1. BASIC PRINCIPLES OF ELECTRODE PROCESSES Heterogeneous kinetics II

2. Electron-transfer processes must satisfy the Frank-Condon restrictions, i.e. a)the act of electron transfer (ET) is much shorter than atomic motion, b)the consequences are that no angular momentum can be transferred to or from the transition state during electron transfer, there is also restrictions in changes in spin. Franck- Condon principle Electron Transfer Reactions Potential energy curves for the ground state and an excited state of a diatomic molecule vibrational states r interatomic distance A absorption F fluorescence femto-seconds ground state excited state

4. Electron transfer in biochemistry A ox + B red  A red + B ox A ox is the oxidized form of A (the oxidant in the reaction shown) B red is the reduced form of B (the reductant). For such an electron transfer, one may consider two half-cell reactions : 1.A ox + z e -  A red......e.g., Fe +++ + e -  Fe ++ 2.B ox + z e -  B red For each half reaction: E = E°'   RT/zF (ln [red]/[ox]) e.g., for the first half reaction: E = E°'  RT/zF (ln [a red ]/[a ox ]) [a red ] = [a ox ],.. E = E°' E°' is the mid-point potential, or standard redox potential. It is the potential at which [oxidant] = [reductant] for the half reaction. For an electron transfer:  E°' = E°' (oxidant)  E°' (reductant) = E°' (e - acceptor)  E°' (e - donor)  G o ' = - nF  E o '

5. Exercise: Consider ET of 2 electrons from NADH to oxygen: a. ½O 2 + 2H + + 2 e -  H 2 O E°' = + 0.815 V b. NAD + + 2H + + 2 e -  NADH + H + E°' =  0.315 V Subtracting reaction b from reaction a: ½O 2 + NADH + H +  H 2 O + NAD +  E°' = + 1.13 V  G o ' =  nF  E o ' = - 2(96485 Joules/Volt · mol)(1.13 V) =  218 kJ/mol ½O 2 + NADH + H +  H 2 O + NAD +

6. The solid metallic electrode φ M (Galvani potential)  (Volta potential)  (surface potential) Electrode Solution φ x φ M (Galvani potential – inner potential) is associated with with E F  (Volta potential – outer potential) is associated with the potential outside the electrode´s electronic distribution  (surface potential) E F = E redox – e  φ =  + 

7. From without potential insertion on solid phase over / below E r more positive / more negative  electrode polarization, overpotential  = E p - E r  begins lead an electrode process As well as each electrode process, it consists of more follow steps – levels rds - rate determining step a most slow step a most slow step E p = E polarization = E polarizační E r = E equilibrium = E rovnovážný  = overpotential = přepětí

8. Electrode reactions steps Substance crossing from within of electrolyte to a level of maximal approximation  transport (diffusion) overpotential three transport mechanisms  migration – movement of ions through solution by electrostatic attraction to charged electrode  diffusion – motion of a species caused by a concentration gradient  convection – mechanical motion of the solution as a result of stirring or flow 2.Adsorption (localization) of ions or molecules in space of electric double layer 3.Dehydration (desolvation)  absolute  partial  none  = overpotential = přepětí

9. 4. Chemical reactions on a metal surface, coupled with making of intermediates capable of obtaining or losing of electrons  reaction overpotential 5. Electrode reaction - solitary electron crossing through interface  activation overpotential 6. Adsorption of primary product of electrochemical process on a metal surface

10. 7. Desorption of a primary product 8. Transport of product from a metal surface a) Soluble product – by diffusion (the most used style) b) Gas products – by bubbling c) Products can be integrated to an electrode crystal lattice  crystalization ( nucleation) overpotential g) By diffusion to inside of electrode (for ex. amalgam)

11. z.e - Electron transfer adsorption desorption chemical reaction dehydration R solv R desolv R´ R ads O ads hydration adsorption desorption chemical reaction dehydration hydration O´ O desolv O solv Electrode surface Bulk solution Electrode General mechanism of electrode process O + ze - R DYNAMIC ELECTROCHEMISTRY Electrode kinetics - can be controlled by electrode potential

12. Heterogeneous reactions – velocity to surface unit: Velocity of electrode process Experimental dependences:  = f ( j ) j = f (  ) polarization curves current-potential curves = for transformation of 1 mol of substance with a charge of z, charge of nF coulomb is consumed ; F = 96484 coulomb/mol For transformation of dn mol of substance at time dt, a current I is consumed Current density Faraday : I t = N nF = Q

13. Activation overpotential k red k ox k red k ox k red k ox k red k ox

14. An expression for the rate of electrode reaction Arrhenius Gibbs-Helmholtz

15. Δφ for reduction.... α c E Δφ for oxidation.... α a E = (1- α c ) E α is a coefficient of charge transfer = symmetry coefficient  a +  c = 1  c =  ;  a = 1 -  An expression for the rate of electrode reaction Reaction coordinate E = E(neg.) G E = 0 V nEF  n EF Ox Red  G a,o  GcGc GaGa  G c,o  Effect of a change in applied electrode potential on the reduction of Ox to Red GG

16.   0   0.5   1 G G G Reaction coordinate  n = 1.5   = 0.75 rds …… rate - determining step In many cases electrode processes involving the transfer of more than one electron take place in consecutive steps. The symmetry of the activation barrier referred to the rate-determining step. nn

17. Balance of electrode process v ox = v red j 0 is charge current density

18. k 0 = standard velocity constant (members independence on E) j red = j c - j ox = j a + determination of E eq

19. Current - overpotential  crossing j red = j c j ox = j a Butler- Volmer equation for electrode process, where rds is charge transfer

20. j, k a and k c depends exponentially on potential linear free energy relationship the parameters: I and E E eq gives the exchange current I o = j o A  standard rate constant for transport the Tafel law must be corrected Butler-Volmer equation electrode as a powerful catalyst

21. the observed current is proportional to the difference between the rate of the oxidation and reduction reactions at the electrode surface concentrations of Red and Ox next to the electrode do not grow indefinitely – limited by the transport of species to electrode diffusion-limited current IdId

22. jcjc E eq Red = Ox + e - Ox + e - = Red jaja -E E jaja jcjc j = j a j0j0 j0j0 EpEp Polarization curves without overpotential E eq equilibrium potential j = j a + (- j c )

23. 1 Red = Ox + e - Ox + e - = Red jaja jcjc E E eq 11 22 33 23 Polarization curves with activation overpotential j

24. 0,5 j a / j 0 ++ -- j c / j 0 0,25 0,75 Ratio dependence of current density and change current density on overpotential for different  values

25. Polarization curve:  = f ( j ) or I-E curves: j = f (  ) a) Small values of overpotential b) Large values of overpotential positive   process of oxidation negative   process of reduction Development of e -x function R p = polarization resistance Tafel relations

26. log j c log j a log j 0 log j ++ -  E eq Tafel diagram for cathode and anode current density  = 0,25 j 0 = 0,1 mA koko

27. k´ (cm.s -1 )  (V) 0.0002 10 -3 10 -4 10 -6 10 -10 10 -14 0.0030.12 0.59 1.06  = f(k´) reversible x irreversible process current density j j = 10 -6 A.cm -2 ; n = 1; c Ox = 1mM;  = 0.5; T=298 K  oxygen (V)  hydrogen (V) metal Ag 0.48 0.58 Au 0.24 0.67 Cu 0.48 0.42 Hg 0.88 - Ni 0.56 0.35 Pt(smoothed) 0.02 0.72 Pt(platinized) 0.01 0.40 j = 10 -3 A.cm -2 T = 298 K

28. I. Fick law: the natural movement of species isolution without the effects of the electrical field ….. concentration gradient diffusion coefficient [cm 2 s -1 ] ; 10 -5 - 10 -6 in aqeous solutions II. Fick law: What is the variation of concentration with time ??? DIFFUSION: the natural movement of species in solution without the effects of the electrical field

29. Coordinates Laplace operator Cartesian Cylindrical Spherical Laplace operator in various coordinate systems Cartesian x y z x r   r  Cylindrical Spherical

30. For any coordinate system LT for Fick´s second law under conditions of pure diffusion control  the potential is controlled, the current response and its variation in time is registrated chronoamperometry  the current is controlled and the variation of potential with time is registrated chronopotentiometry IdId

31. Diffusion-limited current: planar and spherical electrodes Mass transport No reaction Reaction of all species reaching the electrode t t = 0 E Potential step to obtain a diffusion-limited current of the electroactive species IdId planar electrode ….. semi-infinite linear diffusion Boundary conditions t = 0 c 0 = c  no electrode reaction t  0 lim c = c  bulk solution t  0 and x = 0 c 0 = 0 diffusion –limited current I d

32. Cottrell equation to planar electrode linear diffusion to spherical electrode spherical diffusion

33.  small t (spherical diffusion linear diffusion)  large t (the spherical diffusion dominates, which represents a steady state current) Microelectrodes  -electrodes and ultra-  -electrodes  small size at least one dimension 0.1-0.5  m  steady state  high current density  low total current (% electrolysis is small)  interference from natural convection is negligible (supporting electrolyte)

34. c i,0 c0c0 electrode solution c i,  x distance from electrode  Diffusion overpotential

35. Solitary electrode process is in balance (  = 1  a i = c i ) (E 0 i = standard potential) overpotential required for getting over of concentration difference

36. I. Fick law: in stationary state Faraday: Nernst diffusion layer

37. in limit: c i,0 = 0  j k, lim = n i F D (c i /  ) Diffusion overpotential

38. j -- ++ -j -j d,l Polarization curves for diffusion controlled processes

39. j d,l E 1/2 jaja jcjc - E + E Diffusion overpotential - polarography

40. -- ++ j -j j d,l,cat j d,l,anod Polarization curves for diffusion controlled processes Electrode cici  x c i, 0 j D,lim,o x j D,lim,r ed  mV  mV + j A/m -2 - j A/m -2

41. Jaroslav Heyrovský * Dec. 20, 1890, Prague, Bohemia, Austro-Hungarian Empire [now Czech Rep.] † March 27, 1967, Prague, Czechoslovakia Jaroslav Heyrovský was an inventor of the polarographic method, father of electroanalytical chemistry, recipient of the Nobel Prize (1959). His contribution to electroanalytical chemistry can not be overestimated. All voltammetry methods used now in electroanalytical chemistry originate from polarography developed by him.

42. a) ½ wave potential (E ½ ) characteristic of M n+ (E) b) height of either average current maxima (i avg ) or top current max (i max ) is ~ analyte concentration c) size of i max is governed by rate of growth of DME > drop time (t, sec) rate of mercury flow (m, mg/s) diffusion coefficient of analyte (D, cm 2 /s) number of electrons in process (n) analyte concentration (c, mol/ml) Mn + + ne - +Hg = M(Hg) amalgam Ilkovič equation (i d ) max = 0.706 n D 1/2 m 2/3 t 1/6 c (i d ) avg = 0.607 n D 1/2 m 2/3 t 1/6 c Residual currentHalf-wave potential i max i avg Limiting diffusion current Half-wave potential, limited diffusion current

43. Instrumentation, common techniques Electrochemical analyzer AUTOLAB Autolab Ecochemie Utrecht The Netherlands VA-Stand 663 Metrohm Zurich Switzerland Autolab 20 Autolab 30

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