3.3.3  Electrochemical impedance spectroscopy
The aforementioned electrochemical methods involved responses based on step changes or continuous sweeps in the applied current or voltage that drove the electrode to a condition far from equilibrium. Alternatively, frequency response methods, often referred to as impedance-based or impedimetric methods, are based on frequency response analysis (i.e., the response of the system to periodic applied current or potential waveforms at either a fixed frequency or over a range of frequencies) (Bard and Faulkner, 2000). This provides several advantages, including measurement over a wide range of times and frequencies and high precision in time-averaged responses. We next discuss impedance-based electrochemical methods for detection of pathogens using electrochemical biosensors.
In EIS the impedance and phase angle of the system are measured as a function of the frequency of the applied electrical potential. EIS is a diverse electrochemical method, which can be done as a faradaic or non-faradaic process, and enables the study of intrinsic material properties, experiment-specific processes, or biorecognition events at the electrode surface. EIS is often performed using an applied low-amplitude sinusoidal electrical potential and a three-electrode configuration. Equivalent circuit models are commonly fit to experimental impedance and phase angle data to interpret the electrochemical process in terms of passive circuit elements, such as resistors and capacitors. For example, the electric double layer is typically modeled as a capacitive element, while the resistance to faradaic charge transfer at the electrode-electrolyte interface is represented as a resistor, often referred to as the charge transfer resistance. Additional circuit elements, such as constant-phase or Warburg elements, can also be included to represent other features of the electrochemical cell and process, such transport characteristics of the species at the electrode-electrolyte interface. The Randles model is a commonly used equivalent circuit for interpretation of biosensor EIS data. The circuit consists of an electrolyte resistance in series with a parallel combination of the double-layer capacitance with the charge transfer resistance and the Warburg impedance element (Randles, 1947). Variations of this model have been formulated for a variety of biosensing studies. For example, the equivalent circuit model and associated Nyquist plot for electrochemical detection of S. typhimurium using EIS with a poly(pyrrole-co-3-carboxyl-pyrrole) copolymer supported aptamer can be found in Fig. 5c (Sheikhzadeh et al. 2016). The equivalent circuit model consists of the solution resistance, charge transfer resistance at the copolymer-aptamer/electrolyte interface, and constant phase element for the charge capacitance at the copolymer-aptamer/electrolyte interface (Sheikhzadeh et al. 2016).
While the impedance can be measured across a range of frequencies and interpreted using equivalent circuit models that describe impedance response over a wide frequency range, fixed-frequency measurements are also useful for biosensing applications. Fixed-frequency measurements are typically based on the identification of single frequencies or small frequency ranges in the impedance spectra that are most sensitive to molecular binding events. Fixed-frequency approaches have the advantage of increasing the sampling frequency of the biosensor. As a result, impedance-based electrochemical methods generate biosensor responses in terms of changes in the measured physical quantities (e.g., changes in impedance) or calculated equivalent circuit elements (e.g., double-layer capacitance or charge-transfer resistance).
As shown in Table 1, Table 2, EIS is one of the most commonly used methods for electrochemical detection of pathogens. For example, Zarei et al. used EIS with an Au nanoparticle-modified carbon-based electrode for detection of Shigella dysenteriae (S. dysenteriae) at a LOD of 1 CFU/mL (Zarei et al. 2018). Primiceri et al. used EIS with Au interdigitated microelectrode arrays and Fe(CN)6 3 - /4- to detect L. monocytogenes at a LOD of 5 CFU/mL (Primiceri et al. 2016). Andrade et al. used EIS with a CNT-based electrode for multiplexed detection of E. coli, B. subtilis, and Enterococcus faecalis (Andrade et al. 2015).
Redox reactions at the electrode-electrolyte interface are typically established using a redox probe. Owing to its high reversibility, the Fe(CN)6 3 - /4- redox couple has been widely investigated as an electrochemical probe for biosensing applications and is regarded as a standard model for highly reversible electrochemical reactions (Daum and Enke, 1969). While useful electrochemical probes, redox reactions may also affect the electrode and immobilized biorecognition elements. For example, redox reactions associated with the Fe(CN)6 3 - /4- probe can cause etching of Au electrodes due to the presence of CN− ions when using the redox couple for EIS measurements (Vogt et al. 2016). This observation warrants further investigation, particularly in the context of establishing the effects on biosensor repeatability and reusability. The use of alternative redox probes or electrode materials may mitigate such effects. For example, ferrocene and ferrocenemethanol have also been used as redox probes for pathogen detection. Ruthenium(III)/ruthenium(II) (Schrattenecker et al. 2019) and immobilized quinone pairs (Piro et al. 2013) are also potentially useful alternatives.
Biosensors that use impedance-based methods and whose impedance response can be modeled using equivalent circuit models can be used to calculate the capacitance of the electric double layer. The double-layer capacitance is recognized to be sensitive to the structure of the electrode, the characteristics and concentration of analytes at the electrode surface and in the electrolyte, and the characteristics of the electrolyte (Lisdat and Schäfer, 2008). As a capacitor, the double-layer is not only dependent on the dielectric material but also the thickness of the dielectric layer. Importantly, both characteristics could be affected by molecular binding events on an electrode. For example, when a target analyte binds to an immobilized biorecognition element, counter ions around the electrode surface are displaced, leading to a change in the capacitance (Berggren et al. 2001). The capacitance can be determined from the reactive component of the impedance or by fitting of an equivalent circuit model (Barsoukov and Macdonald, 2018).
Idil et al. used the capacitive response of a MIP electrode for the detection of E. coli (Idil et al. 2017). Jantra et al. similarly used the capacitive response of an Au rod electrode for the detection of E. coli (Jantra et al. 2011). Luka et al. used the capacitive response of an Au interdigitated microelectrode array based on equivalent circuit analysis for the detection of C. parvum (Luka et al. 2019). See Table 1, Table 2 for a detailed list of studies that have used the capacitive response of an electrochemical biosensor for pathogen detection.