Diffusion controlled currents

An increase in pressure will also affect the rate of the diffusion of molecules to and from the electrode surface it will cause an increase in the viscosity of the medium and hence a decrease in diffusion controlled currents. The consequences of increased pressure on the electrode double layer and for the adsorption of molecules at the electrode surface are unclear and must await investigation. 

When the applied current was much less than the maximum current and more than the diffusion-controlled current, the sustained oscillation was observed. 

As at the limiting (diffusion-controlled) current c0 - 0, the Ilkovic equation... 

Fig. 3.15. Diffusion-controlled current, (a) vs. Hg drop growth, (b) average value.

K. Aoki and J. Osteryoung, Diffusion-controlled current at the stationary finite disk electrode - theory. J. Electroanal. Chem. 122, 19-35 (1981). 

Measurement of the diffusion-controlled current flowing in an electrolysis cell in which one electrode is polarizable. The current is directly proportional to the concentration of an electroactive species. 

Another advantage of SWV over CV can be seen when dealing with a separate multi-electron transfer reaction. The CV current wave of each or each group of electrons always contains the contribution from the previous electron transfer, particularly the diffusion-controlled current. Separating currents from different electron transfers can be tedious, if not impossible. It can be even worse when we have to take into account the capacitive charging current. Since both capacitive and diffusion-controlled currents are absent or at least minimized on the 7net vs E curve of an SW voltammogram, current waves from each electron transfer are much better resolved and more accurate information can be obtained. 

When the regeneration of the dye is insufficient the stationary sensitized current depends on quantities characterizing the oxidation of the reduced dye and becomes simply the diffusion controlled current of the oxidizing redox ion at a very high light intensity. 

The typical voltammetric curve for a solution of SWNTs in organic solvents displays a continuum of diffusion-controlled current, with onset, in both the negative and the positive potential region, that depends on the nanotube average diameter and ultimately on the NT preparation technique. In fact, SWNTs prepared according to the arc-discharge method display an anticipated onset with respect to HiPco ones... 

In work connected with the theory of the growth of dendrites on electrodes, it was found (Barton and Bockris, 1961) that for a spherical electrode of a radius less than this diffusion layer thickness (i.c., less than 0.05 cm), the maximum diffusion-controlled current is no longer given by DcF/r, but rather by Dcf/r. 

Rearrangement of the equation to make an expression for tm will show the reader the similarity between Cottrell s equation for a diffusion-controlled current as a function of time at constant potential and Sand s equation for the time at which, under diffusion control at constant current, the potential takes off to seek a new supply of charge carriers for its electron stream. 

For the pseudo-capacity of adsorbed intermediates and for double-layer charging, cyclic voltammetric currents increase linearly with the sweep rate. For diffusion-controlled currents, the variation of the current increases with the square root of the sweep rate. 

The profiles in D correspond to a potential that is sufficiently negative of the formal electrode potential that the concentration of O is effectively zero at the electrode surface. The conditions for these profiles are analogous to those for chronoamperometry (Sec. II.A, Fig. 3.1). Once the potential has reached a value sufficient for a zero reactant-surface concentration, the potential and its rate of change become immaterial to the diffusion-controlled current. In other words, should the scan be stopped at the potential for D, the current will follow the same time course as if the scan had been continued. 

A difference in wave-heights, exploited in cases in which the difference in half-wave potentials is so small that the waves merge, can be caused either by the fact that the number of electrons consumed in the electrode reaction of the electroactive reactant differs from that involved in the electrode reaction of the electroactive product, or by a difference in the values of the diffusion coefficients of reactant and product, or by a difference in the character of the limiting current. This can occur, for example, in the case where a reactant gives a diffusion-controlled current and the product a kinetic current, or vice versa. 

In practice the current is measured under varying conditions. Because the rate of most of the reactions studied so far depends on pH, the current is measured in buffers of various composition and of controlled ionic strength and temperature. After the diffusion-governed value id has been determined, the ratio ik/ia or /( < — ) is plotted as a function of pH. In some of the treatments mentioned below, it proved useful to determine the pH value at which the kinetic current attained half the value of the diffusion-controlled current. The numerical pH value at which t = taj2, which corresponds to the inflexion point of the ik/ia — pH plot, is denoted as the polarographic dissociation constant, pK . 

For a given concentration in the gas phase, the current causes a depletion immediately at the boundary where the reaction takes place. Usually the width over which the gradient is established, remains finite for hydrodynamic reasons. If the concentration at the interface has essentially decreased to zero at the boundary, the diffusion controlled current cannot be increased any longer... 

We now repeat the measuring procedure in the same manner, but with an organic substrate added to the SSE. The polarogram in a standard case now looks as curve B, Fig. 2. It is evident that a new anodic process involving the substrate takes place in the system, since the current starts to rise at a much lower anode potential. If the concentration of substrate is not too high, we observe that the current reaches a plateau value, the diffusion-controlled current. At the plateau,... 

Although the experimental conditions for diffusion-controlled current may be in effect for a polarographic measurement, the resultant current may not be controlled purely by diffusional processes. A convenient way to test whether this is true is to vary the height of the mercury column. The fluid flow characteristics of a capillary with a hydrostatic head are such that the diffusion current is directly proportional to the square root of the height of the column (small corrections for the surface tension of mercury on glass and for the hydrostatic backpressure of the water-immersed portion of the capillary are necessary for the most precise measurements)... 

While experiments involving solution-phase reactants have provided deep insights into the dynamics of heterogeneous electron transfer, the magnitude of the diffusion-controlled currents over short timescales ultimately limits the maximum rate constant that can be measured. For diffusive species, the thickness of the diffusion layer, S, is defined as S = (nDt)1/2, where D is the solution-phase diffusion coefficient and t is the polarization time. Therefore, the depletion layer thickness is proportional to the square root of the polarization time. One can estimate that the diffusion layer thickness is approximately 50 A if the diffusion coefficient is 1 x 10-5 cm2 s-1 and the polarization time is 10 ns. Given a typical bulk concentration of the electroactive species of 1 mM, this analysis reveals that only 10 000 molecules or so would be oxidized or reduced at a 1 pm radius microdisk under these conditions The average current for this experiment is only 170 nA, which is too small to be detected with high temporal resolution. 

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