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The ultimate goal of any researcher is to contribute to the progress of society by pioneering exploration beyond the known limits. Depending on the research type and application field, one way to fulfill this is to collect reliable experimental data on rapidly occurring processes (less than 1 ms).
Having insight into the fundamentals of these reaction mechanisms can ultimately lead to the discovery of new materials or the improvement of current solutions. In electrochemical research, reaction mechanisms and intermediates are investigated by measuring the kinetics and dynamics of the electrochemical processes happening at the surface of the electrode on a sub-ms timescale.
This article provides a short overview of the factors that have a direct influence on fast and ultra-fast electrochemical measurements from an experimental setup perspective.
Considering the following factors in the experimental design and execution is the first condition to obtain reliable experimental results for such measurements.
Additional challenges which researchers must be aware of when experimenting with «transient electrochemistry», i.e. doing electrochemical measurements at very low time scales, is presented in the featured article from E. Maisonhaute et al. [1].
Transient electrochemistry: beyond simply temporal resolution
Main factors that influence the reliability of fast electrochemical experimental results
The primary components of an electrochemical experimental setup are:
- The electrochemical cell including the electrodes and electrolyte
- The electrochemical instrument, i.e., the potentiostat/galvanostat (PGSTAT)
To perform reliable electrochemical experiments in general, and fast electrochemical measurements in particular, the specifications of the complete work system must be considered and the optimal settings must be used for all of the individual parts of the experimental setup.
Time constant of the electrochemical cell
The electrochemical cell and its specifications must be taken into account as it is an important element of the experimental setup.
Transient electrochemical experiments are not meaningful unless the cell time constant is small relative to the timescale of the measurement, regardless of the high-frequency characteristics of the control circuitry.
The cell time constant RuCdl (s) depends directly on the uncompensated resistance Ru (Ω) (i.e. the resistance of the electrolyte between the reference and the working electrode) and the double-layer capacitance Cdl (F) of the electrode [2].
As a consequence, when the potential is stepped or scanned rapidly, the true measured potential Etrue (V) lags behind the applied potential Eappl (V), according to the following equation:
Where RuCdl (s) is the time constant of the cell and t (s) is the time at which the measurement is taken.
![Figure 1. Theoretical and true waveform applied to a real electrochemical cell [1].](https://s7e5a.scene7.com/is/image/metrohm/Fig-1-time-constant-of-cell?qlt=85&ts=1665730245891&dpr=off "Theoretical and true waveform applied to a real electrochemical cell [1].")
For fast scan rates (i.e., when 𝑡 is much smaller than RuCdl ), the exponential term approaches 1 and significant errors in 𝐸true with respect to 𝐸appl can arise. For slow scan rates (i.e., when 𝑡 is much larger than RuCdl), the exponential approaches 0 and the errors become negligible.
The time constant of the cell can be reduced in three ways:
- Reduce Ru via increasing the conductivity of the electrolyte by either increasing concentration of supporting electrolyte or decreasing viscosity
- Reduce the size of the working electrode (e.g., by using microelectrodes) so that Cdl will be minimized
- Move the reference electrode as close as possible to the working electrode (e.g., by using a Luggin capillary) so that Ru will be minimized
The electrochemical instrument: potentiostat/galvanostat (PGSTAT)
The potentiostat/galvanostat (PGSTAT) is used to accurately control the applied signal (potential or current) and measure the response (current or potential, respectively) from the electrochemical cell. The accurate control of the applied signals is achieved by using a control loop (or feedback loop) circuit.
Learn more about the working principle of the potentiostat/galvanostat in our free Application Note.
When fast electrochemical measurements are executed, the following specifications will have a direct influence on the results and must be considered.
Bandwidth of the control loop of the PGSTAT
In general terms, bandwidth can be described as the parameter that defines how fast the instrument is able to react to any changes in the signal.
In electrochemical terms, the bandwidth is the frequency beyond which the performance of the system is degraded.
The bandwidth of the control loop of the PGSTAT (i.e. bandwidth of the instrument) indicates how fast the applied signal is controlled through the feedback loop.
Higher bandwidth means that the instrument uses a faster control loop (faster feedback). As a result, the applied signal will reach the desired set point faster, and in ideal circumstances the output signal will be identical to the theoretical waveform. However, depending on the properties of the electrochemical cell connected to the instrument, the applied signal might overshoot. In extreme cases, the instrument feedback loop might get out of control causing the potentiostat to oscillate. This is more likely when high-capacitance electrochemical cells are connected to the PGSTAT.
When a lower bandwidth is used, the overall stability of the PGSTAT increases by reducing the speed of the control loop. In this case, the consequence is that at very high measurement speeds, the output of the applied signal may be slightly less accurate due to a slower slew rate. Nevertheless, when measuring fast transients is not within the scope of the experiment, using the instrument with a lower bandwidth setting is recommended for highly accurate experimental results.
Therefore, it is important to choose the control loop bandwidth settings according to the type of the measurement. For ultra-high speed measurements, a higher bandwidth setting must be used with the following considerations:
- The higher the bandwidth, the higher the noise and the probability that the control loop will go out of control and oscillate.
- When working with a High bandwidth setting, it is necessary to pay special attention and use adequate cell shielding and electrode connectors. The use of a Faraday cage is recommended in these cases.
- The use of a high impedance reference electrode (RE) (e.g., double junction reference electrode, a salt bridge with frit) in combination with a High bandwidth of the control loop might lead to instability of the PGSTAT and even to oscillations.
Bandwidth of the current sensor (current range)
The measurement of the current response of an electrochemical cell (in potentiostatic mode) and the control of the applied current value (in galvanostatic mode) is executed with specially designed current sensors. In order to achieve the best sensitivity and resolution for the measurement, individual current sensors are used depending on the magnitude of the measured (or applied) current.
Each current sensor circuit (which corresponds to a current range) has a specific bandwidth or response time. Therefore for the most accurate results (especially important for fast, time resolved experiments), the current range must be selected so that the bandwidth of the current sensor will not be the limiting factor for the time response (speed) of the measurement.
In general, the lower the measured currents, the lower the bandwidth of the current sensor.
Data sampling interval vs the timescale of the investigated transient signal
The measured electrochemical response can have a complex shape with components at many frequencies. The highest frequency component of the measured or applied signal determines the bandwidth of that signal. The bandwidth of the signal should not be higher than the bandwidth of the measuring device.
If the highest frequency component of the signal is fSIGNAL, then according to the Nyquist Theorem [3] the sampling rate fSAMPLE must be at least 2 fSIGNAL (i.e., two times higher than the highest frequency component of the signal).
![Figure 3. Effect of the sampling frequency of an ideal sinusoidal signal [3]. Shown here are the theoretical signal (dashed line), sample points, and resulting measured signal (orange line).](https://s7e5a.scene7.com/is/image/metrohm/Fig-3-Sampling-interval?qlt=85&ts=1665730246004&dpr=off "Effect of the sampling frequency of an ideal sinusoidal signal [3]. Shown here are the theoretical signal (dashed line), sample points, and resulting measured signal (orange line).")
In other words, the data sampling interval must be lower than the timescale in which the time resolved (transient) measurement from the investigated electrochemical process is expected to occur. There is a practical correlation between the sampling interval and instrument bandwidth. When the sampling interval is:
- higher than 100 μs: the 10 kHz (High Stability) bandwidth should be selected.
- between 10–100 μs: the 100 kHz (Fast) bandwidth should be selected.
- smaller than 10 μs: the 1 MHz bandwidth (Ultra-Fast) should be selected.
Summary
To measure reliable experimental data, all elements of the experimental setup must be considered with their own specifications and limitations. The overview above highlights the main factors and parameters which can have a direct influence on fast electrochemical measurements.
Your knowledge take-aways
Learn more about the variety of potentiostats/galvanostats from Metrohm Autolab
References
[1] Maisonhaute, E.; et al. Transient electrochemistry: beyond simply temporal resolution, Chem.Commun., 2016, 52, 251–263. doi:10.1039/C5CC07953E
[2] Bard, A.J.; Faulkner, L.R. Electrochemical Methods: Fundamentals and Applications, New York: Wiley, 2001, 2nd ed. Russian Journal of Electrochemistry, 2002, 38, 1364–1365. doi:10.1023/A:1021637209564
[3] Keim, R. The Nyquist–Shannon Theorem: Understanding Sampled Systems. All About Circuits, May 26, 2020. https://www.allaboutcircuits.com/technical-articles/nyquist-shannon-theorem-understanding-sampled-systems/
