Electrical Double Layer + - SOLVENT MOLECULES - - + + - - + Counter ion Co-ions + - Water molecule OHP Helmholtz (100+ years ago) proposed that surface charge is balanced by a layer of oppositely charged ions

Gouy-Chapman Model (1910-1913) + - -- + + - - + - + - Counter ion Co-ions + - Water molecule Diffusion plane Assumed Poisson-Boltzmann distribution of ions from surface ions are point charges ions do not interact with each other Assumed that diffuse layer begins at some distance from the surface

Stern (1924) / Grahame (1947) Model Gouy/Chapman diffuse double layer and layer of adsorbed charge. Linear decay until the Stern plane. x - Diffusion layer Shear Plane Gouy Plane Counter ion Co-ions + - Water molecule Stern Plane + ζ + + - + + - - + - - - Ψ0 Bulk Solution

Stern (1924) / Grahame (1947) Model In different approaches the linear decay is assumed to be until the shear plane since the charges until there considered static. In this course however it is assumed that the decay is linear until the Stern plane. x - Diffusion layer Shear Plane Gouy Plane OHP - + + + + - - ζ + + - + - - Ψ0 Bulk Solution

Current Model BDM (Bockris, Devanathan, Muller)

A charge transfer reaction provides an additional channel for current Electrode reaction as a series of multiple consecutive steps A charge transfer reaction provides an additional channel for current to flow through the interface. The amount of electricity that flows through this channel depends on the amount of species being oxidized or reduced according to the Faraday law: This expression may be rearranged to give expression for current: n- number of electrons in a redox reaction, N-number of moles, MA- molecular weight, F- Faraday constant

This equation described average current flowing through the electrode During time – t. During infinitesimal period dt the number of electrolyzed moles is dN and the expression for the instantaneous current is: The rate of a chemical reaction is : Hence faradaic current is a measure of a reaction rate

For a multistep reaction

2. Mass transport phenomena

3. Reactions controlled by charge transfer step

4.Reactions controlled by mixed charge transfer-mass transfer step - Butler – Volmer equation with correction for mass transport

5. Electrical circuits for: - ideally polarized electrode - non-polarized electrode

Eeq - equilibrium potential Example: Pt electrode in Fe3+/ Fe2+ solution Fe2+ = Fe3+ + e Fe3+ + e = Fe2+ Eeq

Polarization and Overpotential Electrode reactions are assumed to induce deviations from equilibrium due to the passage of an electrical current through an electrochemical cell causing a change in the electrode potential. This electrochemical phenomenon is referred to as polarization. The deviation from equilibrium causes an electrical potential difference between the polarized and the equilibrium (unpolarized) electrode potential known as overpotential

Polarization and Overpotential Equilibrium potential for cathodic reaction = Eoc Equilibrium potential for anodic reaction = Eoa Real potential = E Cathodic Overpotential ηc = E – Eoc < 0 anodic Overpotential ηa = E – Eoa > 0

Exchange Current Density At the equilibrium potential of a reaction, a reduction and an oxidation reaction occur, both at the same rate. For example, on the Zn electrode, Zn ions are released from the metal and discharged on the metal at the same rate The reaction rate in each direction can also be expressed by the transport rate of electric charges, i.e. by current or current density, called, respectively, exchange current, Io, and (more frequently used) exchange current density, io. The net reaction rate and net current density are zero

How Polarization is Measured B: Working Electrode L: Luggin Capillary R: Reference Electrode D: Auxiliary Electrode

Causes of Polarization Depending on the type of resistance that limits the reaction rate, we are talking about three different kinds of polarization activation polarization concentration polarization and resistance (ohmic) polarization or IR Drop

Activation Polarization When current flows through the anode and the cathode electrodes, their shift in potential is partly because of activation polarization An electrochemical reaction may consist of several steps The slowest step determines the rate of the reaction which requires activation energy to proceed Subsequent shift in potential or polarization is termed activation polarization Most important example is that of hydrogen ion reduction at a cathode, H+ + e- → ½ H2, the polarization is termed as hydrogen overpotential

Hydrogen Overpotential Hydrogen evaluation at a platinum electrode: H+ + e- → Hads 2Hads → H2 Step 2 is rate limiting step and its rate determines the value of hydrogen overpotential on platinum

Tafel Equation Activation polarization (η) increases with current density in accord with Tafel equation: The Tafel constant is given by:

Overpotential Values Pronounced activation polarization also occurs with discharge of OH − at an anode accompanied by oxygen evolution: The polarization corresponding to this reaction is called oxygen overpotential . Overpotential may also occur with Cl − or Br − discharge, but the values at a given current density are much smaller than those for O2 or H2 evolution. Activation polarization is also characteristic of metal - ion deposition or dissolution. The value may be small for nontransition metals, such as silver, copper, and zinc, but it is larger for the transition metals, such as iron, cobalt, nickel, and chromium

Concentration Polarization Sometimes the mass transport within the solution may be rate determining – in such cases we have concentration polarization Concentration polarization implies either there is a shortage of reactants at the electrode or that an accumulation of reaction product occurs

Concentration Polarization: reduction of oxygen

Contd.. Fick’s Law: Faraday’s law: Under steady state, where dn/dt is the mass transport in x direction in mol/cm2s, D is the diffusion coefficient in cm2/s, and c is the concentration in mol/liter Faraday’s law: Under steady state, mass transfer rate = reaction rate

Contd.. Maximum transport and reaction rate are attained when C0 approaches zero and the current density approaches the limiting current density:

Contd.. The most typical concentration polarization occurs when there is a lack of reactants, and (in corroding systems) therefore most often for reduction reactions This is the case because reduction usually implies that ions or molecules are transported from the bulk of the liquid to the electrode surface, while for the anodic (dissolution) reaction, mass is transported from the metal, where there is a large reservoir of the actual reactant

Contd.. Equations (1) to (4) are valid for uncharged particles, as for instance oxygen molecules If charged particles are considered migration will occur in addition to the diffusion and the previous equation must be replaced by where t is the transference number of all ions in solution except the ion getting reduced

Overpotential due to concentration polarization If copper is made cathode in a solution of dilute CuSO4 in which the activity of cupric ion is represented by (Cu+2 ), then the potential φ1 , in absence of external current, is given by the Nernst equation:

Contd.. When current flows, copper is deposited on the electrode, thereby decreasing surface concentration of copper ions to an activity (Cu2+ )s . The potential φ2 of the electrode becomes:

Contd.. Since (Cu2+ )s is less than (Cu2+ ), the potential of the polarized cathode is less noble, or more active, than in the absence of external current. The difference of potential, φ2 − φ1 , is the concentration polarization , equal to:

Contd..

IR Drop When polarization is measured with a potentiometer and a reference electrode-Luggin probe combination, the measured potential includes the potential drop due to the electrolyte resistance and possible film formation on the electrode surface The drop in potential between the electrode and the tip of Luggin probe equals iR. If l is the length of the electrode path of cross sectional area s, k is the specific conductivity, and i is the current density then resistance iR drop in volts =

Combined Polarization Total polarization of an electrode is the sum of the individual contributions, If neglect IR drop or resistance polarization is neglected then: