電化學(xué)阻抗譜分析方法

1、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

2、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

3、 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 sinus

4、oidal 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 asWhere φ is a phase angle.,Revie

5、w 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/ωCA comparison of R and Xc shows that Xc must carry dimensions of resistance, but th

6、e 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 a

7、nd along the abscissa are real, thus, we handle these parameters mathematically as “real” or “imaginary”.A voltage E is applied across R and CWhere Z=R-jXc, called the impedance.,Review of ac circuits,The magnitude o

8、f Z and phase angle are given by the following, respectivelyThe impedance is a kind of generalized resistance. The phase angle expresses the balance between capacitive and resistance components in the series circuit.

9、 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 t

10、he 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 t

11、o 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, solu

12、tion resistance Rs, charge transfer resistance Rct, Warburg impedance Zw.,A Resistance and capacitancein series,f is low:f is high:,In electrochemical cell:R=Rs: solution resistanceC=Cd: double layer capacitance,Elec

13、trochemical Impedance Spectroscopy,A resistance and capacitance in parallel (Randles circuit),Z=Rs at high frequencyZ=Rct+Rs at low frequency,Electrochemical Impedance Spectroscopy,,Mixed kinetic and diffusion control,,

14、,,,,,,,,,,,,,,,,,,,,,,,,C,dl or CPE,RP,R,W,,,,,,,ZW,,,,,,,,with 0?n?1,Electrochemical Impedance Spectroscopy,Abstract the cell into an equivalent circuit model Before starting to fit, get good initial guess values Use

15、?find circle“ optionUse linear regression to evaluate a Warburg impedanceTake care of: Non uniqueness of equivalent circuit modelsWeighting the data,Electrochemical Impedance Spectroscopy,Data Analysis:,復(fù)平面圖,,,Cyclic

16、 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 ferroce

17、ne 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

18、 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 ferroc

19、ene 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. 整個(gè)電解池的電化學(xué)阻抗和雙電層電容隨電位變化。,,,,Lef

20、t: 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.,電化學(xué)極化控制的交流阻抗復(fù)平面圖,反應(yīng)粒子濃度高施加于電極上的交流電信號(hào)的幅度低且頻率高通過(guò)電極的交流電流的振幅遠(yuǎn)