Impedance : Other Transfer Functions (TF) TF-

Transcription

1 Impedance : Other Transfer Functions (TF) TF- 1

2 CONTENTS Background on EIS Other Transfer Functions: Photo-electrochemical TF (IMVS/IMPS) Electro-hydrodynamic TF (EHD) Magneto-hydrodynamic TF Electro-gravimetric TF Raman spectro TF Thermo-electrochemical TF (TEC) Pneumato-chemical Impedance Spectroscopy (PIS) Summary TF - 2

3 BACKGROUND Current response has a the same frequency with an amplitude di and phase F Perturbation in potential, (it is also possible to perform the same in Galvano) Increasing the frequency moving away from the steady state I ss vs E curve TF Some Basics 3

4 BACKGROUND Z(f) = LE(t)/LI(t) L: Laplace Transform The impedance is a complex number: Z = a + jb = Re(Z) + jim(z) (with j 2 = -1) Z = ρ(cosφ + jsinφ) with ρ the modulus and φ the phase Nyquist diagram Bode diagram In the Nyquist plot, the impedance for each frequency is plotted in the complex plane -Im(Z) vs Re(Z). In the Bode Plot, the modulus and the phase of the impedance are plotted against the frequency of the modulation. TF Some Basics 4

5 BACKGROUND What if we replace U and/or I by other input/output quantities? Not only electrical quantities. It is not Electrochemical Impedance Spectroscopy but Transmittance spectroscopy This allows one to study the dependence (output) of the system to an input It is a measurement of magnitude and phase of the output as a function of frequency, in comparison to the input. Unit is not in Ohm but is the ratio of the two quantities H = output/input input TF = output/input output TF Some Basics 5

6 BACKGROUND What if we replace U and/or I by other input/output quantities? Not only electrical quantities. It is not Electrochemical Impedance Spectroscopy but Transmittance spectroscopy This allows one to study the dependence (output) of the system to an input It is a measurement of magnitude and phase of the output as a function of frequency, in comparison to the input. Unit is not in Ohm but is the ratio of the two quantities H = output/input input TF = output/input output F(input) = input x TF = input x output input = output TF Some Basics 6

7 BACKGROUND What about if we replace E and/or I by other input/output quantities? Not only electrical quantities. Potential Current Temperature Pressure Rotation speed of the electrode Magnetic field Light intensity Potential Current of the electrode Current of the secondary electrode Temperature Pressure Magnetic field TF Some Basics 7

8 CONTENTS Other Transfer Functions: Input Output ref IMPS/IMVS Light intensity/φ PhotoCurrent/I Photovoltage/E Electro-hydrodynamic TF (EHD) Rotation speed/ω Current/I Magneto-hydrodynamic TF Magnetic field/b Current/I Electro-gravimetric TF Quartz resonator frequency/f or adsorbed mass/m Sauerbrey relationship: DF = kdm Raman Raman intensity/count.s -1 Current/I Thermo-electrochemical TF (TEC) Temperature/T Current/I Pneumato-chemical Impedance Spectroscopy (PIS) Pressure/P Halme, J. Phys. Chem. Chem. Phys., 2011, 13, Tribollet et al. J. of Electroanal. Chem., 2004, Vol. 572, 2, Pages Olivier at al. J. of Electrochem. Soc., 2004, Vol 151, 2, C112-C118, Perrot et al. The Journal of Physical Chemistry B, 2002, Vol. 106, 12, Deslouis et al. Electrochimica acta, 2010, 55, Olivier, A. et al. Electrochimica Acta, 1996, Vol 41, 17, Millet, P. et al. J. Phys Chem B; TF - 8

9 CONTENTS Other Transfer Functions: Input Output ref TF - IMPS/IMVS Light intensity/φ PhotoCurrent/I Photovoltage/E Electro-hydrodynamic TF (EHD) Rotation speed/ω Current/I Magneto-hydrodynamic TF Magnetic field/b Current/I Electro-gravimetric TF Quartz resonator frequency/f or adsorbed mass/m Sauerbrey relationship: DF = kdm Raman Raman intensity/count.s -1 Current/I Thermo-electrochemical TF (TEC) Temperature/T Current/I Pneumato-chemical Impedance Spectroscopy (PIS) Pressure/P Each type of Transfer Functions is a disciplin itself. We will see only the two first Halme, J. Phys. Chem. Chem. Phys., 2011, 13, Tribollet et al. J. of Electroanal. Chem., 2004, Vol. 572, 2, Pages Olivier at al. J. of Electrochem. Soc., 2004, Vol 151, 2, C112-C118, Perrot et al. The Journal of Physical Chemistry B, 2002, Vol. 106, 12, Deslouis et al. Electrochimica acta, 2010, 55, Olivier, A. et al. Electrochimica Acta, 1996, Vol 41, 17, Millet, P. et al. J. Phys Chem B;

10 IMVS/IMPS φ: light intensity IMVS= LF(t)/LE(t) I: PhotoCurrent - IMPS IMPS= LF(t)/LI(t) U: PhotoVoltage - IMVS IMVS: Intensity Modulated photovoltage Spectroscopy IMPS: Intensity Modulated Photocurrent Spectroscopy TF - 10

11 IMVS/IMPS Which system? Solar cell, Grätzel cell, PV cell E/I Which information? D a. d 2 / τ IMPS where a for weakly absorbed modulated light D: diffusion coefficient of electrons/m 2.s -1 d: photoelectrode film thickness/m τ IMPS τ L = (D τ) 1/2 L: electron diffusion length/m η COL 1 (τ IMVS / τ IMPS ) η COL :Efficiency electron collection TF - IMVS/IMPS Application Note #30 11

12 <I>/mA IMVS/IMPS LP_PV.mpr <I> vs. Ewe IMPS E= IMVS I= Ewe/V 2 3 IMVS= LF(t)/LE(t) IMPS= LF(t)/LI(t) TF - IMVS/IMPS 12

13 <I>/mA IMVS/IMPS LP_PV.mpr <I> vs. Ewe In that case, there is a relatiosnhip bewteen EIS, IMPS and IMVS. For the same condition (same E, same I, same light intensity), EIS = IMVS/IMPS Ewe/V 2 3 IMVS= LF(t)/LE(t) IMPS= LF(t)/LI(t) TF - IMVS/IMPS 13

14 IMVS/IMPS -Im(Z)/Ohm SGEIS 5to 30mA 1 ma led white SP300.mpr - -Im(Z) vs. Re(Z) SGEIS_IMVS.mpr 10 f = 100 khz 5 fmin = Hz 0 f = 0.5 Hz fmin = Hz fmin = Hz 50 Re(Transmittance)/Arbitrary Unit Re(Z)/Ohm 60 cycle number Lifetime of the electron τ n is related to the characteristic frequency f c by the following equation τ n = 1/(2 π f c ) TF - IMVS/IMPS 14

15 R1/Ohm C1/µF IMVS/IMPS SGEIS 5to 30mA 1 ma led white SP300_zfitparam.mpp R1/Ohm vs. <I> # C1/F vs. <I> f min = 1/(2 π RC) Resistance, Capacitor, Minimum frequency and Electron lifetime of white LED vs. light intensity Light intensity/ W.m -2 R/ Ohm C/ µf f min / Hz τ n / ms <I>/mA TF - IMVS/IMPS 15

16 Electro-HydroDynamic TF (EHD) Ω: rotation speed EHD E = LE(t)/LW (t) I: current EHD I = LI(t)/LW (t) U: voltage Z = EHD E / EHD I TF - 16

17 EHD Which system? Useful for analysis electrochemical system that are either partially or completely limited by mass transport Which information? Method to isolate the influence of mass transfer from the electrochemical impedance response of a system Mass transport TF - EHD 17

18 SUMMARY What was the aim of this overview? EIS is only a part of what is possible to do with Function Transfer. Other method exist and maybe other can be developed to investigate the dynamic behavior of the system. User has to find the appropriate input and output. TF - 18

19 SUMMARY ElectroHydrodynamic TF (EHD) PhotoElectrochemical TF (IMVS/IMPS) System Electrochemical system that are either partially or completely limited by mass transport Partially blocked electrode Solar cell Information Mass transfer from the electrochemical impedance response of a system Electron lifetime Diffusion MagnetoHydrodynamic TF Metal electrode deposition Kinetic of the processes ElectroGravimetric TF Insertion in film Reaction with adsorbed species Kinetic of the processes Chemical identification of the species Raman TF Reaction with adsorbed species dynamic information on the interface ThermoElectrochemical TF (TEC) PneumatoChemical Impedance Spectroscopy Redox system Insertion reaction Hydrogen insertion kinetic of mass transport phase transformation TF - 19

20 MORE INFO. Feel free to visit our web site, some application notes or EIS handbook may be helpful for your applications: Thank you for your attention Lets move to the instruments EIS exp side 20