of the model that were attributed to mass transfer effects. 

A pH meter or electrometer draws very small currents and is best suited for irreversible reactions that are slow to reestablish equilibrium. They are also required for high-resistance electrodes, like glass pH or ion-selective electrodes. 

High-input impedance circuits must be used with high-resistance electrodes (e.g., several megohms—10 O). Also, the current drawn must be very small in order for the voltage drop across the cell =iR or current X cell resistance) to be low enough not to cause error in the measurement the cell resistance is high since it includes the glass electrode. 

The signal-to-noise ratio can be improved if a low-noise battery-operated potentiostat is used and it is usually not necessary to resort to a two-electrode configuration unless the photocurrents are very small or the electrode capacitance unusually large. It is often useful to reduce the sample area to match the illumination spot so as to eliminate the noise contribution from the part of the electrode that is not illuminated. Particular care is necessary to eliminate earth loops and high-frequency pick-up and a screened Faraday cage is essential. Commercial reference electrodes can be replaced by low-resistance electrodes if they cause problems or bridging capacitors can be used to bypass high-resistance liquid junctions. 

Electroceramics with ac-tive functions Electric conductors Electron conductivity, temperature- and stress-dependent electrical resistance Electrodes, heating rods, varistors, igniters, thermistors, high-temperatuie superconductors... 

Consider of the interference performance, corrosion resistance electrodes were used in the level detection switch of water pool, clear pool, water tank. With PLC own 24 V DC power supply, the power supply capacity were considered when external load. The third grounding was used to improve anti-jamming capability in the PLC ground terminal. 

In section 1.5.3.1 the effect of resistive electrodes was treated and in fact one subdomain could be an electrode (e.g. fig. 3.12). The boundary conditions on the interphase electrode-solution would then contain the overvoltages ... 

The introduction of cyclic boundary conditions and resistive electrodes was already mentioned (section 3.2.2), but also the possibility to deal with membrane potentials and more than two electrodes, each having a different overpotential, should be considered. 

The equations governing mass and charge transport in dilute solutions are derived and it is established that for many practical problems these equations can be reduced to a potential model. This model describes transport of charge in the solution and deals with electrode kinetics and mass transport in the diffusion layer which are considered as boundary conditions. Particular boundary conditions involved by resistive electrodes or coatings are also mentioned. The concepts primary, secondary and tertiary distribution are discussed and the Wagner number, characterizing a current distribution, is defined. The local form of Faraday s law is derived and extended to deal with moving electrodes. 

Potential as a function of position (X) along the bar is shown in Fig, lb. The zero of the potential scale is chosen as the low resistivity plate which is an equipotential surface. The left hand side of the high resistivity electrode is held at V +Vq while the right hand side is held at Vq, One particular voltage is of special interest for all LCD s the threshold voltage Vc Figure 2 shows that the optical properties of an LCD exhibit a threshold behavior at The threshold voltage is plotted on... 

FIGURE 10.3.8. A resistant electrode in parallel with a perfectly conductive electrode. 

Let us examine a flat-plate electrode at zero potential, positioned in a cell in parallel with a perfectly conductive counter electrode, as shown in Fig. 10.3.lOA. The current is fed from the top end of the resistive electrode. In this case, the electrolytic current decreases graducilly along the working surface from the top to the bottom because of the ohmic resistance within the electrode. The current density, i(x), at the distance x from the current feed, calculated by using the equivalent circuit shown in (B), is as follows [1,13] ... 

FIGURE 10.3.11. Current distribution for a resistant electrode. Current is fed flxjm the top [13). 

W. Klaus, M. Ide, S. Morokawa, et al.. Angle-independent beam steering using a liquid crystal grating with multi-resistive electrodes. Opt. Commun. 138, 151 (1997). 

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