Electrodes spherical

Fig. 2.13 Influence of the c /cq ratio on the anodic-cathodic waves when species R is soluble in the electrolytic solution (solid curves) (Eq. (2.137) considering the upper sign) and when it is amalgamated in the electrode (dotted curves) (Eq. (2.137) considering the lower sign), jsphe.ss pAsDoC 0/rs (see Eq. 2.148). Three electrode sphericity values ( JD-g t/rs) are considered 0.071 (green curves), 0.214 (blue curves), and 0.451 (red curves), and two different initial concentration ratios Cq = 1 mM, = 0 (a), co = cr = 1 mM (b). Do = 10-5 cm2 s 1, y = 0.7. Reproduced with permission [52]...

Fig. 4.7 Variation of the DDPV peak potential (solid line) and the half-wave potential (dotted line) with respect to the formal potential with the electrode sphericity parameter corresponding to the second pulse (Rq = rs/ D0Ti ) for different values of y indicated on the graph. AE = -50 mV, n = 5 s, t2 = 0.025 s...

The number of terms to be considered in series Seven(a, and. S odd( . c, ) obviously depends on the electrode sphericity (through 0 and on the duration of the potential pulses (through a), so that the higher sphericity and the greater a value, the higher order of /-powers and /-powers, respectively, must be considered. In reference [5], a discussion about this point is presented, showing that to obtain a relative error less than 1 % when y = 0.7, E —> —oo, 2 —> +00, t = Is, and... 

Corrections for electrode sphericity are available. See the original literature for details (28, 32). 

The shape of the cylindrical microtool and form of the tip of the microtool also play an important role in machining microfeatures in EMM [32]. There can be various types of the cylindrical microtools according to the shape of the shank and shape at the tip. Schematics of some microtools such as cylindrical, conical, reverse conical, cut edge electrode, spherical and disk-end shaped microelectrode are as shown in Fig. 6.16. 

The deviation expected as a result of (i) unequal diffusion coefficients of the oxidized and reduced species, and (ii) electrode sphericity can be described as follows [3] ... 

The solution for i-E curves is also available for a slow electrode reaction or for considering electrode sphericity. 

The flux of species to an electrode is described by Pick s laws, which varies according to the electrode geometry flat electrode, cylindrical electrode, disk electrode, spherical electrode, etc. Applying electrochemical boundary conditions, the solution of the diffusion equation is obtained. Considering a chronoamperom-etry experiment at a disk microelectrode where a potential step is applied to the electrode and the reaction proceeds under diffusion control without convection or migration, the following equations are obtained ... 

For applications that demand an exceptional installed reproducibility of better than 0.05 pH, the best technical choice is a spherical glass measurement electrode and a flowing junction reference electrode. The glass must be selected to match the pH and temperature range of the process. The reference electrode aperture area and reservoir pressure must be chosen to maintain a small constant flow of electrolyte into the process. However, this choice of electrode has special installation and maintenance requirements that make them an extremely unpopular choice compared to throwaway solid state combination electrodes. Spherical bulbs are more... 

Microelectrodes with several geometries are reported in the literature, from spherical to disc to line electrodes each geometry has its own critical characteristic dimension and diffusion field in the steady state. The difhisional flux to a spherical microelectrode surface may be regarded as planar at short times, therefore displaying a transient behaviour, but spherical at long times, displaying a steady-state behaviour [28, 34] - If a... 

This expression is the sum of a transient tenu and a steady-state tenu, where r is the radius of the sphere. At short times after the application of the potential step, the transient tenu dominates over the steady-state tenu, and the electrode is analogous to a plane, as the depletion layer is thin compared with the disc radius, and the current varies widi time according to the Cottrell equation. At long times, the transient cunent will decrease to a negligible value, the depletion layer is comparable to the electrode radius, spherical difhision controls the transport of reactant, and the cunent density reaches a steady-state value. At times intenuediate to the limiting conditions of Cottrell behaviour or diffusion control, both transient and steady-state tenus need to be considered and thus the fiill expression must be used. Flowever, many experiments involving microelectrodes are designed such that one of the simpler cunent expressions is valid. 

Of course, in order to vary the mass transport of the reactant to the electrode surface, the radius of the electrode must be varied, and this unplies the need for microelectrodes of different sizes. Spherical electrodes are difficult to constnict, and therefore other geometries are ohen employed. Microdiscs are conunonly used in the laboratory, as diey are easily constnicted by sealing very fine wires into glass epoxy resins, cutting... 

For a line spark source, the flame volume is initially cylindrical with the cylinder length equal to the separation distance between the electrodes. Thus, for a cylindrical flame, = e, and the critical ignition volumes are equation 7 for a spherical flame and equation 8 for a cylindrical flame where = critical ignition volume, m /kg e = thickness of flame front, m and d = flame height, m. 

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 ... 

Tests were conducted using an approximately 30-cm-diameter, 80-/rm-thick polycarbonate film with brass backing plate. A 50-mm-diameter spherical discharge electrode was used to initiate discharge of the charged film... 

PLATE 4. Spark discharge between spherical electrodes. 

Yazami et al. [128, 129] studied the mechanism of electrolyte reduction on the carbon electrode in polymer electrolytes. Carbonaceous materials, such as cokes from coal pitch and spherical mesophase and synthetic and natural graphites, were used. The change in with composi-... 

This equation reflects the rate of change with time of the concentration between parallel planes at points x and (x + dx) (which is equal to the difference in flux at the two planes). Fick s second law is vahd for the conditions assmned, namely planes parallel to one another and perpendicular to the direction of diffusion, i.e., conditions of linear diffusion. In contrast, for the case of diffusion toward a spherical electrode (where the lines of flux are not parallel but are perpendicular to segments of the sphere), Fick s second law has the form... 

Solving equation (1-8) (using Laplace transform techniques) yields the time evolution of the current of a spherical electrode ... 

FIGURE 1-3 Planar (a) and spherical (b) diffusional fields at spherical electrodes. 

Sodium-silicate glass, 151 Sol-gel films, 120, 173 Solid electrodes, 110 Solid state devices, 160 Solvents, 102 Speciation, 84 Spectroelectrochenristry, 40 Spherical electrode, 6, 8, 9, 61 Square-wave voltammetry, 72, 92 Staircase voltammetry, 74 Standard potential, 3 Standard rate constant, 12, 18 Stripping analysis, 75, 79, 110 Supporting electrolyte, 102 Surface-active agents, 79... 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

A first approximate approach for estimating N,pb, or /tpb.n is to use scanning electron microscopy to estimate the average grain size, d, of the electrode. One then assumes spherical grains for the electrode film and semispherical grains in contact with the solid electrolyte to obtain ... 

The answer is "NO." In the combustible mixture, an electric spark produces a flame kernel. Initially, its shape is elliptical (like an American football), and then becomes a torus (like an American doughnut). Afterwards, it changes into almost spherical shape, and propagates spherically in the unbumed mixture. This process is formed by the existence of spark electrodes, which is necessary for spark discharge. Spark electrodes lead not only to heat loss from the flame kernel but also a change in the kernel shape. Both affect the minimum ignition energy. 

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