Electrode, area

Measurement of Electrode Area. Because of surface toughness, the real or true surface area of a solid electrode is greater than the projected or geometric area. However, if the electrode is polished to a smooth surface finish, this will be of no consequence in most voltammetric work. The depth of the depleted region around the electrode surface (the diffusion-layer thickness) is substantially larger than the characteristic dimensions of surface toughness for electrolysis times that are greater than 1 s. [The diffusion-layer thickness may be crudely approximated by the term (Dt)m, where D is the diffusion coefficient (cm2 s 1) and t is the time.] 

The area of a polished electrode (taken to be the projected or geometric area in most voltammetric experiments at times 1 s) usually is measured directly or electrochemically. If the electrode is of regular geometry, such as a disk, sphere, or wire of uniform diameter, its characteristic dimensions can be measured by use of a micrometer, optical comparator, or traveling microscope and the area calculated. 

In practice two methods are used for stationary planar electrodes in quiescent solution chronoamperometry and chronopotentiometry. By use of an electroactive species whose concentration, diffusion coefficient, and n value are known, the electrode area can be calculated from the experimental data. In chronoamperometry, the potential is stepped from a value where no reaction takes place to a value that ensures that the concentration of reactant species will be maintained at essentially zero concentration at the electrode surface. Under conditions of linear diffusion to a planar electrode the current is given by the Cottrell equation [Chapter 3, Eq. (3.6)]  

The product it112 should remain essentially constant at a shielded planar electrode for electrolysis periods from 1 to 30 s or more. By use of a servorecorder accurate data usually can be obtained for times between 10 and 30 s. 

In the chronopotentiometric method the transition time is measured for constant current and the electrode area is calculated from the relation [Chapter 4, Eq. (4.17)]  

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The combination of electrochemistry and photochemistry is a fonn of dual-activation process. Evidence for a photochemical effect in addition to an electrochemical one is nonnally seen m the fonn of photocurrent, which is extra current that flows in the presence of light [, 89 and 90]. In photoelectrochemistry, light is absorbed into the electrode (typically a semiconductor) and this can induce changes in the electrode s conduction properties, thus altering its electrochemical activity. Alternatively, the light is absorbed in solution by electroactive molecules or their reduced/oxidized products inducing photochemical reactions or modifications of the electrode reaction. In the latter case electrochemical cells (RDE or chaimel-flow cells) are constmcted to allow irradiation of the electrode area with UV/VIS light to excite species involved in electrochemical processes and thus promote fiirther reactions. 

The theory and appHcation of SF BDV and COV have been studied in both uniform and nonuniform electric fields (37). The ionization potentials of SFg and electron attachment coefficients are the basis for one set of correlation equations. A critical field exists at 89 kV/ (cmkPa) above which coronas can appear. Relative field uniformity is characterized in terms of electrode radii of curvature. Peak voltages up to 100 kV can be sustained. A second BDV analysis (38) also uses electrode radii of curvature in rod-plane data at 60 Hz, and can be used to correlate results up to 150 kV. With d-c voltages (39), a similarity rule can be used to treat BDV in fields up to 500 kV/cm at pressures of 101—709 kPa (1—7 atm). It relates field strength, SF pressure, and electrode radii to coaxial electrodes having 2.5-cm gaps. At elevated pressures and large electrode areas, a faH-off from this rule appears. The BDV properties ofHquid SF are described in thehterature (40—41). 

Westinghouse Electric Corp. initiated a program to develop air-cooled PAFC stacks, containing cooling plates at six-ceU intervals. Full size 100-kW stacks (468 cells, 0.12-m electrode area) were built, and a module containing four of these stacks was tested. An air-cooled stack operated at 0.480 MPa yielded a cell voltage of 0.7 V at 267 m A /cm (187 mW/cm ). Demonstration of this technology is plarmed for a site in Norway. 

Cost is 4000 per cell, corresponding to a cell cost of 4700/m electrode area. 

Current Flow Corona discharge is accompanied by a relatively small flow of electric current, typically 0.1 to 0.5 mA/m" of collecting-electrode area (projected, rather than actual area). Sparking usually involves a considerably larger flow of current which cannot be tolerated except for occasional periods of a fraction of a second duration, and then only when smtable electrical controls are provided to hmit the current. However, when suitable controls are provided, precipitators have been operated continuously with a small amount of sparking... 

Type of precipitator Type of dust Gas volume, cu ft/ min Average gas veloc- ity, ft/sec Collecting electrode area, sq ft Over-all collection efficiency, % Average particle migration velocity, ft/sec... 

As A will be a function of current density, T will be a function of electrode area, and comparisons should therefore be made with cells of standard size. Equation 12.12 shows that high throwing indices will result when polarisation rises steeply with current (AE, AEj) and cathode efficiency falls steeply (cj >> f i)- The primary current ratio, P = affects the result because... 

Accurate control of potential, stability, frequency response and uniform current distribution required the following low resistance of the cell and reference electrode small stray capacitances small working electrode area small solution resistance between specimen and point at which potential is measured and a symmetrical electrode arrangement. Their design appears to have eliminated the need for the usual Luggin capillary probe. 

The potential of the electrode surface is determined by the Nernst equation introduced in Sec. 1.3.3. In an equilibrium, the currents in anodic and cathodic directions are equal. If they are related to an electrode area, they are called exchange-current densities, j0 ... 

Figure 9. CV of 0.2 mol kg 1 lithium bis[2,2 -biphenyldiolato(2-)-0,0 ]borate solution in PC at a stainless steel electrode, area 0.5 cm 2, showing the passivation of the electrode.

Once in an operational battery, the separator should be physically and chemically stable to the electrochemical environment inside the cell. The separator should prevent migration of particles between electrodes, so the effective pore size should be less than 1pm. Typically, a Li-ion battery might be used at a C rate, which corresponds to 1-3 mAcm2, depending on electrode area the electrical resistivity of the separator should not limit battery performance under any conditions. 

Let us see now what happens in a similar linear scan voltammetric experiment, but utilizing a stirred solution. Under these conditions, the bulk concentration (C0(b, t)) is maintained at a distance S by the stilling. It is not influenced by the surface electron transfer reaction (as long as the ratio of electrode area to solution volume is small). The slope of the concentration-distance profile [(CQ(b, t) — Co(0, /))/r)] is thus determined solely by the change in the surface concentration (Co(0, /)). Hence, the decrease in Co(0, t) duiing the potential scan (around E°) results in a sharp rise in the current. When a potential more negative than E by 118 mV is reached, Co(0, t) approaches zero, and a limiting current (if) is achieved ... 

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... 

FIGURE 4-17 Preconcentrating surfaces based on covalent binding of the ligand to a polymer backbone. Q = charge A = electrode area T = surface coverage. (Reproduced with permission from reference 52.)... 

As discussed before, very high turnover numbers of the catalytic site and a large active electrode area are the most important features for effective catalysis. In the following sections three relatively successful approaches are illustrated in detail, all of which make use of one or both of these parameters. A further section will deal with non-redox modified electrodes for selectivity enhancement of follow-up reactions. 

Figure 3. Frequency shift of the Raman band at 612 cm for Fe-TsPc adsorbed on a sliver electrode as a function of the applied potential vs. SCE In 0.05 M H2S0. Laser excitation line 514.5 nm potential sweep rate 10 mV s electrode area 0.27 cm. See caption Fig. 2.

With solid (and particularly polymeric) electrolytes which at the same time function as separators, one can appreciably reduce the distance between the electrodes and hence increase the electrode area per unit of reactor volume. Very compact equipment for water electrolysis which has no liquid electrolyte has been designed. 

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