Charge of the double layer

The charging of the double layer is responsible for the background (residual) current known as the charging current, which limits die detectability of controlled-potential techniques. Such a charging process is nonfaradaic because electrons are not transferred across the electrode-solution interface. It occurs when a potential is applied across the double layer, or when die electrode area or capacitances are changing. Note that the current is the tune derivative of die charge. Hence, when such processes occur, a residual current flows based on die differential equation... 

There is a displacement contribution of SJ arising from the charging of the double layer. This can simply be represented by a capacitance, Cdh that is in parallel with RCT and —W—. 

A related technique is the current-step method The current is zero for t < 0, and then a constant current density j is applied for a certain time, and the transient of the overpotential 77(f) is recorded. The correction for the IRq drop is trivial, since I is constant, but the charging of the double layer takes longer than in the potential step method, and is never complete because 77 increases continuously. The superposition of the charge-transfer reaction and double-layer charging creates rather complex boundary conditions for the diffusion equation only for the case of a simple redox reaction and the range of small overpotentials 77 [Pg.177]

In the previous section, we introduced the way that coulometry can be employed as an analytical tool, looking speciflcally at some simple forms of the technique. We saw that the charge passed was a simple function of the amount of material that had been electromodified, and then looked at ways in which the coulometric experiment was prone to errors, such as non-faradaic currents borne of electrolytic side reactions or from charging of the double-layer. 

There are not many models that do transients, mainly because of the computational cost and complexity. The models that do have mainly been discussed above. In terms of modeling, the equations use the time derivatives in the conservation equations (eqs 23 and 68) and there is still no accumulation of current or charging of the double layer that is, eq 27 still holds. The mass balance for liquid water requires that the saturation enter into the time derivative because it is the change in the water loading per unit time. However, this treatment is not necessarily rigorous because a water capacitance term should also be included,although it can be neglected as a first approximation. 

Galvanostatic Transient Technique Double-Layer Capacitance Measurements. The value of the fractional surface coverage 9 may be inferred by means of doublelayer capacitance data. As discussed in Section 6.9, the double-layer capacitance C may, in turn, be determined by means of a transient technique. In the galvanostatic transient technique (as in Fig. 6.18), the duration of the constant-current (density) pulse is on the order of microseconds. In the microsecond time range the only process taking place at the electrode is charging of the double layer. Flence, in this case, Eq. (6.96) reduces to... 

Fig. 8.2. An early transient. Current density is constant. Potential builds up first through charging of the double layer, but at a higher potential, electrons pass across the interface, i.e., current flows and the double layer behaves as a leaky capacitor. The very early sections of the transient (double-layer condenser not leaking) can be used to obtain the capacity of the double layer because, there, there is a negligible Faradaic current through the interfacial region and the current goes overwhelmingly to charging the double layer. C = (dq/dV) = (idt/dV).

Calculating x this way is somewhat advantageous since the rate of charging of the double layer is minimal (not zero) at (dE/dt)min. Derivative chronopoten-tiometry has not been widely used, probably because the improvement over the ordinary E versus t response is insufficient to justify the more complex instrumentation required. A more serious criticism is that the minimum dE/dt occurs at a time that is dependent on the kinetics of the heterogeneous reaction. For fast (reversible) reactions, = 4i/9, and for very slow (irreversible) reactions, tmin = t/4. Unfortunately, a great many reactions fall somewhere in between, and the relation of to i is not likely to be clearly defined. 

Another distortion reason is related to the charging of the double layer formed at the electrode-solution interphase. The reorganization of solvent dipoles and ions at the solution phase layer adjacent to the electrode as a response to the application... 

Mobility is also reduced slightly by another phenomenon termed the relaxation effect. Here the charged species, as it is displaced by the electric field from the center of the double layer, is acted on by the opposite charge of the double layer to pull it back [38]. 

At short times the currents response deviates from that expected theoretically due to the charging of the -> double layer and possibly inadequate power of the -> potentiostat (see also - chronocoulometry). 

Now consider the course of events when a potential step is applied. The current first rises very quickly with time, while the main process taking place is the charging of the double-layer capacitance. Even as... 

Some electrochemical systems can be described as blocking electrodes for which no Faradaic reaction can occur. At steady state, the current density for such a system must be equal to zero. The transient response of a blocking electrode is due to the charging of the double layer. At short times or high frequency, the interfacial impedance tends toward zero, and the solution adjacent to Ihe electrode can then be considered to be an equipotential surface. The short-time or high-frequency current distribution, therefore, follows the primary distribution described in the... 

If the current density consists of contributions from Faradaic reactions and charging of the double layer as... 

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