Autolab交流阻抗拟合方法简介

1、Electrochemical Impedance spectroscopy理论理论欧姆定律给出直流电位和直流电流的简单关系欧姆定律给出直流电位和直流电流的简单关系: E = i R(1)当有交流参与时，关系式为当有交流参与时，关系式为: Eac = iac Z(2), 其中其中Z为阻抗为阻抗Electrochemical Impedance spectroscopyWorking ElectrodeCounterElectrodeReferenceElectrodePOTENTIOSTATGALVANOSTATDiff.ampl.senseDEFGABCHIElectrochemicalCe

2、llElectrochemical Impedance spectroscopy+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -WECEREPOTENTIOSTATGALVANOSTATDiff.ampl.sDEFGABCHIElectrochemical Impedance spectroscopy+ -+ -+ -+ -+ -SolutionResistanceCapacitordouble layerDE+ -+ -+ -+ -+ -PolarizationResistanceElectrochemical Impedance spectroscopyI0E0I0 + DI

3、sin ( wt + f)E0 + DE sin wtIEElectrochemical Impedance SpectroscopyFRA: Frequency Response AnalysisPotentiostatic or galvanostatic 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.

4、The current lags the voltage, it can be expressed generally as Where is a phase angle.sineEtwsin()iItwfReview 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/C A comparison of R and Xc shows that Xc must carry dimension

5、s of resistance, but the magnitude of Xc falls with increasing frequency.sin()2CEitXwResistance:ZREIF 0oCapacitance:Z C1w IEF -90oElectrochemical Impedance SpectroscopyReview of ac circuits Components along the ordinate are assigned as imaginary and along the abscissa are real, thus, we handle these

6、 parameters mathematically as “real” or “imaginary”. A voltage E is applied across R and C Where Z=R-jXc, called the impedance.CEjX I -()RCCEEEI RjXIZ-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.

7、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, intermediate phase angles are observed. 22 1/2()1tanCCZRXXRRCwF Electrochemical Impedance spectroscopyRsolRctCdlDEFHIGH

8、FREQUENCYLOW FREQUENCYElectrochemical Impedance spectroscopyElectrochemical Impedance spectroscopyFRA test procedure with dummy cell: connect WE(c)-2-112342.02.32.52.83.03.30102030405060log(f)log(Z)(o)-phase / deg(+)Bode图: lg(Z)lg(f) 和 lg(f)Nyquist图: Z -Z”FRA test procedure with dummy cell: connect

9、WE(c)0.1K0.4K0.6K0.9K1.1K00.3K0.5K0.8K1.0KZ / ohm-Z / ohmElectrochemical Impedance spectroscopyCdlRp ( RC)并联元件并联元件RC串联元件串联元件Electrochemical Impedance spectroscopy常用元件常用元件: 电阻电阻 R相位角: 00Electrochemical Impedance spectroscopy常用元件常用元件: 电容电容 C相位角: 900Electrochemical Impedance spectroscopyCPE 常相元素常相元素CON

10、STANT PHASE ELEMENTSURFACE ROUGHNESSHETEROGENEOUSSURFACEn = 1 ONLY CAPACITANCEn = 0 ONLY RESISTANCECIRCUIT ELEMENTZ = 1/ (w wQ)nQ =Electrochemical Impedance spectroscopyPERFECT ELECTRODE = CHETEROGENEOUS SURFACE = QElectrochemical Impedance spectroscopyFRA test procedure with dummy cell: connect WE(

11、c)-2-112342233330102030405060log(f)log(Z)(o)-phase / deg(+)FRA test procedure with dummy cell: connect WE(c)0.K0.K1K1K1K00.K1K1K1KZ / ohm-Z / ohm n = 1 Q = C n 1 n = 0.8Q C FRA test procedure with dummy cell: connect WE(c)-2-11234223333010.020.030.040.050.060.0log(f)log(Z)(o)-phase / deg(+)FRA test

12、procedure with dummy cell: connect WE(c)0.K0.K1K1K1K00.K1K1K1KZ / ohm-Z / ohmElectrochemical Impedance spectroscopy单纯电阻: RFRA test procedure with dummy cell: connect WE(e)R-2-112342.02.53.03.54.04.55.0-1015406590log(f)log(Z)(o)-phase / deg(+)FRA test procedure with dummy cell: connect WE(e)R05K10K15

13、K20K25K30K35K40K45K50K-75-50-250255075Z / ohm-Z / ohm高频高频低频低频Electrochemical Impedance spectroscopy单纯电容: CC-2-10123-10123456780255075100log(f)log(Z)(o)-phase / deg(+)C-1M2M4M7M9M12M14M17M19M-3M03M5M8M10M13M15MZ / ohm-Z / ohm高频高频低频低频Electrochemical Impedance spectroscopyR and C in serialsRC-2-1012345

14、63.54.04.55.05.56.06.57.07.50102030405060708090log(f)log(Z)(o)-phase / deg(+)R and C in serialsRC-1M2M4M7M9M12M14M17M19M03M5M8M10M13M15MZ / ohm-Z / ohm电阻与电容串联RC高频高频低频低频RRCElectrochemical Impedance spectroscopy电阻与电容并联(RC)R and C in parallel(RC)-2-101234564.04.55.05.56.06.57.07.50255075100log(f)log(Z)

15、(o)-phase / deg(+)R and C in parallel(RC)-3M03M5M8M10M13M15M18M20M23M03M5M8M10M13M15M18M20M23M25MZ / ohm-Z / ohm高频高频低频低频Electrochemical Impedance spectroscopyR(RC)-2-112342.02.32.52.83.03.30102030405060log(f)log(Z)(o)-phase / deg(+)R(RC)0.1K0.4K0.6K0.9K1.1K00.3K0.5K0.8K1.0KZ / ohm-Z / ohmR(RC)低频低频高频

16、高频C1R2C1R1R2R1R1R1+R2Electrochemical Impedance spectroscopy复复合体系合体系R(RC)( RC) Circuit1000200030004000500060007000800001000200030004000500060007000Z / ohm-Z / ohm这三种等效电路的曲线都一样这三种等效电路的曲线都一样!必须结合实际体系来选择合适用的电路。必须结合实际体系来选择合适用的电路。Electrochemical Impedance spectroscopyHoogovens cell, steel with coating.Far

17、aday cage-2-101234562.02.53.03.54.04.55.05.56.06.50102030405060708090log(f)log(Z)(o)-phase / deg(+)Hoogovens cell, steel with coating.Faraday cage00.3M0.5M0.8M1.0M1.3M1.5M1.8M2.0M2.3M00.3M0.5M0.8M1.0M1.3M1.5M1.8M2.0M2.3MZ / ohm-Z / ohm R(QR(RQ)R(RQ)(RQ)Electrochemical Impedance spectroscopyMeasureme

18、nt during 1 mA dischargeof a Duracell Alkaline Battery-2-11234-0.-0.-0.-0.-0.-0.-0.-0-0012345678910log(f)log(Z)(o)-phase / deg(+)Measurement during 1 mA dischargeof a Duracell Alkaline Battery0.0.1111100.0.0.0.11Z / ohm-Z / ohmR(RQ)(RQ)Electrochemical Impedance spectroscopy025K50K75K100K125K025K50K7

19、5K100K125KZ / ohm-Z / ohm-4-214601234501020304050607080log(f)log(Z)(o)-phase / deg(+)0100200300400500-269-19231481731Z / ohm-Z / ohmR(CR(RQ)(RQ)Electrochemical Impedance spectroscopyCRRPdl or CPEWZWR1(CR2W)Ferri/ferro-1.0-0.500.51.01.52.02.53.03.51.82.02.32.52.83.03.312.515.017.520.022.525.027.530.0

20、32.535.0log(f)log(Z)(o)-phase / deg(+)Ferri/ferro01002003004005006007008009000100200300400500600700800900Z / ohm-Z / ohm扩散元件: W通常扩散都发生在低频的通常扩散都发生在低频的时候时候,故一般与电阻串联故一般与电阻串联!Electrochemical Impedance spectroscopyRRPWZWR1(CR2W)C or CPEFerri/ferro-1-101122334222333312.515.017.520.022.525.027.530.032.535.

21、0log(f)log(Z)(o)-phase / deg(+)Ferri/ferro01002003004005006007008009000100200300400500600700800900 Z / ohm-Z / ohmR1R1+R2与电阻串联与电阻串联!Ferri/ferro01002003004005006007008009000100200300400500600700800900Z / ohm-Z / ohm45W=lineElectrochemical Impedance spectroscopyImpedance measurement at liquid- liquid interface1M1M2M2M3M3M4M4M5M5M01M1M2M2M3M3M4M4M5MZ / ohm-Z / ohmImpedance measurement at liquid- liquid interface-2-1-1011223666775.010.015.020.025.030.035.040.045.0log(f)log(Z)(o)-p