电化学阻抗谱分析方法

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 is generally driven to a condition far from equilibrium and the response is obse

2、rved, 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 gal

3、vanostatic measurements,Review of ac circuits,A purely sinusoidal voltage can be expressed as Where is the angular frequency, which is 2 times the conventional frequency in hertz. The current lags the voltage, it can be expressed generally as Where is a phase angle.,Review of ac circuits,A pure resi

4、stance R, E=IR, where the phase is zero. A pure capacitance C, Where Xc is the capacitive reactance, 1/C 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 Spe

5、ctroscopy,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 magn

6、itude 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, =0; for a pure capacitance, =/2; and for mixtures, i

7、ntermediate 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

8、.,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,

9、 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

10、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 fi

11、nd 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

12、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 (1/2) for ferrocene,Left: Voltammetric curves of 1 mmol/L ferrocene on the GC

13、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 (1/2) 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),