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Techniques based on concepts of impedance,We have discussed ways of studying electrode reactions through large perturbations on the system, for example, potential sweeps, potential steps, or current steps, the electrode is generally driven to a condition far from equilibrium and the response is observed, which is usually a transient signal.
Another approach is to perturb the cell with an alternating signal of small magnitude and observe the way in which system follows the perturbation at steady state.,Electrochemical Impedance Spectroscopy,FRA: Frequency Response Analysis,Potentiostatic or galvanostatic measurements,Review of ac circuits,A purely sinusoidal voltage can be expressed as
Where ω is the angular frequency, which is 2π times the conventional frequency in hertz.
The current lags the voltage, it can be expressed generally as
Where φ is a phase angle.,Review of ac circuits,A pure resistance R, E=IR, where the phase is zero.
A pure capacitance C,
Where Xc is the capacitive reactance, 1/ωC
A comparison of R and Xc shows that Xc must carry dimensions of resistance, but the magnitude of Xc falls with increasing frequency.,Resistance:,,E,,I,,Capacitance:,,I,,E,Electrochemical Impedance Spectroscopy,,,,,,,,,,,,,,Review of ac circuits,Components along the ordinate are assigned as imaginary and along the abscissa are real, thus, we handle these parameters mathematically as “real” or “imaginary”.
A voltage E is applied across R and C
Where Z=R-jXc, called the impedance.,Review of ac circuits,The magnitude of Z and phase angle are given by the following, respectively
The impedance is a kind of generalized resistance. The phase angle expresses the balance between capacitive and resistance components in the series circuit. For a pure resistance, φ=0; for a pure capacitance, φ=π/2; and for mixtures, intermediate phase angles are observed.,Review of ac circuits,For impedances in parallel, the inverse of the overall impedance is the sum of the reciprocals of the individual vectors. Sometimes it is advantageous to analyze ac circuits in terms of the admittance, Y, which is the inverse impedance 1/Z.,Equivalent circuit of a cell,In a general sense, we ought to be able to represent its performance by an equivalent circuit of resistors and capacitors under a given excitation.
The elements of equivalent circuit of a cell: double-layer capacitance Cd, faradaic impedance Zf, solution resistance Rs, charge transfer resistance Rct, Warburg impedance Zw.,A Resistance and capacitance
in series,f is low:
f is high:,In electrochemical cell:
R=Rs: solution resistance
C=Cd: double layer capacitance,Electrochemical Impedance Spectroscopy,A resistance and capacitance in parallel (Randles circuit),Z=Rs at high frequency
Z=Rct+Rs at low frequency,Electrochemical Impedance Spectroscopy,,Mixed kinetic and diffusion control,,,,,,,,,,,,,,,,,,,,,,,,,,C,dl or CPE,RP,R,W,,,,,,,ZW,,,,,,,,with 0n1,Electrochemical Impedance Spectroscopy,Abstract the cell into an equivalent circuit model
Before starting to fit, get good initial guess values
Use „find circle“ option
Use linear regression to evaluate a Warburg impedance
Take care of:
Non uniqueness of equivalent circuit models
Weighting the data,Electrochemical Impedance Spectroscopy,Data Analysis:,复平面图,,,Cyclic voltammograms(a) and differential pulse voltammograms(b) of different concentrations of ferrocene on the GC electrode,
C(mmol/L): (1 ) 0.2, (2) 0.5, (3) 1; scan rate: 100 mV/s,,,Cyclic voltammograms of 1 mmol/L ferrocene on the GC electrode, Plot of oxidation peak current (Ip,a) vs. square root of scan rate (υ1/2) for ferrocene,,,Left: Voltammetric curves of 1 mmol/L ferrocene on the GC eletrode with different rotation rate, rotation rate (r/min): (1) 300, (2) 600, (3) 900, (4) 1200, (5) 1500; scan rate: 5 mV/s; Right: plot of limiting diffusion current (Il) square root of angular velocity (ω1/2) for ferrocene,,Left: Nyquist plots of 1 mmol/L ferrocene at different potentials on the rotating GC electrode and its fitting results (solid line), E (V):■0.40,●0.45,▲0.50; rotation rate=900 r/min; Right: the corresponding equivalent circuit. 整个电解池的电化学阻抗和双电层电容随电位变化。,,,,Left: Nyquist plots of 1 mmol/L ferrocene on the rotating GC electrode and its fitting results (solid line), E=0.50 V. Right: the corresponding equivalent circuit.,电化学极化控制的交流阻抗复平面图,反应粒子浓度高
施加于电极上的交流电信号的幅度低且频率高
通过电极的交流电流的振幅远小于极限电流值
此时电极附件不会出现可察觉的浓度变化
电极过程只受电化学极化控制。,Diffusion coefficient and standard heterogeneous rate constant,
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