Sand equation

The transition time x is related to the diffusion coefficient by the Sand equation ... 

Salie and Lorenz and partial chaige transfer, 922 Sands equation. 1120. 1220. 1223. 1411 Saturated dielectric, 898... 

Just as the fundamental equation for a potential step experiment is the Cottrell equation, for the current step it is, in quiescent solution, the Sand equation [245]... 

The potential response of the RDE to current steps has been treated analytically [3, 237, 251] and accurately by Hale using numerical integration [252] this enables the elucidation of kinetic parameters [185, 253]. A current density—transition time relationship at the RDE has been established which accounts for observed differences from the Sand equation [eqn. (218)] and which has been applied to EC reactions [254]. Other hydrodynamic solid electrodes have not been considered in detail, although reversible reactions at channel electrodes have been discussed [255, 256]. 

The product ix1/2 is a significant diagnostic parameter in chrono-potentiometry. It is apparent from the Sand equation that the quantity ixI/2 is a constant for a given concentration of electroactive species. The application of... 

In the case in which the electroactive species O is adsorbed on the electrode, ixI/2 increases with increasing i (Fig. 4.4D). The Sand equation considers only those molecules of O that have reached the surface by diffusion. As x decreases, the charge contribution to the reduction of Oads consumes an increasingly large fraction of the total current, causing ixI/2 to increase. A typical example of this behavior is the reduction of Alizarin Red S at mercury [7],... 

Some comments about the size of the input parameter 5 are necessary. If 8 is too large, not enough iterations will take place before the transition time to make the simulation accurate. If 8 is too small, a great deal of computer time will be wasted reaching the transition point. A useful technique is to estimate the number of iterations that one would like to represent the transition time. One may then use this estimate to calculate 8 by means of the Sand equation ... 

The final boundary condition is expressed by the Nernst equation. Substituting the Sand equation (10.39), together with (10.40) and (10.41) into the Nernst equation... 

The potential at a planar electrode varies only to a small extent until the end of the transition time r, which corresponds to the total consumption of the electroactive species in the neighborhood of the electrode, described by the Sand equation. If the capacitive current contribution, larger at the beginning and at the end of the chronopotentiogram, is neglected, one gets for a reversible system E = Tt/4 + In T 1, where... 

Galvanostatic techniques — In galvanostatic techniques the - current is controlled and the -> potential is the dependent variable. The current is usually held constant or stepped by programming, while the potential is measured as a function of time. The experiment is carried out by applying a - galvanostat. See also -> constant current techniques, -> Sand equation -> chronopotentiom-... 

Sand equation — Consideration of the concentration c(x=o,t) at a planar working electrode in contact with a stagnant (unstirred) electrolyte solution for a reaction, where the oxidized species in the bulk is present at a concentration c and the reduced species is initially absent with an applied constant current 7, yields... 

Transition time (for chronopotentiometry) — Electrolysis time required before the surface concentration of a redox species drops to zero in - chronopotentiometry. In constant-current chronopotentiometry (see also -> constant-current techniques), the transition time r is given by the - Sand equation ... 

What information can be extracted from an experiment conducted in this manner From Eq. 4K (the Sand equation) we note that the transition time T is proportional to the square of the bulk concentration in solution ... 

The time at which the this rapid potential shift is observed, called the transition time T, can, for reversible electron transfer, be calculated from the Sand equation ... 

This equation, known as the Sand equation, was first derived by H. J. S. Sand (1). 

Again, defining the transition time r as that time when Co(0, t) = 0, an expression equivalent to the constant-current Sand equation results, but with r (rather than r ) proportional to Cq and j8 ... 

Equivalent expressions can be obtained by using the Sand equation and substituting for 1/2. 

If the current has a constant magnitude, it is most convenient in this treatment to define the known time, 1, as the transition time given by the Sand equation (8.2.14) for species A. Thus, iterations correspond to... 

The meaning of the last condition is that the diffusion can freely expand into the electrolyte (semi-infinite condition). The solution of Eq. (5.13) gives the Sand equation. If formulated for a decrease of concentration on the surface the equation is... 

Two limiting equations for the concentration-time dependence on the interface between melt and alloy electrode are obtained. For shorter times than for the characteristic diffusion time (t r /D) the Sand equation is obtained which in this case is... 

Figure 5.19 Galvanostatic pulses of lithium deposition into an aluminum alloy electrode, E it (limiting law for r << r /D (Sand equation), after John Wen et al.), i = 14 mA cm , r = 0.9 mm, 415 °C. (Reproduced with permission from Ref. [13], 1979, The Electrochemical Society.)...

It can be shown, for a reversible system, by substituting the concentrations of O and R at the electrode surface together with the Sand equation in the relevant Nemst equation that the variation of potential with time for an oxidation is given by... 

Transition time analysis for different Ti(I V) concentrations is given in Fig. 6.9. The product is approximately constant and linearly depends on the concentration (Fig. 6.10) in accordance with Sand equation ... 

Fig. 6.9 Analysis of the obtained transition times in terms of the Sand equation BMMImNs with different TiCl4 concentrations temperature 65 °C Pt working electrode...

Fig. 6.19 Transition time analysis in tenns of Sand equation for three consecutive cathodic waves (filled triangle) peak I at 0.03 V (filled square) peak II at —0.4 V and (open circle) peak III at -0.9 V...

Table 6.1 Diffusion coefficients of Ti(IV) species in the system calculated from chronopoten-tiometric data by Sand equation...

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