Concentration profile near electrode

Figure 4.21 Concentration profiles near electrode surface at the limiting current (a) reactant, (b) product.

Concentration Profile near an Electrode due to an Electrode Reaction... 

Solving the diffusion equation under the foregoing conditions yields the concentration profile near the electrode surface, as a function of time. 

Figure 5.8 Concentration profile near an electrode surface showing the presence of a concentration diffusion layer.

In principle, impedance measurements are possible only for stationary systems, i.e., those systems for which a steady solution is possible. However, after a sufficient time, the concentration profile near the electrode can be considered to be stationary wifii respect to the time required for the impedance measurement. 

It has the same functional form as for the sphere or hemisphere, however the at a disk is smaller (by a factor of 2/tt) than at a hemisphere with the same radius. This difference manifests the different shapes of the concentration profiles near the electrode surface." ... 

At this point, the concentration profiles near the electrode are like those shown in Figure 6.1.2c. Let us consider what happens if we reverse the potential scan (see Figure... 

Figure 18.1.2 Concentration profiles near an electrode during an ECL step experiment. Data apply to 1 mM R and 1 mM TMPD. (a) Profiles of R and R at the end of the forward step.

Fig. 9 Concentration profile near an electrode covered by a salt filnn and dissolving under mass transport control.

Fig. 1.7 The concentration profile near the electrode. The Nernst diffusion-layer thickness 6 is obtained by extrapolating the...

It should be noted that the charge marked as zero in Fig. 14 does not correspond to the time at which the deposition current was first turned on. It corresponds to a time when the deposition process has reaehed steady-state conditions, the potential was eonstant, and there were no further changes of the concentration profile near the electrode surfaee. Otherwise, depending on conditions at the beginning of deposition, one might observe deviations from the predieted frequency shift. An example of such behavior was considered in detail in Refs. 141,142. 

Figure 2.12 Copper ion concentration profile near the electrode during copper dissolution.

Figure 5.8 Concentration profiles near an electrode after the applieation of a potential step. The steady state is reached when the thickness of the non-steady-state diffusion layer, 5p(t), becomes equal to 5, the thickness of the steady-state diffusion layer.

Figure 5.16 Non-steady-state concentration profiles near the electrode during a linear potential sweep.

The program Cprof (provided on the diskette) simulates and graphs the concentration profiles near the electrode for a reductive EC mechanism. 

Notice that now the dielectric constant has disappeared from this relation. This means that the electrostatic contribution in a solvent of high dielectric constant like water, is now much smaller than in the primitive model, and that the hard core term plays a much larger role in the makeup of the concentration profile near the electrode. 

The accumulation is a dynamic process that may turn into a steady state in stirred solutions. Besides, the activity of accumulated substance is not in a time-independent equilibrium with the activity of analyte in the bulk of the solution. All accumulation methods employ fast reactions, either reversible or irreversible. The fast and reversible processes include adsorption and surface complexation, the majority of ion transfers across liquid/liquid interfaces and some electrode reactions of metal ions on mercury. In the case of a reversible reaction, equilibrium between the activity of accumulated substance and the concentration of analyte at the electrode surface is established. It causes the development of a concentration profile near the electrode and the diffusion of analyte towards its surface. As the activity of the accumulated substance increases, the concentration of the analyte at the electrode surface is augmented and the diffusion flux is diminished. Hence, the equilibrium between the accumulated substance and the bulk concentration of the analyte can be established only after an infinitely long accumulation time (see Eqs. II.7.12-II.7.14 and II.7.30). The reduction of metal ions on mercury electrodes in stirred solutions is in the steady state at high overvoltages. Redox reactions of many metal ions, especially at solid... 

TG/SC is usually used in the studies of homogeneous chemical reactions, where the reaction of species R as it transits between tip and substrate causes a decrease in the snbstrate current (see Chapters 7 and 16). An alternative mode, where the substrate is the generator and tip the collector (SG/TC mode), can also be employed and is used in the studies of reactions at a snbstrate surface (Chapters 6, 9,11, and 13). The SG/TC mode was first used to study concentration profiles near an electrode snrface without scanning and imaging. " ... 

Figure 17-12 (a) Rotating disk electrode. Only the polished bottom surface of the electrode, which is typically 5 mm in diameter, contacts the solution, (b) Schematic concentration profile of analyte near the surface of the rotating disk electrode when the potential is great enough to reduce the concentration of analyte to 0 at the electrode surface. 

Fig. 6.6 Relative concentration profiles for O (solid line) and R(dots) near a planar working electrode (a) at f = 0.5, 2 and 7 seconds, corresponding to a chronoamperometry experiment, and (b) at f = 10.5,12 and 17 seconds, corresponding to the second half of a double potential step chronoamperometry experiment.

Consider the process of plating copper on a plane electrode. Near the electrode, copper ions are being discharged on the surface and their concentration decreases near the surface. At some point away from the electrode, the copper ion concentration reaches its bulk level, and we obtain a picture of the copper ion concentration distribution, shown in Fig. 6. The actual concentration profile resembles the curved line, but to simplify computations, we assume that the concentration profile is linear, as indicated by the dashed line. The distance from the electrode where the extrapolated initial slope meets the bulk concentration line is called the Nernst diffusion-layer thickness S. For order of magnitude estimates, S is approximately 0.05 cm in unstirred aqueous solution and 0.01 cm in lightly stirred solution. 

Formally, the above process is equivalent to (6.4), extended for any n and solving that system. The u-v device is a more efficient way of solving it than any linear equation solver that might otherwise have been used, as n becomes larger. The u-v device will be extensively used in this book, even with implicit methods for coupled equation systems, where we must solve for a number of concentration profiles (see below). There are practitioners who believe that n = 2, that is the two-point G-approximation, is good enough. This is justified in cases where H is very small, as it often is, at least near the electrode, when unequal intervals are used (see Chap. 9). In that case, one can simply use (6.5). 

Consider Fig. 2.4 on p.16, showing the concentration profile for a Cottrell simulation at different times. It is clear that especially the profiles at small T values are strongly compressed near the electrode, and that equal intervals in X would be wasteful at larger X. An unequal spacing of the intervals could not only provide more detail near the electrode where it is needed, but also make do with fewer points by wide spacing far away from the electrode. So some kind of grid stretching is indicated on this account. 

Formation or consumption of reacting species at the electrode surface causes concentration distribution of electroactive species in the solution phase during electrolysis. Equi-concentration contours stand for a concentration profile. A concentration profile can be measured by detecting current or potential by use of a small probe electrode at various locations near a target large electrode. A typical method is scanning electrochemical microscopy. See also diffusion layer, - scanning electrochemical microscope. 

Fig. UK Evolution of the concentration profile with time near an electrode surface, just after the potential has been stepped to the limiting current region.

Let us consider, for example, the simple nernstian reduction reaction in Eq. (221) and a solution containing initially only the reactant R. Before any electrochemical perturbation the electrode rest potential Ej is made largely positive to E . At time zero the potential is stepped to a value E2, sufficiently negative to E , so that the concentration of R is close to zero at the electrode surface. After a time 6, the electrode potential is stepped back to El, so that the concentration of P at the electrode surface becomes zero. When this potentiostatic perturbation, represented in Fig. 21a, is applied in a steady-state method, the R and P concentration profiles are linear and depend only on the electrode potential but not on time, as shown in Fig. 20a (for k 0). Yet when the same perturbation is applied in transient methods, the concentration profiles are curved and time dependent, as evidenced in Fig. 21b. Thus it is seen from this figure that a step duration at Ei, much longer than the step duration 0 at E2, is needed for the initial concentration profiles to be restored. This hysterisis corresponds to the propagation of the diffusion perturbation within the solution, which then keeps a memory of the past perturbation. This information is stored via the structuring of the concentrations in the space near the electrode as a function of the elapsed time. 

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