Voltage relaxation

Figure 13. Voltage relaxation method for the determination of the diffusion coefficients (mobilities) of electrons and holes in solid electrolytes. The various possibilities for calculating the diffusion coefficients and from the behavior over short (t L2 /De ) and long (/ L2 /Dc ll ) times are indicated cc h is the concentration of the electrons and holes respectively, q is the elementary charge, k is the Boltzmann constant and T is the absolute temperature.

Figure 9. Typical discharge (lithiation) voltage profile of the Li/11.7%Cu-graphite cell at 50 °C in 1 1 EC DEC (1 MLiPF6 LP-40). Inset is an expanded region showing the voltage relaxation change during current interruption at about 0.08 V of the Li/11,7%Cu-graphite...

If we switch-off the current after the steady state has been reached, the voltage relaxes to the initial zero-level. The electrical behavior can be taken into account by introducing in the simple equivalent circuit (eqc) (Eq. (60)) a capacitor Cl in series to Rioa or to R,.ml (if ions or electrons are blocked) In the language of system theory the equivalent circuit of the bulk represents a PDTi-element and reads3 15 e.g., for cells 3 and 4 Par (Cx. Par (Rm , Ser ( AJrai, Cl))). 

A drawback is that measuring of OCV requires disconnecting a battery from load this is not possible for some applications. Moreover, time required for full voltage relaxation is long and can be in the range 0.5-4 h. 

Fig. 8.4 Voltage relaxations aftercurrent interruption of 10 A current loads at a 100 cm class MCFC single cell (From [38]). (a) 200 ps time range (b) 200 ms (c) 10 s...

The series RC circuit can play a role in describing this phenomenon, since it is a passive low-pass filter. More precisely, an RC transmission line or infinite RC delay line may be used to model the battery voltage relaxation after operation. Expressing the voltage change with respect to time through this line leads to a partial differential equation equivalent to Pick s second law (Equation 9.59). 

The voltage relaxation and the charge transfer technique are generally apphcable for obtaining information about the two contributiorrs to the electronic conductivity. However, tmder some conchtions one technique is more favorable than the other. The voltage relaxation... 

For DC applied voltage relaxation experiments 100 mV was applied across electrodes A and A. The potential drop across electrodes B and B, i.e., essentially the applied potential difference across the crystal, was measured with a Keithley 610 electrometer. After steady state had been obtained the applied voltage was removed and the potential decay measured across electrodes B and B was recorded with a Varian G-14A-1 recorder. 

The conductivity is proportional to the product of the diffusivity and the concentration. To separate these two contributions, the voltage-relaxation [47] and the charge-transfer techniques [25] may be employed to obtain separately the diffusivity and concentration, respectively. 

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