CHEM-E4106 - Electrochemistry D, Lecture, 9.1.2023-21.2.2023

The measurement of impedance using modern computer-controlled workstations is very fast and easy. The only responsibility of the operator is to make sure that the parameters in the experiment are reasonable. The amplitude of the input signal is not recommended to be greater than approximately 50 mV (peak-to-peak), in order to maintain the linearity of the system. The required frequency range usually depends on the system being examined. At low frequencies, the system is controlled by mass transfer, which is not necessarily interesting in the impedance measurements. In addition to this, the measurements at low frequencies last longer, as a result of which the instability of the system may pose a problem. On the other hand, at high frequencies, the connections of the cell and the potentiostat add to the perturbation. The connections of the electrode are observed as inductance in the series combination with the cell.

One of the most important parameters in terms of the quality of the measurement data is the integration time, i.e. how many measurement cycles are averaged in the mathematical treatment of the data. It is recommended to have at least 10 cycles; 5 is the absolute minimum. In some systems, it is possible to use what is known as multisine mode, in which the input signal consists of various frequencies at low frequencies in particular. The analysis is based on the Fourier transform, which separates the contribution of each frequency in the output signal. For some unknown reason, the impedance data obtained using the Fourier analysis may deviate from the ordinary impedance data, and a dummy connection, for example, must be used to make sure that the Fourier analysis is giving the correct data.

The fitting software is usually integrated into the measurement software, and the only task left for the operator is to find the equivalent circuit that fits the data. The greatest challenge, however, is the physical interpretation of the equivalent circuit. It is possible to improve the quality of the fit by adding elements to the circuit, but this kind of circuit lacks physical meaning because it fits any given data. Usually the software gives an error function $\chi^2$, which describes the sum of squares of the error. A general rule for an acceptable fitting of the equivalent circuit is $\chi^2$ < 10^-4. Data points can be added in order to improve the convergence of the fit. In addition, the fitting software usually gives various alternatives for the weighting of the data. In practice, the best result is obtained using modulus weighting, in which the weight of the data point is proportional to the length of the impedance vector.

Finally, the importance of the design of the measurement cell has to be emphasized. The current distribution at the working electrode should be as even as possible. The area of the counter electrode should be greater than that of the working electrode because otherwise the impedance of the counter electrode is included in the data. The ohmic resistance between the working electrode and the counter electrode or between the working electrode and the reference electrode should not be too large in magnitude, or the potentiostat may not be able to control the measurement properly. In addition, the measurement should be repeated without the examined electroactive species in order to separate the factors caused by the geometry of the cell from the measurement data.