Measuring photoelectrochemical performance

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This talk is on some of the basics of making proper solar cell efficiency measurements and deriving correct information from 2 and 3 electrode measurements.
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  • Hello, my name is Jeff Christians and I’m a second year graduate student in the Kamat Lab. Today I would like to talk to you about Measuring Photoelectrochemical Performance of QDSCs. Interpreting 2 and 3 electrode measurements.
  • A potentiostat is generally used in photoelectrochemical measurements. Potentiostats are simply instruments that measure current between two electrodes when a potential is applied. When the potential of the electrode is higher – or more negative – electrons flow from the electrode into the electrolyte solution, causing a reduction reaction. Likewise, when the potential of the electrode is below – or more positive – electrons flow from the electrolyte into the electrode, causing an oxidation.
  • When two ideal electrodes are immersed in an electrolyte solution with resistance Rs, as shown on the right, we obtain an ohmic, V= I*R response. Where the IV curve is linear with a slope of Rs.
  • Now, when this same experiment is performed with 2 real electrodes, the response is ohmic for low current densities, but, at high currents, the response deviates from the linear response seen with two ideal electrodes. This deviation is know as electrode polarization.
  • Electrode polarization also happens at the counter electrode in liquid junction solar cells. An ideal, non-polarizable, counter electrode would be able to pass any amount of current at the reduction potential of the redox couple, however, real counter electrodes are polarizable. Therefore, depending on how well suited the counter electrode is to the redox couple, to pass a desired current extra voltage needs to be applied.
  • The extra voltage that needs to be applied in order to pass the desired current is termed overpotential. Overpotential is the difference between the thermodynamic potential of a reaction and the actual potential at which it occurs. As seen below, to pass the desired current with this real, polarizable, electrode, we must apply a potential equal to the thermodynamic potential plus delta V, the overpotential.
  • This overpotential needed to drive a reaction can be caused by a variety of different factors, some of which are, electron transfer across the charge double layer formed at the electrode/electrolyte boundary, depletion of concentration at the electrode surface, chemical reactions that must occur before electron transfer, and others. In general, the overpotential can be minimized by selecting an appropriate electrode material for use with your redox couple.
  • Another important concept in semiconductor physics and in understanding solar cell operation is the fermi level. The fermi level of a material is a pseudo-state that has a 50% probability of being occupied, and it is a measure of the potential energy of electrons in a solid. In semiconductors, the fermi level lies between the valance band and conduction band, and does not necessarily correspond with an actual electronic state in the material. In the examples below, we can see that as we raise the relative concentrations of electrons in the conduction band of our semiconductor, we raise the fermi level closer to the conduction band edge and vise versa.
  • QDSCs are constructed with semiconductor heterojunctions in the working electrode, commonly TiO2 coated with a CdSe sensitizing layer. When two semiconductors with different fermi levels are place in electrical contact with one another,
  • There is both hole transfer and electron transfer between the semiconductors until the fermi levels reach equilibrium.
  • Now that we have an understanding of the basic physics needed to understand solar cell performance, let us look at the different measurement techniques employed. Electrochemical measurements can be performed using either a 2 or 3 electrode configuration. In a 2 electrode cell, there is a working electrode, generally the photoactive electrode in QDSCs, and a counter electrode that also functions as the reference electrode. The potential between these two electrodes is then controlled by the potentiostat and the current between the electrodes is measured. In a 3 electrode cell, the counter electrode and reference electrode are separated into two distinct electrodes. The potential of the working electrode is set with respect to the reference electrode and the current between the working electrode and counter electrode is measured.
  • Let’s first look at solar cell performance using a 2-electrode cell.
  • In this example, we have a QDSC that has a TiO2/CdSe working electrode on FTO glass, a sulfide/polysulfide redox couple, and a copper sulfide/RGO composite counter electrode. In the dark, there is fermi level equilibration of the entire solar cell to the potential of the sulfide/polysulfide redox couple. The cell is at equilibrium and no current flows between the electrodes. If we illuminate the cell at open circuit conditions, when no current is allowed to flow through the external circuit,
  • Electrons are excited from the valance band to the conduction band in CdSe.
  • These excited electrons are then able to be transferred fromCdSe into the conduction band of TiO2
  • Upon further illumination, some of these conduction band electrons recombine with holes in the CdSe or are scavanged by the redox couple.
  • Eventually, an equilibrium is reached where the rate of excitation of the CdSe by the incoming light is equal to the rate of recombination. Since we are exciting electrons into the conduction band of CdSe, the steady state concentration of electrons in the conduction band of the TiO2/CdSe composite is increased from its dark concentration, thus increasing the fermi level of the TiO2/CdSe. The difference between the fermi level of the TiO2/CdSe and the potential of the copper sulfide/RGO counter electrode is the open circuit voltage of the cell.
  • If we were to image the same system with a larger recombination rate, the steady state concentration of electrons in the conduction band of the TiO2/CdSe would decrease, causing a decrease in the fermi level and therefore, a decrease in the cell open circuit voltage.
  • When we begin to draw current from our solar cell, the counter electrode performance begins to play a significant role because the current in each electrode must be the same since they are in series. In this example, the red IV curve is for a working electrode with an ideal, non-polarizable, counter electrode, and the blue curve is the polarization curve of the actual counter electrode in the cell. When actually measuring a solar cell in a 2-electrode configuration, these two curves become convoluted.
  • For example, let’s think of the case where we are drawing 10mA/cm2 or current from the working electrode. The potential at which the photoelectrode can provide this current is 390mV, but we must also take into account counter electrode polarization. From the blue counter electrode polarization curve, we see that it requires an overpotential of 95mV to pass 10mA/cm2 or current. Therefore, when we are actually measuring the IV characteristics of our solar cell, the potential that we will be able to draw 10mA/cm2 will be 390mV – 95mV = 295mV. By repeating this same analysis for every current, we can obtain the dashed red curve, the actual measured IV curve of the cell, which is a convolution of the photoelectrode and counter electrode. Now, let’s look at what is happening in a solar cell while we are taking these IV measurements with different counter electrodes.
  • Let’s start by looking at the case of an ideal counter electrode that can pass any amount of current with no overpotential. When we start scanning potential at Voc, current is zero and the rate of excitation is equal to the rate of recombination.
  • As we begin scanning the voltage, we decrease the potential of the TiO2/CdSefermi level, drawing current from the working electrode.
  • We continue to decrease the fermi level of the working electrode until it reaches the potential of the counter electrode. At this point, since there is no potential difference between the working electrode and the counter electrode, we have reached the short circuit current condition. For an ideal counter electrode, at short circuit current, the potential of the counter electrode is equal to the redox potential of the electrolyte because, by definition, an ideal counter electrode can pass any amount of current at the thermodynamic potential of the redox couple.
  • Now, instead of the case of an ideal counter electrode, let’s consider a solar cell employing a counter electrode with low overpotential, such as the copper sulfide/RGO counter electrode developed in our lab. In this case, at Voc, since there is no current flowing in the cell, the potential of this good counter electrode is the same as that of the ideal counter electrode, so Voc does not change.
  • As we begin to draw current from the cell we now have a slight overpotential at the counter electrode that is needed to pass this same current. As we saw earlier, this overpotential takes some of the potential that the working electrode is supplying, thus decreasing cell efficiency slightly.
  • As we continue to scan, we still reach short circuit current conditions when the fermi level of the working electrode is equal to the potential of the counter electrode, but now the potential of the counter electrode is no longer the same as the redox potential of the electrolyte because we need to supply a small overpotential in order to pass the current.
  • Finally, let’s examine the case of a very poor counter electrode for our sulfide/polysulfide redox couple, platinum. Again, at open circuit conditions, the cell looks the same as it did with the ideal counter electrode because there is no current flowing through the cell.
  • Unlike with the ideal or Cu2S/RGO counter electrode, as we begin to decrease the potential of the working electrode and draw current however, we immediately see a very large overpotential. This causes a very large decrease in the potential seen for each current density, drastically decreasing the cell’s fill factor.
  • As we continue to scan the potential we now reach short circuit current conditions, where there is no potential difference between the fermi level of the working electrode and the potential of the counter electrode, at a potential vastly different from the redox potential of the electrolyte. For this counter electrode, much of the voltage of our cell is taken up by the overpotential of the Pt counter electrode.
  • So, we have seen how 2-electrode measurements can give us real world performance information for solar cells. Using a 2-electrode system, we are able to measure cell open circuit voltage, short circuit current, and calculate cell efficiency. We have also seen how the individual electrode energies change as we measure the IV characteristics of our cell and how each electrode affects the performance of the system. When making 2-electrode measurements it is important to remember that the performance of the working and counter electrodes are convoluted. 2-electrode measurements are the only way to determine overall cell performance, but it is not a suitable method for determining individual electrode performance information.
  • For individual electrode performance information, we must use a 3-electrode cell.
  • In a 3-electrode cell, the potential of the working electrode is controlled with respect to the potential of a reference electrode which is designed to hold its potential across a wide variety of conditions. This gives us direct control over the working electrode potential. We then apply a potential to the counter electrode so that the counter electrode is able to pass the same current as the working electrode. This ensures that the current that we measure between the working electrode and the counter electrode is controlled only by working electrode performance, rendering the counter electrode unimportant.
  • So, in 3- electrode measurements, the potential of the working electrode is set with respect to a reference electrode. The potential of the counter electrode is set so that it passes the same current as the working electrode. This allows us to measure the performance of the working electrode in isolation.
  • When looking at IV data obtained using a 3-electrode cell, the potential scale is now potential versus the reference potential. Depending on the reference electrode chosen, this could change significantly, therefore, to extract meaningful information about the working electrode performance we must convert this potential scale into a more meaningful one.
  • Since we know the potential of our saturated calomel reference electrode, 0.24 V, and we know the redox potential of our sulfide/polysulfide electrolyte with respect to the reference electrode, we can adjust our voltage scale to show cell potential. This adjusted IV curve now shows the performance of the working electrode without any counter electrode effects.
  • Using a 3-electrode cell, it is possible to determine the performance characteristics of an individual electrodes. Providing photoelectrode IV curves or counter electrode polarization curves. These results can be very informative and are often important in characterizing solar cells, but 3-electrode measurements are not able to give information about solar cell efficiencies.
  • Both 2 and 3 electrode measurements can be used in determining QDSC performance characteristics. Using a 2-electrode setup, the potentiostat controls the voltage between the working and counter electrodes. This measurement gives real world performance information of the solar cell, such as, solar energy conversion efficiency, open circuit voltage, and short circuit current.
  • 3-electrode measurements can also be used for characterizing QDSCs. Using a 3-electrode cell removes the complications of the counter electrode by controlling the potential of the working electrode with respect to a reference electrode. In this way, it is possible to isolate the performance of the individual solar cell electrodes, but it is not possible to determine overall device properties such as efficiency.
  • Thank you for listening to this presentation on measuring photoelectrochemical performance. I would especially like to thank those people in other research groups who’s research contributed to this presentation. For more information on the Kamat research group here at the University of Notre Dame, visit us on the web at www.kamatlab.com. Thank you.
  • Measuring photoelectrochemical performance

    1. 1. Measuring PhotoelectrochemicalPerformance of QDSCs.Interpreting 2 and 3 Electrode MeasurementsJeff Christians and Prashant V. KamatRadiation LaboratoryDepartment of Chemical & Biomolecular EngineeringDepartment of Chemistry & BiochemistryUniversity of Notre DameNotre Dame, IN 46556
    2. 2. What is a Potentiostat? • Potentiostats measure current in a cell when a potential is applied (or voltage when a current is applied) - Electrode Solution Reduction Reaction - Electrode Solution A + e -  A-Potential Potential Oxidation Reaction A - e-  A+ + + Bard, A. J., Electrochemical Methods Introduction 2-Electrode 3-Electrode Summary
    3. 3. Ideal Electrodes - + Power Supply Eappl V=ixR + - i EapplEappl = i x Rsol’n Rsol’n i - + Equivalent Circuit i Slope = Rsol’n Ideal Electrode Ideal Electrode Eappl Rsol’n Bard, A. J., Electrochemical Methods Introduction 2-Electrode 3-Electrode Summary
    4. 4. Real Electrodes - + Power Supply• Ideal vs. Real Electrodes – Ex. 2 SCEs in a KCl solution Eappl i i - + Eappl Rsol’n SCE SCE Ideal electrodes Real electrodes Bard, A. J., Electrochemical MethodsIntroduction 2-Electrode 3-Electrode Summary
    5. 5. Ideal vs. Real Counter Electrodes• Ideal Counter Electrode non-polarizable i Ideal Counter Reduction Potential Real Counter Electrodes V Very Poor Good Poor Hodes, G., J. Phys. Chem. Lett., 2012, 3 (9), pp 1208–1213Introduction 2-Electrode 3-Electrode Summary
    6. 6. Overpotential• Overpotential – The difference between the thermodynamic potential of a reaction and the potential at which it actually occurs. i Thermodynamic Potential ΔV VDesired current Bard, A. J., Electrochemical MethodsIntroduction 2-Electrode 3-Electrode Summary
    7. 7. Overpotential• Overpotential – The difference between the thermodynamic potential of a reaction and the potential at which it actually occurs. • Electron transfer across charge double layer • Depletion of concentration at electrode surface • Chemical reactions that must occur before electron transfer • And MORE!! Bard, A. J., Electrochemical MethodsIntroduction 2-Electrode 3-Electrode Summary
    8. 8. Fermi Level• The Fermi level is a pseudo-state that has a 50% probability of being occupied – A measure of the potential energy of an electron in a solid CB CB CB CB - - - - - - - - - - + + + + + + + + + + VB VB VB VB Bard, A. J., Electrochemical MethodsIntroduction 2-Electrode 3-Electrode Summary
    9. 9. Semiconductor Heterojunctions CB ? CB - - - - - - ? + VB + + + VBIntroduction 2-Electrode 3-Electrode Summary
    10. 10. Semiconductor Heterojunctions CB CB - - - - - - + + VB + + VBIntroduction 2-Electrode 3-Electrode Summary
    11. 11. Electrochemical Measurements 2 – Electrode Cell 3 – Electrode Cell Power Supply Power Supply Measure Current Measure Current Working Electrode Working Electrode i i Counter Electrode Eapp Eapp Reference/Counter Reference Electrode Electrode Control Voltage Control Voltage Bard, A. J., Electrochemical MethodsIntroduction 2-Electrode 3-Electrode Summary
    12. 12. 2-Electrode Measurements 2 – Electrode Cell 3 – Electrode Cell Power Supply Power Supply Measure Current Measure Current Working Electrode Working Electrode i i Counter Electrode Eapp Eapp Reference/Counter Reference Electrode Electrode Control Voltage Control Voltage Bard, A. J., Electrochemical MethodsIntroduction 2-Electrode 3-Electrode Summary
    13. 13. Recombination and VOC Step by Step: -Potential EFermi S2-/Sn2- Cu2S/RGO CdSe FTO Desired Electron + TiO2 Transfer Recombination Introduction 2-Electrode 3-Electrode Summary
    14. 14. Recombination and VOC Step by Step: - 1. Excitation 1Potential EFermi S2-/Sn2- Cu2S/RGO CdSe FTO Desired Electron + TiO2 Transfer Recombination Introduction 2-Electrode 3-Electrode Summary
    15. 15. Recombination and VOC Step by Step: - 1. Excitation 2 2. Electron Transfer 1Potential EFermi S2-/Sn2- Cu2S/RGO CdSe FTO Desired Electron + TiO2 Transfer Recombination Introduction 2-Electrode 3-Electrode Summary
    16. 16. Recombination and VOC Step by Step: - 1. Excitation 2 2. Electron Transfer 3. Recombination 3 1Potential EFermi S2-/Sn2- Cu2S/RGO CdSe FTO Desired Electron + TiO2 Transfer Recombination Introduction 2-Electrode 3-Electrode Summary
    17. 17. Recombination and VOC Step by Step: - 1. Excitation 2 2. Electron Transfer 4 3. Recombination EFermi 3 4. Build up e- in CB until VOC 1 Rexcitation = RrecombinationPotential S2-/Sn2- Cu2S/RGO CdSe FTO Desired Electron + TiO2 Transfer Recombination Introduction 2-Electrode 3-Electrode Summary
    18. 18. Recombination and VOC Step by Step: - 1. Excitation 2 2. Electron Transfer 3. Recombination 4 5 3 4. Build up e- in CB until EFermi VOC 1 Rexcitation = RrecombinationPotential Cu2S/RGO 5. If recombination rate S2-/Sn2- is increased, VOC is decreased CdSe FTO Desired Electron + TiO2 Transfer Recombination Introduction 2-Electrode 3-Electrode Summary
    19. 19. Role of the Counter Electrode • Current in each electrode must be the same so we must count polarization losses at the counter electrode Photocurrent (mA cm-2) Red – Working electrode with ideal 15 counter electrode (no-polarization) 10 Blue – Counter electrode polarization curve 5-.6 -.4 -.2 Potential (V) -5 - 10 Hodes, G., J. Phys. Chem. Lett., 2012, 3 (9), pp 1208–1213 Introduction 2-Electrode 3-Electrode Summary
    20. 20. Role of the Counter Electrode • Look at 10mA/cm2 – Photoelectrode potential = 390mV – Counter Electrode polarization = 95mV Photocurrent (mA cm-2) – Actual cell potential at 15 10mA/cm2 = 390mV – 95mV 10 = 295mV 5-.6 -.4 -.2 Potential (V) -5 - 10 Hodes, G., J. Phys. Chem. Lett., 2012, 3 (9), pp 1208–1213 Introduction 2-Electrode 3-Electrode Summary
    21. 21. An Ideal Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 + - 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Ideal Counter EFermi FTO Potential S2-/Sn2- S2-/Sn2- Ideal CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    22. 22. An Ideal Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 + - 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Ideal Counter EFermi FTO Potential S2-/Sn2- S2-/Sn2- Ideal CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    23. 23. An Ideal Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 + - 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Ideal Counter FTO Potential S2-/Sn2- EFermi S2-/Sn2- Ideal CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    24. 24. A Good Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 Good + - 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Cu2S/RGO EFermi FTO Potential S2-/Sn2- S2-/Sn2- Cu2S/RGO CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    25. 25. A Good Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 Good + - 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Overpotential Cu2S/RGO EFermi FTO Potential S2-/Sn2- S2-/Sn2- Cu2S/RGO CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    26. 26. A Good Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 Good + - 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Overpotential at JSC Cu2S/RGO FTO Potential EFermi S2-/Sn2- S2-/Sn2- Cu2S/RGO CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    27. 27. A Poor Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 Good + - Poor 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Platinum EFermi FTO Potential S2-/Sn2- S2-/Sn2- Pt CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    28. 28. A Poor Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 Good + - Poor 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Overpotential Platinum EFermi FTO Potential S2-/Sn2- S2-/Sn2- Pt CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    29. 29. A Poor Counter Electrode 15 Photocurrent (mA cm-2) Ideal 10 Good + - Poor 5 i Eappl 0 -.6 -.4 -.2 - + Potential (V) TiO2/CdSe - Overpotential at JSC Platinum EFermi FTO Potential S2-/Sn2- S2-/Sn2- Pt CdSe FTO + TiO2 Hodes, G., Gratzel, M. et. al, J. Phys. Chem. B, 2000, 104, 2053-2059Introduction 2-Electrode 3-Electrode Summary
    30. 30. Summary• “Real world” device performance – Cell Efficiency – Open Circuit Voltage – Short Circuit Current• Both electrodes affect performance• DOES NOT give information about the performance of individual electrodesIntroduction 2-Electrode 3-Electrode Summary
    31. 31. 3-Electrode Measurements 2 – Electrode Cell 3 – Electrode Cell Power Supply Power Supply i i Eapp Eapp Bard, A. J., Electrochemical MethodsIntroduction 2-Electrode 3-Electrode Summary
    32. 32. 3 – Electrode Measurements i This voltage is setcontrol the so the counterpotential of the electrode can passworking electrode Eappl the same currentvs. known - + as the workingpotential of the electrode Reference Electrodereference Working Electrode Counter Electrodeelectrode Bard, A. J., Electrochemical Methods Introduction 2-Electrode 3-Electrode Summary
    33. 33. 3 – Electrode Measurements• Set potential of working electrode with respect to reference electrode• Potential of the counter electrode is set so that it passes same current as working electrode• Measures only the performance of the working electrode, counter electrode does not matterIntroduction 2-Electrode 3-Electrode Summary
    34. 34. Interpretation• Ex. QDSSC with S2-/Sn2- electrolyte Photocurrent (mA cm-2) 15 10 5 0 1.6 1.2 0.8 0.4 0 Potential (V vs. SCE) Hodes, G., J. Phys. Chem. Lett., 2012, 3 (9), pp 1208–1213Introduction 2-Electrode 3-Electrode Summary
    35. 35. Interpretation• Ex. QDSSC with S2-/Sn2- electrolyte – SCE potential = +0.24V – S2-/Sn2- redox potential = -0.5V vs. SHE (-0.74V vs SCE) Cell Voltage (V) JSC 0.8 0.6 0.4 0.2 0 Photocurrent (mA cm-2) 15 10 5 0 1.6 1.2 0.8 0.4 0 Potential (V vs. SCE) Hodes, G., J. Phys. Chem. Lett., 2012, 3 (9), pp 1208–1213Introduction 2-Electrode 3-Electrode Summary
    36. 36. Summary• CANNOT determine device performance• CAN Determine individual electrode performance information – Photoelectrode performance – Counter electrode polarization curvesIntroduction 2-Electrode 3-Electrode Summary
    37. 37. Measuring Efficiency• 2-Electrode measurements + - i – Control potential difference Eappl + between two electrodes of - TiO2/CdSe unknown absolute potential Cu2S/RGO – Gives performance of the entire FTO S2-/Sn2- cellIntroduction 2-Electrode 3-Electrode Summary
    38. 38. Individual Electrode Performance• 3-Electrode measurements – Control potential of one electrode with respect to a reference of known potential – Gives performance information of only one electrode i Power Supply Eappl + - Reference Electrode Working Electrode Counter Electrode i EappIntroduction 2-Electrode 3-Electrode Summary
    39. 39. Thank You! ®Thank you to those whose work contributed tothis presentation!More information on the Kamat Research Group can be found at: www.kamatlab.com

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