Planar electrode, current

Fig. 6.1 Cyclic voltammograms corresponding to an EE mechanism at planar electrodes (current versus E — Ef l (a), and versus E — E (b), calculated from Eq. (6.33) for different values of the difference between formal potentials AE (values in mV shown in the curves). E = 0 mV, T = 298 K...

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

Eig. 1. Current flow (—) and electrical potential distribution (—) between two planar electrodes separated by an iasulated channel. 

Verbrugge MW, Tobias CW (1985) Triangular current-sweep chronopotentiometry at rotating disk and stationary, planar electrodes. J Electroanal Chem 196 243-259... 

Investigations on mass-transfer rates along planar electrodes (F2, H3) in which the rate of increase of current, or of cell voltage, was varied systematically from one measurement to the other revealed that the time taken for attaining the limiting current influenced the limiting-current curve. This unsteady-state effect was noticeable both in the quality of definition of the... 

Up until the mid-1940s, most physical electrochemistry was based around the dropping mercury electrode. However, in 1942, Levich showed that rotating a disc-shaped electrode in a liquid renders it uniformly accessible to diffusion, yet the hydrodynamics of the liquid flow are soluble and the kinetic equations relatively simple. In addition, in contrast to the case of a stationary planar electrode, the current at an RDE rapidly attains a steady-state value. 

Davis et. al. (64) have calculated the steady-state thin-layer current component for a series of electrode geometries. In their derivation, these authors have assumed that the flux between the electrodes is one-dimensional (perpendicular to the plane). Particularly relevant to the STM geometry are the equations for the current in a conical electrode/planar electrode TLC, Icon, and those for a hemispherical electrode/planar electrode TLC, Xhsph (64> ... 

If only linear diffusion is the operating mass transport process, it has been shown that the current (i) in a planar electrode is related to the concentration (c) gradient at the surface of the electrode (x = 0) by [332]... 

This being stated, applying Laplace s transform one obtains from Fick s second law that the maximum current (i.e. the current at the potential corresponding to the maximum of the peak) for a planar electrode is expressed by ... 

As already discussed, it indicates that for a diffusion controlled process (i.e. one which does not involve adsorption processes) taking place at a planar electrode, the current (which is proportional to... 

Additional experiments were performed in 2001 in the same laboratory by Storm et al. [59], in which longer DNA molecules (>40 nm) with various lengths and sequence compositions were stretched on the surface between planar electrodes in various configurations (see Fig. 5). No current was observed in these experiments suggesting that charge transport through DNA molecules longer than 40 nm on surfaces is blocked. 

However, advantageous applications of micro- and ultramicroelectrodes are not limited to fundamental investigations. Such electrodes open up possibilities for work in very low concentrations of solute. Whatever can be done at a planar electrode can be done at a concentration about a thousand times lower by using an ultramicroelectrode without reaching the limiting diffusion current. This means that one could even obtain responses from solutes of 1 ppb (assuming a measured current density of 1 pA cm-2). 

Another advantage in the use of microelectrodes is that the limiting diffusion current is independent of disturbances in the solution. Thus, for a planar electrode, the... 

Reducing Ohmic Errors by the Use of Microelectrodes. In Section 1.5.12, it is shown that the IR drop between the end of a Luggin capillary and a planar electrode is given by iL/k, where these quantities have been defined. Consider now the arrangement shown in Fig. 7.33, which shows a microelectrode of radius r surrounded by a radial counter-electrode, e.g., a basket of platinum mesh of radius R. Then since the current / equals iA, where i is the current density and A is the area of the microelectrode ... 

Assume that the reaction ox + c <=> red at the planar electrode is diffusion controlled. Sketch and correlate the concentration profiles Cox =f(x), where x is the distance from the electrode surface to the bulk of the solution, with the shape of the current-potential curve for electrolysis carried out at (a) a stationary disk electrode and (b) a rotating disk electrode. Support your explanation by the equations. (Skompska)... 

Earlier it was pointed out that the use of ultramicroelectrodes could also give a several hundred times increase in iL compared with the diffusion-free currents at planar electrodes. The advantage of increasing the ability to measure at higher current densities by using short times in a transient technique with a planar electrode is that the magnitude of the currents is normal and is not forced down to the difficult-to-measure picoampere region that microelectrodes require. 

In the case of mass transport by pure diffusion, the concentrations of electroactive species at an electrode surface can often be calculated for simple systems by solving Fick s equations with appropriate boundary conditions. A well known example is for the overvoltage at a planar electrode under an imposed constant current and conditions of semi-infinite linear diffusion. The relationships between concentration, distance from the electrode surface, x, and time, f, are determined by solution of Fick s second law, so that expressions can be written for [Ox]Q and [Red]0 as functions of time. Thus, for... 

Recall that at a planar electrode, one operation, namely the semiintegration of the current, provides the information from which both concentrations may be calculated. At a spherical electrode, two distinct operations are necessary one to generate Cq and a second to generate... 

The important concept in these dynamic electrochemical methods is diffusion-controlled oxidation or reduction. Consider a planar electrode that is immersed in a quiescent solution containing O as the only electroactive species. This situation is illustrated in Figure 3.1 A, where the vertical axis represents concentration and the horizontal axis represents distance from the electrodesolution interface. This interface or boundary between electrode and solution is indicated by the vertical line. The dashed line is the initial concentration of O, which is homogeneous in the solution the initial concentration of R is zero. The excitation function that is impressed across the electrode-solution interface consists of a potential step from an initial value E , at which there is no current due to a redox process, to a second potential Es, as shown in Figure 3.2. The value of this second potential is such that essentially all of O at the electrode surface is instantly reduced to R as in the generalized system of Reaction 3.1 ... 

The product D0 (dCo/dx)x=0 t is the flux or the number of moles of O diffusing per unit time to unit area of the electrode in units of mol/(cm2 s). (The reader should perform a dimensional analysis on the equations to justify the units used.) Since (3Co/3x)x=01 is the slope of the concentration-distance profile for species O at the electrode surface at time t, the expected behavior of the current during the chronoamperometry experiment can be determined from the behavior of the slope of the profiles shown in Figure 3. IB. Examination of the profiles for O at x = 0 reveals a decrease in the slope with time, which means a decrease in current. In fact, the current decays smoothly from an expected value of oo at t = 0 and approaches zero with increasing time as described by the Cottrell equation for a planar electrode,... 

Dimensionless current representations also exist. If the electrode is placed at the center of the first volume element in the model, this current will be proportional to the material flux into the first element from the second. For electroactive species A, this flux is given by DMA [fA(2) - fA(l)], where fA(J) is the fractional concentration of A in the Jth element. This fractional flux may be converted to moles of flux through multiplication by C (bulk concentration) and A Ax (volume-element volume, assuming a planar electrode of area A). Appropriate electrochemical conversion and the recognition that this material flux occurs during the interval At yield the current expression... 

The exact solution for the time-dependence of the current at a planar electrode embedded in an infinitely large planar insulator, the so-called semi-infinite linear diffusion condition, is obtained. Solving the diffusion equation under the proper set of boundary and initial conditions yields the time-dependent concentration profile. 

Fig. 7.2 (a) Dependence of current at macroscopic planar electrode placed in unstirred solution (b) current dependence for hemispherical microelectrode... 

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