Electro-Kinetics. Description of Electrochemical Techniques The technique is named according to the...

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Transcript of Electro-Kinetics. Description of Electrochemical Techniques The technique is named according to the...

  • Slide 1
  • Electro-Kinetics
  • Slide 2
  • Description of Electrochemical Techniques The technique is named according to the parameters measured E.g. Voltammetry measure current and voltage Potentiometry measure voltage Chrono-potentiometry measure voltage with time (under an applied current) Chrono-amperometry measure current with time (under an applied voltage)
  • Slide 3
  • Electro-Kinetics Movement of Ions Butler Volmer Equation Rotating Disc Electrode Rotating Cylinder Electrode Voltammetry Cyclic Voltammetry Chrono-potentiometry Chrono-amperometry
  • Slide 4
  • Movement of Ions in Solution Diffusion Movement under a concentration gradient. If an electrochemical reaction occurs the current due to this reaction is called, i d, the diffusion current. Migration or Transport Movement of ions under an electric field due to coulombic forces. If an electrochemical reaction occurs the current due to this reaction is called, i m, the migration current. Convection Movement due to changes in density at the electrode solution interface. This occurs due to depletion or addition of a species due to the electrochemical reaction.
  • Slide 5
  • The Capacitance Current The charging or capacitance current, i c, is due to the presence of the electrical double layer and it is always present. This current, of course, is not related to any movement of ions. I c = C dl x V Where: C dl = the capacitance of the electrical double layer V= voltage scan rate The capacitance current makes its presence felt when measuring charge transfer (Faradaic) processes at concentrations of 10 -5 M.
  • Slide 6
  • Diffusion Molecular diffusion, often called simply diffusion, is a net transport of molecules from a region of higher concentration to one of lower concentration by random molecular motion.
  • Slide 7
  • Migration or Transport Is the fraction of current carried by the ions. For example in a solution of copper sulphate the transport number of Cu 2+ is 0.4 and that of SO 4 2- = 0.6. t + + t - = 0.4 + 0.6 = 1 Since the migration current depends on the ionic strength of the solution it is usually eliminated by addition of excess of an inert supporting electrolyte (100 1000 fold excess in concentration) The current is carried by the inert supporting electrolyte (e.g. NaCl, KNO 3 etc) because the ions produced do not undergo any electrochemical reaction the transport current is effectively removed. In excess inert supporting electrolyte, the current measured due to the electro-active species of interest is due only to diffusion which can be related to mass transfer.
  • Slide 8
  • Voltammetry the following example shows how the migration current is eliminated. Pb 2+ + 2e Pb 0 The supporting electrolyte Ensures diffusion control of limiting currents by eliminating migration currents Table: Limiting currents observed for 9.5 x 10 -4 M PbCl 2 as a function of the concentration of KNO 3 supporting electrolyte
  • Slide 9
  • Voltammetry The example shown is for the reduction of Pb 2+ at an inert mercury electrode. Pb 2+ + 2e Pb(Hg) At low inert electrolyte concentration a large fraction of the total current is due to the migration current, i.e. the currents due to the electrostatic attraction of ions to the electrode. For solution 1: i migration i m 17.6 8.45 = 9.2 A i diffusion i d = 8.45 A
  • Slide 10
  • Ficks First Law of Diffusion Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). In one (spatial) dimension, this is
  • Slide 11
  • Ficks First Law of Diffusion where J is the diffusion flux in dimensions of [(concentration of substance) length 2 time -1 ], example mole (M) m -2 s -1. J measures the amount of substance that will flow through a small area during a small time interval. D is the diffusion coefficient or diffusivity in dimensions of [length 2 time 1 ], example m 2 s -1 (for ideal mixtures) is the concentration in dimensions of [(concentration of substance) length 3 ], example M m -3 x is the position [length], example m
  • Slide 12
  • Ficks First Law of Diffusion D is proportional to the squared velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid and the size of the particles according to the Stokes-Einstein relationship. In dilute aqueous solutions the diffusion coefficients of most ions are similar and have values that at room temperature are in the range of 0.6x10 -9 to 2x10 -9 m 2 /s. For biological molecules the diffusion coefficients normally range from 10 -11 to 10 -10 m 2 /s.
  • Slide 13
  • Ficks First Law of Diffusion In two or more dimensions we must use, , the del or gradient operator, which generalises the first derivative, obtaining J = -D The driving force for the one-dimensional diffusion is the quantity - / x which for ideal mixtures is the concentration gradient. In chemical systems other than ideal solutions or mixtures, the driving force for diffusion of each species is the gradient of chemical potential of this species. Then Fick's first law (one-dimensional case) can be written as:
  • Slide 14
  • Ficks First Law of Diffusion where the index i denotes the ith species, c is the concentration (mol/m 3 ), R is the universal gas constant (J/(K mol)), T is the absolute temperature (K), and is the chemical potential (J/mol).
  • Slide 15
  • Butler-Volmer Equation The Butler-Volmer equation is one of the most fundamental relationships in electrochemistry. It describes how the electrical current on an electrode depends on the electrode potential, considering that both a cathodic and an anodic reaction occur on the same electrode:
  • Slide 16
  • Butler-Volmer Equation where: I = electrode current, Amps I o = exchange current density, Amp/m 2 E = electrode potential, V E eq = equilibrium potential, V A = electrode active surface area, m 2 T = absolute temperature, K n = number of electrons involved in the electrode reaction F = Faraday constant R = universal gas constant = so-called symmetry factor or charge transfer coefficient dimensionless The equation is named after chemists John Alfred Valentine Butler and Max Volmer
  • Slide 17
  • Butler-Volmer Equation The equation describes two regions: At high overpotential the Butler-Volmer equation simplifies to the Tafel equation E E eq = a blog(i c ) for a cathodic reaction E E eq = a + blog(i a ) for an anodic reaction Where: a and b are constants (for a given reaction and temperature) and are called the Tafel equation constants At low overpotential the Stern Geary equation applies
  • Slide 18
  • Current Voltage Curves for Electrode Reactions Without concentration and therefore mass transport effects to complicate the electrolysis it is possible to establish the effects of voltage on the current flowing. In this situation the quantity E - E e reflects the activation energy required to force current i to flow. Plotted below are three curves for differing values of i o with = 0.5.
  • Slide 19
  • Voltammetry Although the Butler Volmer Equation predicts, that at high overpotential, the current will increase exponentially with applied voltage, this is often not the case as the current will be influenced by mass transfer control of the reactive species. Take the following example of the reduction of ferric ions at a platinum rotating disc electrode (RDE). Fe 3+ + e = Fe 2+ The rotation of the electrode establishes a well defined diffusion layer (Nernst diffusion layer) The contribution of the capacitance current will also be demonstrated in this example.
  • Slide 20
  • Effect of the Capacitance Current in Voltammetry. The reduction of Ferric Chloride is carried out in the presence of 1 M NaCl to eliminate the migration current. Slope due to i c Applied Potential -Ve Current 10 -5 M Fe 3+ Fe 3+ + e Fe 2+ Current 10 -3 M Fe 3+ Fe 3+ + e Fe 2+ Applied Potential -Ve (a) (b) Note that the iE curve in Fig. (a) is recorded at a much higher sensitivity than in Fig. (b). i ld
  • Slide 21
  • Charging Current or Capacitance Current Note that due to the presence of the electrical double layer a charging or capacitance current is always present in voltammetric measurements.
  • Slide 22
  • Butler-Volmer Equation where: I = electrode current, Amps I o = exchange current density, Amp/m 2 E = electrode potential, V E eq = equilibrium potential, V A = electrode active surface area, m 2 T = absolute temperature, K n = number of electrons involved in the electrode reaction F = Faraday constant R = universal gas constant = so-called symmetry factor or charge transfer coefficient dimensionless The equation is named after chemists John Alfred Valentine Butler and Max Volmer
  • Slide 23
  • Butler Volmer Equation While the Butler-Volmer equation is valid over the full potential range, simpler approximate solutions can be obtained over more restricted ranges of potential. As overpotentials, either positive or negative, become larger than about 0.05 V, the second or the first term of equation becomes negligible, respectively. Hence, simple exponential relationships between current (i.e., rate) and overpotential are obtained, or the overpotential can be considered as logarithmical