Mean current density

Figure 37. Transform of electrochemical information. J, total current a>, mean current density je local current density A, surface area.

Let us consider a semiconductor electrode, at which a redox reaction of type (1) occurs. Electrons of both the conduction band and valence band may take part in the electrode process. As a result, the reversible reaction considered is characterized by four different types of electron transitions (see Fig. 6a). Transitions in which electrons leave the semiconductor and holes come in contribute to the cathodic current, and those where electrons come in and holes escape contribute to the anodic current. Thus, the resultant current is a sum of four currents i p, i >p (when referring to currents we shall always mean current densities). 

The differential form of eqn. (7) expresses the relation between the rate of an electrode reaction and the mean current density, j... 

Because of the heterogeneous nature of the electrode processes, the mean current density is related to the total current flowing through the electrode interface... 

If the conductivity does not depend on frequency, then in accord with Ohm s law the mean current density is (Je) = c>E. Generalization for a = cr(a>) yields... 

If the nucleation time is much larger then the propagation time, each nucleus has sufficient time to spread over the surface before the next nucleus is formed. Under these conditions, each layer is formed by one nucleus only. The current i corresponding to the development and decay of the peripheral edge of each layer is not stable, and fluctuates with the nucleation and spreading of the layers. Fig. 5.9. The mean current density is given by the nucleation fi-equency l/ nuc = /A and is independent of the propagation rate v ... 

The maps of current densities and reaction rates for the embedded design are shown in Fig. 23 (at the same mean current density through the cell of 0.2 A cm-2). It is seen that the distribution of current... 

The maps of methanol and oxygen concentrations, electrochemical reaction rates, membrane phase potential and proton current density are shown in Fig. 24. The mean current density is 0.3 A cm-2. Several interesting features are seen. 

Fig. 25 Oxygen concentration along the channel (10-6 mol cm-3) for indicated values of the mean current density in the cell (mA cm-2)...

Fig. 32 Maps of hydrogen concentration (10-6 mol cm-3), reaction rates (A cm-3), electrode potentials (mV), and oxygen concentration (10-6 mol cm-3) in the anode and cathode catalyst layers. Shown are the maps forthe elements at the inlet of the White channel and at the outlet of the Grey channel (Fig. 31). Mean current density in the cell is 200 mA cm-2.

Obviously, the mean current density along y has to be zero according to Equation 15.16 ... 

From these results, it vras concluded that the electrochemical performance of the as-prepared single cells with an 8YSZ electrolyte fabricated from a sol-gel route was lower than that of the State-of-the-Art FZJ-type cells, which had a mean current density value of around 1800 mA/cm at 700 mV cell voltage and at a test temperature of 1073 K. There might be three reasons for the limited electrochemical performance. First of all, the cathode was partly delaminated during the cell test. Secondly, the pores in the top electrolyte layers resulted in incomplete contacts with the intermediate electrolyte layers (Figure 5b). The last and most important reason was the diffusion of Strontium (Sr) from the LSCF cathode into the electrolyte during the operation of electrochemical... 

Unit cell. Height (cm) Breadth (cm) Cathode- breadth (cm) Mean current density on anode (mA/cm ) Mean current density on cathode (mA/cm ) ... 

It is convenient to eliminate the cell active area A introducing a mean current density J = IjA. The quantities Vceii and SV are then functions of J via VceiiiJ) = Voc - SV J). A central question is then Which processes contribute to SV J) and how large is each contribution ... 

From (6.57), we find the instant mean current density ahead of the wave J ... 

The role of A is twofold. For fixed mean current density, an increase in A flattens the profile j(z) and lowers j(0) (Figure 6.10), thus giving more time for ageing. On the other hand, if the condition of DW generation is fulfilled, larger A shortens the period of slow propagation (see (6.71)). At large A, once the local current exceeds jcru, the cell potential will drop very fast, on a time scale of the order of t. ... 

The current is the same in both sections. Consequently, the current mean densities at these levels cannot be the same. The mean current density is higher for the small section than that for the larger section, resulting in the following equation ... 

This same result can be extended throughout the electrochemical cell. It remains linked to the overall electroneutrality of the volume in question, even when it includes one or several interfaces. In particular, the current crossing the anodic interface has the same absolute value as that of the current crossing the cathodic interface. This property is of practical importance because the respective surfaces of the two electrodes are not necessarily equal. This implies that the mean current densities at each interface do not generally have the same absolute value. Throughout the rest of this document, unless otherwise specified, j represents the projection of the vector j on the normal vector to the surface, respecting the sign convention shared by electrochemists. 

Let us estimate the platinum wire length required for the mean current density at its surface to be 100 times smaller than the current density at the working electrode when both electrodes are connected to an external power supply. 

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