文档介绍：Techniques based on concepts of impedance
We have discussed ways of studying electrode reactions through large perturbations on the system, for example, potential sweeps, potential steps, or current steps, the electrode is generally driven to a condition far from equilibrium and the response is observed, which is usually a transient signal.
Another approach is to perturb the cell with an alternating signal of small magnitude and observe the way in which system follows the perturbation at steady state.
Electrochemical Impedance Spectroscopy
FRA: Frequency Response Analysis
Potentiostatic or galvanostatic measurements
Review of ac circuits
A purely sinusoidal voltage can be expressed as
Where ω is the angular frequency, which is 2π times the conventional frequency in hertz.
The current lags the voltage, it can be expressed generally as
Where φ is a phase angle.
Review of ac circuits
A pure resistance R, E=IR, where the phase is zero.
A pure capacitance C,
Where Xc is the capacitive reactance, 1/ωC
parison of R and Xc shows that Xc must carry dimensions of resistance, but the magnitude of Xc falls with increasing frequency.
Resistance:
Z
R
=
E
I
F
=
0
o
Capacitance:
Z
C
=
1
w
I
E
F
=
-
90
o
Electrochemical Impedance Spectroscopy
Review of ac circuits
Components along the ordinate are assigned as imaginary and along the abscissa are real, thus, we handle these parameters mathematically as “real” or “imaginary”.
A voltage E is applied across R and C
Where Z=R-jXc, called the impedance.
Review of ac circuits
The magnitude of Z and phase angle are given by the following, respectively
The impedance is a kind of generalized resistance. The phase angle expresses the balance between capacitive and ponents in the series circuit. For a pure resistance, φ=0; for a pure capacitance, φ=π/2; and for mixtures, intermediate phase angles are observed.
Review of ac circuits
For impedances in parallel, the inverse of the overall impedance is