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Electrochemical Theory

Electrochemical Theory. Kinetics of Activation Controlled Reactions. M  M n+ + ne - rate of reaction depends on potential according to the Tafel equation:. Tafel’s Law. Slope . Slope b. b =2.303 . Potential. E 0 a. i 0,a. ln | i |. log | i |. Charge Transfer Resistance.

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Electrochemical Theory

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  1. Electrochemical Theory

  2. Kinetics of Activation Controlled Reactions M  Mn+ + ne- • rate of reaction depends on potential according to the Tafel equation:

  3. Tafel’s Law Slope  Slope b b=2.303 Potential E0a i0,a ln |i| log |i|

  4. Charge Transfer Resistance • Charge transfer resistance = local slope of i versus E curve (not log i)

  5. Charge Transfer Resistance • Note that charge transfer resistance is not a constant, but depends on the applied current density • If we could measure the charge transfer resistance, we could determine the current density

  6. Dependence of Kinetics on Reactant Concentration • More reactant allows reaction to go faster, hence rate is proportional to reactant concentration • e.g. oxygen reduction Surface concentration of oxygen Minus sign because thisis a cathodic reaction(and c is taken as positive)

  7. [O2] [O2] [O2] Tafel’s Law Cathodic reaction - rate increases withdecreasing potential Rate with constantsurface concentrationof oxygen Rate with surface concentration of oxygen varying E0c Potential i0,c ln |i| log |i| ilim

  8. Mixed Potential Theory • Net current density on freely-corroding electrode must be zero. • Therefore potential (Ecorr) will be that at which anodic and cathodic current densities are equal and opposite. • Called a mixed equilibrium (not a true electrochemical equilibrium)

  9. Tafel’s Law Potential log |i|

  10. Tafel’s Law E0c Potential i0,c ln |i| log |i| ilim

  11. Electrical Units

  12. Charge • Results from inbalance between electrons and protons in a metal, or between anions and cations in a solution • Unit the coluomb, C • Charge on the electron = 1.6 x 10-19 C

  13. Current • Flow of charge past a point in a conductor (either electron or ion) • Unit the Amp, A

  14. Conservation of Charge • Charge can be neither created nor destroyed • Hence, the currents into and out of a point in an electrical circuit must add up to zero (Kirchoff’s Law)

  15. Potential • The potential at a point in space is the work done in moving a unit charge to that point from infinity. • Units of volts, V (=J/C)

  16. Potential Difference (or Voltage) • The potential difference or voltage is the difference between the potentials at two points, and hence the work done in moving a unit charge from one point to the other. • Units of Volts

  17. Resistance • A resistor (conventional symbol R) is a device that produces a voltage across its terminals when a current passes through it • Ohm’s Law V=IR • R is the resistance of the resistor • Units Ohms,  • 1 V is produced by a current of 1 A through a resistance of 1 

  18. Capacitance • A capacitor (conventional symbol C) is a device that stores charge when a current is applied to it • Units of capacitance Farads, F • I = C dV/dt • A 1 F capacitor will produce a voltage increase of 1 V/s when a current of 1 A flows into it

  19. Rct Metal Solution Cdl Equivalent Circuits • An electrical circuit with the same properties as a metal-solution interface • The simplest circuit is a resistor, corresponding to the polarization resistance, in parallel with a capacitor, corresponding to the double layer capacitance

  20. Rct Metal Rct Solution Cdl Equivalent Circuits • An electrical circuit with the same properties as a metal-solution interface • The Randles equivalent circuit adds a series resistor, corresponding to the solution resistance

  21. Potential Measurement

  22. Electrode Potential • The potential of a metal electrode with respect to a solution. • BUT the charge carriers in a metal are electrons, while the charge carriers in a solution are ions. • So how do we measure it?

  23. Measurement of Electrode Potential • Use arbitrary reference electrode to convert from ion current to electron current. • Conventional standard reference electrode is based on the reaction Hydrogen ions in solution at unit activity Electrons in the metal Hydrogen gas in solution at unit activity

  24. The Normal Hydrogen Electrode (NHE)

  25. Secondary Reference Electrodes • Reference electrodes of the first kind, a metal in equilibrium with a soluble salt: Potential controlled by Cu2+ concentration

  26. Secondary Reference Electrodes • Reference electrodes of the second kind, a metal in equilibrium with a sparingly soluble salt and a solution containing anions of the salt: Ag+ concentration controls equilibrium potential Chloride concentration controls Ag+ concentration [Ag+][Cl-] = const

  27. The Ag/AgCl Electrode

  28. Potentials of Common Reference Electrodes

  29. Practical Potential Measurement

  30. Potential Measurement Requirements - Input Resistance • High input resistance to minimize errors due to source resistance. • For most corrosion work 107 ohm is sufficient, but for high resistance systems (paints, passive metals etc.) 109 ohm or more may be better.

  31. Potential Measurement Requirements - Frequency Response • Frequency response (ability to detect rapid changes). Often not important for corrosion measurements. • Measurements at around 1 Hz are quite easy • Measurements above 1kHz are rather more difficult • Measurements at around 50 Hz are difficult (due to mains frequency interference).

  32. Potential Measurement Requirements - Resolution • Resolution is the ability to detect small changes in a large value • for most corrosion measurements 1 mV is adequate • for electrochemical noise and similar studies, 1mV may be necessary

  33. Potential Measurement Requirements - Sensitivity • Resolution is the ability to detect small changes in a large value • Sensitivity is the ability to measure small values • e.g. it is relatively easy to obtain a sensitivity of 1 mV when measuring 1 mV, but it is very difficult to obtain a resolution of 1 mV when measuring a 10 V signal • not usually a problem for corrosion measurements

  34. Potential Measurement Requirements - Precision • Resolution is the ability to detect small changes in a large value • Sensitivity is the ability to measure small values • Precision or accuracy is the ability to measure the ‘true’ value

  35. Potential Measurement Methods • Analogue meter (moving coil) • low impedance (typically 20 kohm/V) • poor frequency response (~1 Hz) • low sensitivity (~1 mV) • low resolution (~1%) • low precision (~3%)

  36. Potential Measurement Methods • Analogue meter (electronic) • high impedance (typically 10 Mohm) • poor frequency response (~1 Hz) • possibly high sensitivity (~1mV) • low resolution (~1%) • low precision (~3%)

  37. Potential Measurement Methods • Digital meter • high impedance (typically 10 Mohm or more) • poor frequency response (around 3 Hz) • high sensitivity (10 mV to 100 nV) • high resolution (0.1% to 0.0001%) • high precision (0.1% to 0.0001%)

  38. Potential Measurement Methods • Electrometer (digital) • very high impedance (~1014 ohm) • poor frequency response (<1 Hz) • high sensitivity (1 mV to 100 nV) • high resolution (0.1% to 0.001%) • high precision (0.1% to 0.001%)

  39. Potential Measurement Methods • Chart recorder • impedance depends on instrument (from 103 to 107 ohm) • moderate frequency response (~10 Hz) • moderate sensitivity (~10mV) • moderate resolution (~0.1%) • moderate precision (~0.1%)

  40. Potential Measurement Methods • Oscilloscope • high impedance (106 to 107 ohm) • high frequency response (10 MHz or more) • moderate sensitivity (~100mV) • poor resolution (~1%) • poor precision (~1%)

  41. Potential Measurement Methods • Computer data acquisition • high impedance (~107 ohm) • variable frequency response (10 Hz to 1 MHz or more) • moderate to good sensitivity (~10 mV) • moderate to good resolution (0.5 to 0.01%) • moderate to good precision (0.5 to 0.01%) • facilitates subsequent plotting and analysis

  42. Practical Current Measurement

  43. Current Measurement Requirements - Input Resistance • Low input resistance to minimize errors due to voltage drop across measuring device. • For most corrosion work 1 mV voltage drop will have little effect. • A wide dynamic range (ratio of largest current to smallest current) is required for many corrosion measurements.

  44. Current Measurement Methods • Analogue meter (moving coil) • usually poor input resistance (~ 75 mV drop at full scale) • poor frequency response (around 1 Hz) • low resolution (around 1%) • low precision (around 3%) • dynamic range acceptable using range switching

  45. Current Measurement Methods • Analogue meter (electronic) • usually poor input resistance (~100 mV drop at full scale) • poor frequency response (around 1 Hz) • low resolution (around 1%) • low precision (around 3%) • dynamic range acceptable using range switching

  46. Current Measurement Methods • Digital multimeter • often poor input impedance (~100 mV drop at full scale) • poor frequency response (around 3 Hz) • high resolution (0.1% to 0.0001%) • high precision (0.1% to 0.0001%) • often poor sensitivity (100 mA to 1 mA) • dynamic range acceptable using autoranging

  47. Current Measurement Methods • Electrometer (digital) • essentially zero input impedance • poor frequency response (<1 Hz) • high resolution (0.1% to 0.001%) • high precision (0.1% to 0.001%) • good dynamic range using range switching or autoranging

  48. Current Measurement Methods • Chart recorder • resistor used to convert current to voltage, hence voltage drop depends on sensitivity • moderate frequency response (~10 Hz) • moderate resolution (~0.1%) • moderate precision (~0.1%) • acceptable dynamic range providing range switching is used

  49. Current Measurement Methods • Oscilloscope • resistor used to convert current to voltage, hence voltage drop depends on sensitivity • high frequency response (10 MHz or more) • poor resolution (~1%) • poor precision (~1%) • poor dynamic range

  50. Current Measurement Methods • Computer data acquisition • resistor used to convert current to voltage, hence voltage drop depends on sensitivity • variable frequency response (10 Hz to 1 MHz or more) • moderate to good resolution (0.5 to 0.01%) • moderate to good precision (0.5 to 0.01%) • dynamic range often limited • facilitates subsequent plotting and analysis

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