# An Introduction to Electrochemical Impedance Spectroscopy

Electrode–Electrolyte InterfaceElectrochemical ReactionElectrode–Electrolyte Interface – The Double-LayerElectrical Circuit Model of the InterfaceEffect of Potential on the Rate ConstantDC Current vs. Potential in an Electrochemical ReactionThree-Electrode CellUse of Reference ElectrodesWhat Is EIS?Phase and MagnitudeDC vs. AC PotentialDifferential ImpedanceSeries and Parallel ConnectionsExample Circuit – 1Example Circuit – 2Data VisualizationCircuit Parameter Value Extraction from DataReaction Mechanism AnalysisOther Electrochemical TechniquesOpen-Circuit Potential vs. TimePotentiodynamic PolarizationVoltammetryPotential StepElectrochemical Quartz Crystal Microbalance (EQCM)Scanning Electrochemical Microscopy (SECM)Exercise – Electrochemistry Basics and Circuit-Based ImpedanceExperimental AspectsInstrumentationPotentiostatic vs. Galvanostatic ModesSupporting ElectrolyteLocation of the Reference ElectrodeShielded Cables and Faraday CageSingle Sine vs. Multi-SineSingle Sine InputMulti-SineRepeatability, Linearity, and StabilityRepeatabilityLinearityStabilityData ValidationLab ExperimentsExperimental Variables and Data Acquisition SoftwareSingle-Channel vs. Multi-Channel PotentiostatsEquipment to Cell ConnectionsType of EIS ExperimentDC BiasFrequenciesAmplitudeCurrent/Potential RangeCurrent/Potential OverloadOther OptionsCircuit Impedance MeasurementsSimple Electron Transfer ReactionMetal Deposition in Acidic MediaMetal Dissolution in Acidic MediaPassivationGeneral Issues with EIS Data AcquisitionReproducibilitySignal-to-Noise Ratio, Linearity Requirements, and Experiment DurationExercise – Experimental AspectsData ValidationKramers–Kronig TransformsKKT Validation – Example of a Good Quality SpectrumKKT Validation – Example of an Incomplete SpectrumKKT Validation – Examples of Spectra of Unstable SystemsKKT Validation – Example of Spectra with Nonlinear EffectsTransformation of Data in Impedance vs. Admittance FormKKT Validation – Example of a Spectrum Showing Negative ResistanceChallenges in KKT ValidationApplication of KKTData ValidationExtrapolationAlternatives to Direct Integration of KKT – Measurement ModelsIntroduction to the Measurement Model ApproachAdvantages of the Measurement Model ApproachLinear KKTSummaryExperimental Validation MethodsSoftwareExercise – Impedance Data Validation Using KKTData Analysis – Equivalent Electrical CircuitsEquivalent Electrical Circuits: What Circuit to Choose?What Circuit to Choose?How Many Elements Should One Use in the Electrical Circuit?DistinguishabilityEquivalent CircuitsZeros and Poles RepresentationModel FittingSoftware ChoicesParameter Values – Initial GuessCircuit ChoicesHigh and Low-Frequency Limits of ImpedanceLimitationsInductance and Negative (Differential) ResistanceChallenges in EEC AnalysisExercise – Equivalent CircuitsMechanistic AnalysisReaction Mechanism Analysis – Linearization of EquationsSimple Electron Transfer ReactionLinearizationReaction with an Adsorbed IntermediateLinearization of Charge Balance EquationsLinearization of the Mass Balance EquationTypes of Complex Plane Plots We Can Expect for This MechanismReaction with an Adsorbed Intermediate - Two Electrochemical StepsElectron Transfer – Electroadsorption Reaction (E-EAR) – Negative ImpedanceMore Reactions with One Adsorbed IntermediateReaction with Two Adsorbed IntermediatesLinearization of Mass Balance EquationsLinearization of Charge Balance EquationsMore Reactions with Two Adsorbed IntermediateCatalytic Mechanism – One Adsorbed Intermediate – Negative ImpedancePhysical PictureAn Issue with the Steady-State SolutionA Variation That Admits Steady DissolutionTwo-Step Reaction, With the Frumkin Adsorption Isotherm ModelIdentification of a Reaction Mechanism – EIS Data as Complex Plane PlotsChallenges in Identifying a Reaction MechanismParameter EstimationError CalculationData FormConstraintSoftwareDirect OptimizationUtilizing EEC ResultsGrid SearchRelevance of RMAThe Number of Parameters. EEC vs. RMAPhysical InterpretationMinimum Number of Potentials (E[sub(dc)]) Where Spectra Must Be AcquiredExample – Multiple SolutionsExample - Calculation of Minimum Number of Edc Where EIS Data Must Be AcquiredWhy Is not the Kinetic Parameter Set Unique?Frequency Intervals, Frequency Range, and dc PotentialLimitations of the RMA MethodologySoftware AvailabilityUnambiguous Mechanism IdentificationSummaryExercise – Mechanistic AnalysisEIS – Other Physical PhenomenaConstant Phase Elements (CPE)Experimental ResultsModels to Explain the Origin of CPEEquations to Relate CPE to the Effective CapacitanceDiffusion EffectsFinite Boundary ConditionsUnsteady-State ConditionsZero dc BiasSemi-infinite Boundary ConditionsBlocking Boundary ConditionsReactions with Adsorbed Intermediates, Coupled with DiffusionPorous ElectrodesFilm Formation and PassivationModels EmployedPoint Defect ModelPitting CorrosionSurface Charge ApproachAnion Incorporation ModelExercise – Impedance of CPE, Diffusion, and FilmApplications – A Few ExamplesCorrosionCorrosion of Valve Metals in Acidic Fluoride MediaMechanistic Analysis of a Metal Dissolution ReactionBiosensorsDetection of Chikungunya Protein Using EISDNA SensingBatteriesBattery Status EvaluationApplication of EIS in Battery ResearchExercise: Applications – A Few ExamplesNonlinear EISIntroductionWhat Exactly Is NLEIS?Mathematical BackgroundTaylor Series and Fourier SeriesNLEIS Analysis MethodsEstimation of Nonlinear Charge-Transfer and Polarization ResistancesCalculation of the NLEIS Response of Electrochemical ReactionsSimple Electron Transfer ReactionReaction with an Adsorbed IntermediateSimulation NLEIS under Galvanostatic ConditionsSimulation of Instability in Electrochemical SystemsIncorporation of Solution Resistance Effects in NLEIS SimulationsFrumkin Isotherm – Simulation of the Impedance ResponseExercise – Nonlinear EISAppendix 1: Complex Numbers RefresherAppendix 2: Differential Equations RefresherAppendix 3: Multi-sine WavesAppendix 4: Experiments and Analysis – Few HintsAppendix 5: Manufacturers and Suppliers of EIS Equipment