Photoelectrochemical cells for hydrogen production from solar energy - Solar Energy Sciences and Engineering Applications - page 318

Figure 10.3.7 Graphical representation of the AC impedance of a capacitor in series with a resistor:
(a) Nyquist diagram; (b) impedance Bode diagram; and (c) phase Bode diagram. ω is the
radial frequency; C = 1 µ F and R = 5k .

i being the number of circuit elements. Thus, for an electrochemical reaction the total
impedance may be defined as:

1

Z = (10.3.11)

1 /R + jωC

The corresponding Nyquist diagram, presented in Figure 10.3.8, shows a semicircle
with diameter R . The extension of the semicircle, therefore, provides useful informa-
tion concerning the reaction kinetics of the system: facile reaction kinetics will show a
small diameter, while a blocking electrode will be characterized by a huge semicircle.
Finally, the time constant of the reaction kinetics, τ , is given by:

1
τ =

1
RC

ω max = (10.3.12)

where ω max is the radial frequency at the semicircle maximum (Figure 10.3.8). The
high-frequency intercept of the semicircle is zero, while the low-frequency intercept of
the impedance semicircle is R .

10.3.3 EIS analysis of PEC cells for water-splitting
Photoelectrochemical cells for water-splitting have been extensively characterized by
the well-known Mott-Schottky relation, which allows obtaining the flat-band potential
and the donor density by plotting the inverse square route of the space charge capac-
itance as a function of the applied potential. The capacitance is usually determined
by fitting the experimental data to a simple resistor-capacitor (RC) electrical ana-
logue assembled in parallel - Figure 10.3.9a. In fact, C 1 in Figure 10.3.9a corresponds