Autolab交流阻抗擬合方法簡(jiǎn)介

1、Electrochemical Impedance spectroscopy理論理論歐姆定律給出直流電位和直流電流的簡(jiǎn)單關(guān)系歐姆定律給出直流電位和直流電流的簡(jiǎn)單關(guān)系: E = i R(1)當(dāng)有交流參與時(shí)，關(guān)系式為當(dāng)有交流參與時(shí)，關(guān)系式為: Eac = iac Z(2), 其中其中Z為阻抗為阻抗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圖: lg(Z)lg(f) 和 lg(f)Nyquist圖: 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)并聯(lián)元件并聯(lián)元件RC串聯(lián)元件串聯(lián)元件Electrochemical Impedance spectroscopy常用元件常用元件: 電阻電阻 R相位角: 00Electrochemical Impedance spectroscopy常用元件常用元件: 電容電容 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單純電阻: 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高頻高頻低頻低頻Electrochemical Impedance spectroscopy單純電容: CC-2-10123-10123456780255075100log(f)log(Z)(o)-phase / deg(+)C-1M2M4M7M9M12M14M17M19M-3M03M5M8M10M13M15MZ / ohm-Z / ohm高頻高頻低頻低頻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電阻與電容串聯(lián)RC高頻高頻低頻低頻RRCElectrochemical Impedance spectroscopy電阻與電容并聯(lián)(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高頻高頻低頻低頻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)低頻低頻高頻

16、高頻C1R2C1R1R2R1R1R1+R2Electrochemical Impedance spectroscopy復(fù)復(fù)合體系合體系R(RC)( RC) Circuit1000200030004000500060007000800001000200030004000500060007000Z / ohm-Z / ohm這三種等效電路的曲線都一樣這三種等效電路的曲線都一樣!必須結(jié)合實(shí)際體系來(lái)選擇合適用的電路。必須結(jié)合實(shí)際體系來(lái)選擇合適用的電路。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擴(kuò)散元件: W通常擴(kuò)散都發(fā)生在低頻的通常擴(kuò)散都發(fā)生在低頻的時(shí)候時(shí)候,故一般與電阻串聯(lián)故一般與電阻串聯(lián)!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與電阻串聯(lián)與電阻串聯(lián)!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