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Electrochemical Theory © Bob Cottis 1998 Kinetics of Activation Controlled Reactions M Mn+ + ne rate of reaction depends on potential according to the Tafel equation: ia E E a ln i0,a where Ea0 equilibrium potential for anodic reaction 0 a a Tafel coefficient for anodic reaction ia anodic current density i0,a anodic exchange current density © Bob Cottis 1998 Tafel’s Law b=2.303 Potenti al Slope b E0a i0,a © Bob Cottis 1998 ln |i| log |i| Charge Transfer Resistance Charge transfer resistance = local slope of i versus E curve (not log i) ia E E a ln i0,a 0 a E Ea0 ia i0,a exp a dia 1 ia dE Rct ,a a © Bob Cottis 1998 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 © Bob Cottis 1998 Dependence of Kinetics on Reactant Concentration More reactant allows reaction to go faster, hence rate is proportional to reactant concentration e.g. oxygen reduction Ox + ne Red (E - E 0c ) i c = i 0 ,c C s exp c Surface concentration Minus sign because this is a cathodic reaction of oxygen (and c is taken as positive) © Bob Cottis 1998 Tafel’s Law [O2] Cathodic reaction Rate with constant [O2] rate increases with Rate with surface surface concentration decreasing potential of concentration of oxygen oxygen varying [O2] E0c Potenti al i0,c © Bob Cottis 1998 ln |i| log |i| ilim 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) © Bob Cottis 1998 Tafel’s Law Potenti al log |i| © Bob Cottis 1998 Tafel’s Law E0c Potenti al i0,c © Bob Cottis 1998 ln |i| log |i| ilim Electrical Units © Bob Cottis 1998 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 © Bob Cottis 1998 Current Flow of charge past a point in a conductor (either electron or ion) Unit the Amp, A © Bob Cottis 1998 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) © Bob Cottis 1998 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) © Bob Cottis 1998 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 © Bob Cottis 1998 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 © Bob Cottis 1998 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 © Bob Cottis 1998 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 Metal © Bob Cottis 1998 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 Metal Rct Rct Cdl © Bob Cottis 1998 Solution Potential Measurement © Bob Cottis 1998 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? © Bob Cottis 1998 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 2H Hydrogen ions in solution at unit activity © Bob Cottis 1998 2e Electrons in the metal H2 Hydrogen gas in solution at unit activity The Normal Hydrogen Electrode (NHE) © Bob Cottis 1998 Secondary Reference Electrodes Reference electrodes of the first kind, a metal in equilibrium with a soluble salt: Cu Cu 2 2e Potential controlled by Cu2+ concentration © Bob Cottis 1998 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 Ag Ag e controls equilibrium potential AgCl Ag Cl Chloride concentration controls Ag+ concentration [Ag+][Cl-] = const © Bob Cottis 1998 The Ag/AgCl Electrode © Bob Cottis 1998 Potentials of Common Reference Electrodes Common Name Electrode V vs NHE Saturated Calomel Electrode (SCE) Hg/Hg2Cl2/sat. KCl +0.241 Calomel Hg/Hg2Cl2/1M KCl +0.280 Mercurous sulphate Hg/Hg2SO4/sat. K2SO4 +0.640 Mercurous oxide Hg/HgO/1M NaOH +0.098 Silver chloride Ag/AgCl/sat. KCl +0.197 Copper sulphate Cu/sat. CuSO4 +0.316 Zinc in seawater Zn/seawater ~ -0.8 © Bob Cottis 1998 Practical Potential Measurement © Bob Cottis 1998 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. © Bob Cottis 1998 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). © Bob Cottis 1998 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 © Bob Cottis 1998 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 © Bob Cottis 1998 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 © Bob Cottis 1998 Potential Measurement Methods Analogue meter (moving coil) – – – – – © Bob Cottis 1998 low impedance (typically 20 kohm/V) poor frequency response (~1 Hz) low sensitivity (~1 mV) low resolution (~1%) low precision (~3%) Potential Measurement Methods Analogue meter (electronic) – – – – – © Bob Cottis 1998 high impedance (typically 10 Mohm) poor frequency response (~1 Hz) possibly high sensitivity (~1mV) low resolution (~1%) low precision (~3%) Potential Measurement Methods Digital meter – – – – – © Bob Cottis 1998 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%) Potential Measurement Methods Electrometer (digital) – – – – – © Bob Cottis 1998 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%) 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%) © Bob Cottis 1998 Potential Measurement Methods Oscilloscope – – – – – © Bob Cottis 1998 high impedance (106 to 107 ohm) high frequency response (10 MHz or more) moderate sensitivity (~100mV) poor resolution (~1%) poor precision (~1%) 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 © Bob Cottis 1998 Practical Current Measurement © Bob Cottis 1998 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. © Bob Cottis 1998 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 © Bob Cottis 1998 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 © Bob Cottis 1998 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 © Bob Cottis 1998 Current Measurement Methods Electrometer (digital) – – – – – © Bob Cottis 1998 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 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 © Bob Cottis 1998 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 © Bob Cottis 1998 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 © Bob Cottis 1998