2. ELECTROCHEMISTRY INTRO1 !? THINGS THAT WE ARE FAMILIAR WITH : !? Ohm’s law ( and Kirchoff’s…) (ABC... electrical circuits) U = I  R, R =   L / S Faraday’s law (ABC... electrolysis) m = k  Q, k = M / n  F ( F = ?) Fick’s laws (ABC... diffusion) J =  D  dC/dx  C/  t = D   2 C/  x 2 Electrical properties of condensed phases – conducting electrical current (metals, semiconductors) Ionic compounds, properties of solutions, ionic conductivity Redox reactions ( np. 2Cr 3+ +3 H 2 O 2 + 10 OH - = 2 CrO 4 - + 8H 2 O ) Phase boundary electrolyte - electrode

3. ELECTROCHEMISTRY INTRO2 Me Me+ electrodeelectrolyte Charge transfer transport Oxidation – reduction reaction rate Diffusion transport rate

4. ELECTROCHEMISTRY INTRO3 Each stage can determine the overall reaction rate 1. „obligatory” stages charge transfer Transport (diffusion, convection, migration ) 2. other possible stages Chemical reaction before or after (c t) Crystallisation of new phases Adsorption at the electrode

5. ELECTROCHEMISTRY INTRO4 Reaction rate v = ∆ c A / ∆t, ( or v = k A-B · c A ) ( c A - volumetric concentration – we must do something about it) In electrode kinetics the transferred charge is a measure of reaction rate Following Faraday’s law: m A = k F · I · ∆t = k · Q (here k – electrochem equivalent, not reaction rate constant) And back to general reaction rate formula m A = c A · V or c A surface · S = k F · I · ∆t v = k · I · / S v ( mol · s -1 m) = k F ( mol/C ) · j, j – current density (A/m 2 ) =

6. ELECTROCHEMISTRY INTRO 5 CURRENT DENSITY = MEASURE OF ELECTRODE PROCESS RATE And what makes the reaction happen at all?? Equilibrium – no products ( is anything happening?) Deviation from equilibrium - energy impuls needed Reaction – transformation to new equilibrium state What might be an energy impuls?

7. ELECTROCHEMISTRY INTRO6  energy state of a particle – chemical potential μ i = μ o + RT ( a i )  Charged particle - electrochemical potential, possible responce to electrical field φ= φ o + RT/nF ln ( a i(n+) )  Equilibrium - equal potentials of a particle in two phases (electrode – electrolyte) E = E 0 + RT/nF ln ( a electrode / a electrolyte ) ENERGY IMPULS Change in concentration, temperature Overpotential applied to the electrode

8. ELECTROCHEMISTRY INTRO7 At equilibrium Redox transitions on molecular scale Identical overall charge for oxidation and reduction j k = j a, overall current density j k - j a = 0 At overpotential ∆E j = j k - j a ≠ 0 as measure for reaction rate, so j/nF = v = k rr × C

9. ELECTROCHEMISTRY INTRO8 Reaction rate constant - overpotential: k rr = k s exp[ α n F ΔE / RT] (one equilibrium – two constants: anodic and cathodic) Combining v =.. And k = …. (To get current-overpotential dependence) i = nF S k s [ c utl exp(-αn F ΔE / RT ) – c red (βn F ΔE / RT)] where k s - standard reaction rate constant α i β coefficients for energy barrier symmetry ΔE overpotential

10. ELECTROCHEMISTRY INTRO9 Electrode process – heterogenous, charge transfer at phase boundary + transport Electrode = element of electrical circuit Measurement = two electrodes form a cell Circuit – measurable : voltage and current Difference in V/I response for a.c and d.c.

11. ELECTROCHEMISTRY INTRO10 Transport properties Structure of electrolytes, dissociation Movement of ionic species Mobility, velocity of part i v i = E · u i Conductivity  = e · N i · z i · u i Transference number

12. ELECTROCHEMISTRY INTRO11 Cell voltage or electrode potential Equilibrium at the electrode – Nernst pot. Overpotential – driving force for the reaction Current – electrical measure of reaction rate Voltage – measure of potential difference ! For kinetics – we must know the potential of a single electrode!

13. ELECTROCHEMISTRY INTRO 12 3 –electrode cell 3-electrode cells : WE and CE - „working circuit” reactions at electrodes, current flow WE- RE - measuring circuit, high input impedance on RE no current flow Reference electrodes : very precise potential, examples : Hg/ Hg 2 Cl 2, Ag/ AgCl, Quasi-reference : W, Ta, other non-reactive metals idea : stable potential, easy assembly, Function current-potential – diffusion and kinetics in the cell must be described electroanalysis

14. ELECTROCHEMISTRY INTRO13 CE Cell RE Potentiostat EzEz E I Electrolytic cell and potentiostat Electrodes: Meas. Parameters: CE - counter E - WE potential RE - reference E z - applied potential WE - workingI - current in CE-WE circuit WE

15. ELECTROCHEMISTRY INTRO14 EIS Electrotechnical aspect : a.c.circuit Electrochemical aspect : approximation of electrode process with circuit elements Charge transfer Conductivity Resistance of layer Resistances R Z = R

16. ELECTROCHEMISTRY INTRO15 Double layer capacity Capacity of layers Capacities C Z = -j/  C Diffusion phenomena Roughness of surface Inhomogenity of layer Constant phase element Admittance Y = Yo (j  ) n for n=0 resistance For n=1 capacity Corrosion processes (many reactions and equilibria) Inductance L Z = j  L

17. ELECTROCHEMISTRY INTRO16 Equivalent circuits Electrical model of electrode Connections in series and parallel – interpretation of consecutive or simultaneous reactions / phenomena Physical sense vs. numerical possibilities

18. ELECTROCHEMISTRY INTRO17 Our lab sessions EIS – dr Regina Borkowska ( 5h basic electrode kinetics) Voltammetry – dr Regina Borkowska 5h Conducting polymers dr M. Siekierski 5h Batteries – dr Marek Marcinek (5h basic cells + 5h Li- cells) Transference numbers – Msc Michał Piszcz(5h diffusion coefficient + 5h transference numbers in Li systems) Ion associations – Dr Leszek Niedzicki (5h Fuoss-Kraus formalism – electrochemical approach) Corrosion dr Andrzej Królikowski 5h Instructions and auxillary materials: download from http://pirg.ch.pw.edu.pl/