Slow charging

The activation overpotential Tiac,w is due to slow charge transfer reactions at the electrode-electrolyte interface and is related to current via the Butler-Volmer equation (4.7). A slow chemical reaction (e.g. adsorption, desorption, spillover) preceding or following the charge-transfer step can also contribute to the development of activation overpotential. 

The reason of slow charge/discharge capacity reduction is probably gradual loss of contact between the active particles and current collector. Nevertheless, in the case of copper current collector usage we observed even smaller increase of discharge capacity after 400th cycle (Figure 1). 

Figure 18. Schematic illustration of slow charge recombination via lateral diffusion of electrons and holes in the A and the D layers, respectively, in the A-S-D triad monolayer. Radical anions and cations on A and S moieties were created by photoexcitation of the S moieties followed by the charge separation.

Slow charging time issue at low display brightness levels TFT threshold voltage compensation... 

Fig. 7. Examples of AE vs. t112 curves (response to small amplitude current step perturbation) for three different cases (a) slow charge transfer, (b) intermediate case, and (c) fast charge transfer. From ref. 32.

Next, the argument is that, for not too slow charge transfer, the rate of change of cD (0, ) and cR (0, ) with the auxiliary time variable is much less than the rate of change of (t — u) m. The concentration term, c — c(0, u), can then be considered as a constant in the integration, which allows the integration to be performed, leading to... 

The Cottrell equation states that the product it,/2 should be a constant K for a diffusion-controlled reaction at a planar electrode. Deviation from this constancy can be caused by a number of situations, including nonplanar diffusion, convection in the cell, slow charging of the electrode during the potential step, and coupled chemical reactions. For each of these cases, the variation of it1/2 when plotted against t is somewhat characteristic. 

One serious limitation common to most small-amplitude techniques is the greatly reduced response for systems with slow charge-transfer kinetics. Due to the high activation energy of slow electron-transfer processes, they are particularly sensitive to the presence of other species in the solution. Real-world environmental samples are notoriously dirty and these matrix effects can be difficult to deal with. Applications notes from the instrument manufacturers are frequently an invaluable source of practical information for dealing with these problems for specific elements and matrices. 

Recombination in the depletion layer can become important when the concentration of minority carriers at the interface exceeds the majority carrier concentration. Under illumination minority carrier buildup at the semiconductor-electrolyte interface can occur due to slow charge transfer. Thus surface inversion may occur and recombination in the depletion region can become the dominant mechanism accounting for loss in photocurrent. 

In this section, a non-reversible electrode reaction will be addressed. An exact definition of a slow charge transfer process is not possible because the charge transfer reaction can be reversible, quasi-reversible, or irreversible depending on the duration of the experiment and the mass transport rate. So, an electrode reaction can be slow or non-reversible when the mass transport rate has a value such that the measured current is lower than that corresponding to a reversible process because the rate of depletion of the surface species at the electrode surface is less than the diffusion rate at which it reaches the surface. Under these conditions, the potential values that reduce the O species and oxidize the R species become more negative and more positive, respectively, than those predicted by Nemst equation. 

Fig. 3.9 Current-potential curves for a slow charge transfer reactions at spherical electrodes calculated from Eqs. (3.66) (solid lines), (3.73) (dotted lines), and (3.74) (dashed lines). The values of k° (in cm s-1) and of the electrode electrode radius (in microns) are shown in the curves, a = 0.5,...

Concerning the expression of the stationary charge potential curves for Cyclic Voltcoulometry, the sum that appears in Eq. (6.208) can be transformed into an integral which for the case of fast and slow charge transfer reactions simplifies to... 

Concerning the peak potential shown in Fig. 7.16b, for slow charge transfers, its value moves away from the formal potential E (which coincides with the peak potential for fast charge transfers) toward negative values, and the shift is more pronounced the smaller a. The half-peak width of the SWV net current increases as the charge transfer evolves from fast to slow (see Fig. 7.16c) becoming independent of Kplane for values of the rate constant below 0.01 and a > 0.3. In the case of a reduction process, some anomalies in the general trend are observed for low values of a (see below). 

G. Hartwich, H. Lossau, A. Ogrodnik, M. E. Michel-Beyerle, Slow Charge Separation in a Minority of Reaction Centers Correlated with a Blueshift of the P860-Band in Rb. sphaeroides, in M. E. Michel-Beyerle (Ed.), The Reaction Center of Photosynthetic Bacteria, Springer-Verlag, Berlin, 1996. 

Vfixed is constant as a result of the fixed slow charges qs of the previous calculation, while Khang changes during the iteration procedure. It is defined in terms of the fast charges qf as obtained from the charge distribution of the solute final state. 

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