Electrode size

OPTIMISATION OF MICROBAND ELECTRODE SIZES AND LOCATIONS WITHIN A RECTANGULAR MICROFLUIDIC CHANNEL FOR ELECTROCHEMICAL MONITORING OF HYDRODYNAMIC FLOW PROFILES... 

This formula is useful in the design calculation to determine the electrode size for a maximum allowable surface potential variation during the experiments. 

The great versatility of electrochemical processes, on the other hand, comes from the range of electrode sizes available today. Electrodes are routinely used as small as 1CT12 m2, e.g. as sensors used for monitoring electrochemical processes [53], or, as large as 16 and more m2 in production cells for synthesis or... 

Generally, the droplet size generated in electrostatic atomization is a function of applied electrical potential, electrode size and configuration, liquid flow rate, liquid nozzle diameter, and liquid properties such as surface tension, dielectric constant and electrical conductivity.[121] [124] When a low electrical potential is applied to a liquid, a stream of relatively uniform droplets will form below the liquid discharge nozzle. As the applied electrical potential is increased, the droplets produced become smaller, and the liquid velocity and droplet production rate both increase, with concomitant... 

This last point is particularly important. With the previous electrode type the electrical connection to the cell body could be realised along its periphery only, resulting in a poor current distribution in instances of large electrode size. 

Figure 9.9 illustrates a typical plot of current density distribution across the GDE width for various types of nickel net structures. With a current supply to the back of the electrode structure there is no limitation, in principle, placed on the electrode size, at least from the point of view of current distribution. However, size limitations still... 

Electrochemistry of proteins is another case where electrode size affects the electrochemical results. Direct adsorption of proteins, such as enzymes, onto bulk metal surfaces frequently results in denaturation of the... 

In order to explore the effects of small electrode size, we have used the template method to prepare ensembles of disk-shaped nanoelectrodes with diameters as small as 10 nm. We have shown that these nanoelectrode ensembles (NEEs) demonstrate dramatically lower electroanalytical detection limits compared to analogous macroelectrodes. The experimental methods used to prepare these ensembles and some recent results are reviewed below. 

This is shown in Fig. 2.19. The relationships between A fJ, and nE v, and nIEE do not depend on electrode size [28-30]. So, if nE vi = 25 mV and nAF, = —5 mV, the relationship (2.21) is AWp = 0.465 + 0.45p [26]. If the frequency is high and a hanging mercury drop electrode is used, the spherical effect is usually negh-gible (p < 10 ). However, the influence of sphericity must be taken into consideration under most other conditions, and generally at microelectrodes. The net peak current is a linear function of the square-root of frequency Alp/nFAc QD I =... 

If the electrode reaction (1.1) is kinetically controlled, the response depends on both the parameter p and the kinetic parameter k [26,27]. If the electrode size is constant and the frequency is varied, both parameters p and k ate changed. Also, if a certain reaction is measured at constant frequency, with a range of microelectrodes having various diameters, the apparent reversibility of the reaction decreases with the decreasing diameter because of radial diffusion. So, the relationship between... 

The number of the flies that can be paced at one time is limited by electrode size and the experimenter s experience usually less than ten flies per session. To maintain a constant temperature throughout the experiment, a heating plate (Brook Industries, Lake Villa, IL) that can rest on the microscope stage is used (Fig. la). 

The evolution of R°u21g versus the distance between the working and reference electrodes has been plotted in Fig. 1.24 for the four geometries presented in Table 1.5. From the curves in this figure, it can be seen that spherical and disc geometries are the best at reducing the value of R Aa and, therefore, of the ohmic drop (see Eq. 1.200). This improvement becomes more evident as the electrode size decreases (see Sects. 2.7 and 5.4). 

When compared with the linear concentration profiles of Fig. 2.1a, it can be observed that, in agreement with Eq. (2.146) for spherical electrodes, the Nemst diffusion layer is, under these conditions, independent of the potential in all the cases. As for the time dependence of the profiles shown in Fig. 2.14b, it can be seen that the Nemst diffusion layer becomes more similar to the electrode size at larger times. Analogous behavior can be observed when the electrode radius decreases. 

From these curves it can be seen that the Nemst diffusion layer, ffG, increases with time in all cases. Moreover, Fig. 2.20a shows how these curves are all coincident at short times and only small differences appear between the couples bands and cylinders and spheres and discs at times longer than 0.2 s. This indicates that for this electrode size and time below 0.2 s, the prevalent diffusion field is planar, so the electrode geometry becomes irrelevant. As the electrode size decreases (Fig. 2.20b and c), so does the temporal dependence of < , and the different curves begin to separate until they reach a steady state in the case of discs and spheres, or a pseudo-steady state in the case of bands and cylinders (Fig. 2.20c). Note that the ratio between the diffusion layers corresponding to small discs and spheres <5d clcro and <5(p[ )cro tends to the value ji/A (see also Sect. 2.7). 

Fig. 2.21 Evolution of the half-wave potential with the electrode size for spherical white dots) and cylindrical black dots) electrodes. The value of r 2 for a planar electrode has been included for comparison dashed line), ro = rs for a spherical electrode and ro = rc for a cylindrical one.

In order to analyze the degree of accuracy of Eqs. (3.73) and (3.74), the current-potential curves calculated with rigorous (3.66) (solid lines), approximate quasi-stationary (3.73) (dotted lines), and stationary (3.74) (dashed lines) equations have been plotted in Fig. 3.9 for different values of the electrode radius and two values of k°. From this figure, it can be observed that a decrease of the electrode size facilitates the fulfillment of the Eq. (3.73) for a given value of k° such that the approximate quasi-stationary solution can be used instead of the rigorous one with an error smaller than 5 % for rs < 50 pm if k° = 10-3 cm s-1 and t = 1 s. Equation (3.74) is valid for any value of k° if rs < 3 pm. 

The influence of the kinetics on the voltammograms corresponding to spherical electrodes is conditioned by different variables, and is linked to the electrode size. 

This mixed influence can be observed from the expression of (Eqs. 3.68 and 3.69). In order to analyze the influence of the electrode size, Fig. 3.10a shows the current-potential curves obtained for a charge transfer process with different values of the dimensionless rate constant K°phe for a fixed/ 0 = 10-4 cm s 1 in NPV with a time pulse t = 0.1 s (i.e., for different values of the electrode radius ranging from 100 to 1 pm). As a limiting case useful for comparison, the current-potential... 

Fig. 3.12 Variation of the ratio between the linear diffusion layer thickness of slow and fast electrode reactions for spherical electrodes, <5 /5, with the electrode kinetics (through the dimensionless parameter k° /t/D) and the electrode size (through rsj aJnDt).

Fig. 4.1 Current density-time curves when both species are soluble in the electrolytic solution and only species O is initially present. Three electrode sizes are considered planar electrode (solid lines), spherical electrode with rs = 10 5 cm (dotted lines), and spherical ultramicroelectrode with rs = 10-5 cm (dashed lines), and three y values y = 0.5 (green curves), y = 1.0 (black curves), and y = 2.0 (red curves). The applied potential sequences are Ei -Ef -> -oo, E2 - E — +oo. n = T2 = 1 s, Cq = 1 mM, cR = 0, D0 = 10-5 cm2 s 1. Taken from [20] with permission...

To check this, in Fig. 4.1 the influence of the electrode size on current density-time curves is shown for different y values when both species are soluble in the electrolytic solution, with only species O initially present. As can be observed, the electrode radius has a great influence on the current density corresponding to the first potential pulse, increasing its value when the electrode size decreases as is well known. 

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