Introduction to Electrochemical Impedance Spectroscopy (EIS) Alireza Ostovari Supervisor: Dr. Peikari Advisor: Dr. Shadizadeh № of Slides: 37

Outline AC Circuit Theory and Representation of Complex Impedance Values Physical Electrochemistry and Circuit Elements Common Equivalent Circuit Models EIS Applications

AC Circuit Theory and Representation of Complex Impedance Values Almost everyone knows about the concept of electrical resistance. While this is a well known relationship, its use is limited to only one circuit element: the ideal resistor. Ideal resistor has several simplifying properties: It follows Ohm's Law at all current and voltage levels. Its resistance value is independent of frequency. AC current and voltage signals through a resistor are in phase with each other.

AC Circuit Theory and Representation of Complex Impedance Values Impedance spectroscopy is an extremely powerful non- destructive investigative technique. Electrochemical impedance is usually measured by applying an AC potential to an electrochemical cell and measuring the current through the cell. The real world contains circuit elements that exhibit much more complex behavior. Impedance is a more general circuit parameter.

Linearity of Electrochemistry Systems Definition of a linear system: If x1→y1 & x2→y2 then x1(t) + x2(t) → y1(t) + y2(t) ax1(t) → ay1(t) Electrochemical cells are not linear! Doubling the voltage will not necessarily double the current.

Linearity of Electrochemistry Systems In normal EIS practice, a small (1 to 10 mV) AC signal is applied to the cell. With such a small potential signal, the system is pseudo-linear. If we look at a small enough portion of a cell's current versus voltage curve, it appears to be linear. Measuring an EIS spectrum takes time. The system being measured must be at a steady state throughout the time required to measure the EIS spectrum.

Complex Voltage and Current The impedance is then represented as a complex number: Euler’s relationship:

Data Presentation Nyquist Plot: If the negative of the imaginary part of Zω is plotted versus real part, we get a “Nyquist Plot”.

Data Presentation Bode Plot: The impedance is plotted with log frequency on the X- axis and both the absolute values of the impedance (|Z|) and the phase-shift on the Y-axis.

Electrical Circuit Elements Component Current vs. Voltage Impedance Resistor E=IR Z=R Capacitor I=C dE/dt Z=1/jωC Inductor E=L di/dt Z=jωL EIS data is commonly analyzed by fitting it to an equivalent electrical circuit model. Most of the circuit elements in the model are common electrical elements such as resistors, capacitors and inductors. The impedance of a resistor is independent of frequency and has no imaginary component. The impedance of an inductor increases as frequency increases. Inductors have only an imaginary impedance component. A capacitor’s impedance decreases as the frequency is raised. Capacitors also have only an imaginary impedance component.

Serial and Parallel Combinations of Circuit Elements

Outline AC Circuit Theory and Representation of Complex Impedance Values Physical Electrochemistry and Circuit Elements Common Equivalent Circuit Models EIS Applications

Physical Electrochemistry and Equivalent Circuit Elements Electrolyte Resistance (Rs) Any solution resistance between the reference electrode and the working electrode must be considered when you model your cell.

Physical Electrochemistry and Equivalent Circuit Elements Double Layer Capacitance (Cdl) An electrical double layer exists on the interface between an electrode and its surrounding electrolyte. This double layer is formed as ions from the solution "stick on" the electrode surface. . This double layer is formed as ions from the solution "stick on" the electrode surface.

Physical Electrochemistry and Equivalent Circuit Elements Coating Capacitance (Cc) A capacitor is formed when two conducting plates are separated by a non-conducting media, called the dielectric. The value of the capacitance depends on the size of the plates, the distance between the plates and the properties of the dielectric. The relationship is:

Physical Electrochemistry and Equivalent Circuit Elements Constant Phase Element (CPE) Capacitors in EIS experiments often do not behave ideally. For a constant phase element, the exponent α is less than one.

Physical Electrochemistry and Equivalent Circuit Elements Polarization Resistance (Rp) Whenever the potential of an electrode is forced away from its value at open-circuit, that is referred to as “polarizing” the electrode. When an electrode is polarized, it can cause current to flow through electrochemical reactions that occur at the electrode surface.

Physical Electrochemistry and Equivalent Circuit Elements The open circuit potential ends up at the potential where the cathodic and anodic currents are equal. It is referred to as a “mixed potential”. When there are two simple, kinetically controlled reactions occurring, the polarization resistance is:

Physical Electrochemistry and Equivalent Circuit Elements Charge Transfer Resistance (Rct) A similar resistance is formed by a single kinetically- controlled electrochemical reaction. This charge transfer reaction has a certain speed. In this case we do not have a mixed potential, but rather a single reaction at equilibrium.

Physical Electrochemistry and Equivalent Circuit Elements Diffusion (W) Diffusion also can create an impedance called a Warburg impedance. Finite Warburg impedance:

Outline AC Circuit Theory and Representation of Complex Impedance Values Physical Electrochemistry and Circuit Elements Common Equivalent Circuit Models EIS Applications

Common Equivalent Circuit Models Purely Capacitive Coating A metal covered with an undamaged coating generally has a very high impedance. Rs Cc

Common Equivalent Circuit Models The value of the capacitance cannot be determined from the Nyquist Plot.

Common Equivalent Circuit Models The capacitance can be estimated from the graph but the solution resistance value does not appear on the chart.

Common Equivalent Circuit Models Simplified Randles Cell The simplified Randles cell includes a solution resistance, a double layer capacitor and a charge transfer or polarization resistance. Rs Rp Cdl The simplified Randles cell is one of most common cell models.

Common Equivalent Circuit Models

Common Equivalent Circuit Models The Nyquist Plot for a simplified Randles cell is always a semicircle. =0  (real )i = -(imag )i Rs Rs+ Rp

Common Equivalent Circuit Models

Common Equivalent Circuit Models Rundles Cell and Diffusion Control This circuit models a cell where polarization is due to a combination of kinetic and diffusion processes. Rs Rp Cdl W

Common Equivalent Circuit Models At high frequencies the Warburg impedance is small since diffusing reactants don't have to move very far. At low frequencies the reactants have to diffuse farther, increasing the Warburg- impedance.

Common Equivalent Circuit Models

Outline AC Circuit Theory and Representation of Complex Impedance Values Physical Electrochemistry and Circuit Elements Common Equivalent Circuit Models EIS Applications

EIS Applications Evaluation of Corrosion Inhibitors The inhibition efficiency of corrosion inhibitors can be calculated by using EIS technique in the absence and presence of different concentrations of inhibitor.

EIS Applications

EIS Applications Study the Coating Performance Coatings may experience degradation during service. For example, water may penetrate into coating to decrease its resistivity. EIS technique has been used extensively to study the coating performance and corrosion of steel under the coating. EIS technique has been used extensively to study the coating performance and corrosion of steel under the coating.

EIS Applications There are a Rundles semicircle in the high frequency range and a line with an approximately 45◦ slope in the low frequency range despite the scattered data measured at low frequencies.

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