1. Fundamentals of Electrodics Fall semester, 2011 Shu-Yong Zhang

2. Electrode process The totality of changes occurring at or near an electrode during the passage of current. electrochemical step: involving gain or loss of electron non-electrochemical step Electrochemical thermodynamics Electrochemical kinetics

3. 1.1.1 Electrochemical apparatus: galvanic cell Electrolytic cell Electrodes: positive/negative electrode anode / cathode §1.1 Review of fundamental electrochemistry

4. 1.1.2 Types of electrode: 1) metal / metal ion electrode 2) metal / insoluble salt electrode 3) redox electrode 4) membrane electrode 5) intercalation electrode 6) modification electrode 7) semiconductor electrode 8) insulator electrode

5. Conversion film formation 1.1.3 Kind of electrode reactionDirect Reaction of electrode 1) Active Dissolution 2) Surface finishing 3) Passivation 4) Surface conversion 5) Anodization Reaction of species from solution 1) Oxidation / Reduction 2) Polymerization 3) deposition Indirect via electron media Reaction of species in solution 1) Oxidation via Ce 4+ 2) Reduction via V 2+ 3) Polymerization 4) deposition Direct and indirect electrochemical reactions

6. working electrode (W. E.) counter electrode (auxiliary electrode) (C. E.) reference electrode (R. E.) 1) Three-electrode system/cell: 1.1.4 Measurement of electrode polarization Luggin cappilary

7. Shape of working electrode disk sphere wire ring band foil array Interdigitaled array

8. Commercial SCE 2) Typical reference electrode: Commercial Ag/AgCl or Ag/Ag + electrode

9. 1 ） Faraday’s Law m, mass of liberated matter; Q electric coulomb, z electrochemical equivalence, F Faraday’s constant, M molar weight of the matter.> F = 1.6021917  10 -19  6.022169  10 23 = 96486.69 C mol -1  96500 C mol -1 §1.1.5 Important relationships

10. Valid only for reversible cell 2 ） Nernst equation: Dependent of electrode potential on species activities

11. 3) Tafel equation: The point of intersection of the extrapolation on the line  = 0 is log i 0. A is in fact the  at j = 1 A cm -2.  = a + b log j Valid only for irreversible cell

12. Pt electrode in aq. 0.01 M Fe 3+, Sn 4+, Ni 2+ (1 M HCl) Discharge series: As potential moved to more negative values, the substance which will be reduced first is the oxidant with the least negative . §1.2 Physical meanings of  and I 1) Electrode potential

13. the highest occupied level Electron gas Metal atoms unoccupied Fermi Level occupied Energy bands Fermi-Dirac distribution cf. p. 16-18

14. Electrode Solution A + e -  A - Electrode Solution Occupied MO Vacant MO Electrode Solution Occupied MO Vacant MO Electrode Solution A  A + + e -

15. HOMO approximately corresponds to   of A/A - LUMO approximately corresponds to   of A + /A physical meaning of  ? The tendency to accept or donate electrons is represented by the sign and absolute value of the standard electrode potentials. That means: high positive potential values indicate a strong tendency for accepting electrons A higher positive potential of a given half-cell with respect to another indicates that the former has stronger oxidizing ability than the latter. That means: high positive potential values indicate a strong tendency for accepting electrons A higher positive potential of a given half-cell with respect to another indicates that the former has stronger oxidizing ability than the latter.

16. Current: the index of reaction rate Consider 1 mole of A - is oxidized to A A   A + ne  Q = n N F n: the number of e - transferred, N the number of mole of A 2) Electrochemical current

17. §1.3 Electrochemical methods One cannot simultaneously control both E and I Control E: potentiostatic methods Control I: galvanostatic methods Voltammetry Voltammetric method

18. References: [1] 查全性等，《电极过程动力学导论（第三版）》，科 学出版社，北京， 2002.6. [2] A. J. Bard, Electrochemical Methods–Fundamentals and Applications (2 nd, Ed.), John Wiley & Sons. [3] Encyclopedia of Electrochemistry, (Ed. A.J. Bard), Wiley. [4] Modern Electrochemistry, (Ed. J. O. Bockris ), Springer. [5] Modern Aspects of Electrochemistry, Springer. [6] A. H. Frumkin, Kinetics of Electrode Process, Science Press.

19. Allen J. Bard, Martin Stratmann, Encyclopedia of Electrochemistry, Wiley. Vol. 1: Thermodynamics and Electrified Interfaces Vol. 2: Interfacial Kinetics and Mass Transport Vol. 3: Instrumentation and Electroanalytical Chemistry Vol. 4: Corrosion and Oxide Films Vol. 5: Electrochemical Engineering Vol. 6: Semiconductor Electrodes and Photoelectrochemistry Vol. 7: Inorganic Electrochemistry Vol. 8: Organic Electrochemistry Vol. 9: Bioelectrochemistry Vol. 10: Modified Electrodes Vol. 11: Index

20. Modern Aspects Of Electrochemistry, Vol. 42 Topics include: 1) The electrochemistry and electrocatalysis of Ruthenium in regards to the development of electrodes for Polymer Electrolyte Membrane fuel cells (PEM) 2) Breakthroughs in Solid Oxide Fuel Cell (SOFC) anodes and cathodes leading to improved electrocatalysis 3) Electrocatalysis of the electrochemical reduction of CO 2 on numerous metals 4) The interfacial phenomena of electrodeposition and codeposition, and the need for new theoretical analyses of the electrode-electrolyte interface 5) Advantages of scanning tunneling microscopy (STM) in understanding the basics of catalysis, electrocatalysis and electrodeposition 6) The role of electrochemistry in emerging technologies including electrodeposition and electroforming at the micro and nano levels, semiconductor and information storage, including magnetic storage devices, and modern medicine

21. Bockris, John O'M., Reddy, Amulya K.N., Modern Electrochemistry, Springer. Vol. 1 Ionics Vol. 2A Fundamentals of Electrodics Vol. 2B Electrodics in Chemistry, Engineering, Biology and Environmental Science

22. Electrochemical reactions are interfacial reactions, the structure and properties of electrode / electrolytic solution interface greatly influences the reaction. Influential factors: 1) Chemistry factor: chemical composition and surface structure of the electrode: reaction mechanism 2) Electrical factor: potential distribution: activation energy of electrochemical reaction 1) Chemistry factor: chemical composition and surface structure of the electrode: reaction mechanism 2) Electrical factor: potential distribution: activation energy of electrochemical reaction Chapter 2 Electrode/electrolyte interface: ----structure and properties

23. For process involving useful work,  W’ should be incorporated in the following thermodynamic expression. dG = -SdT + VdP +  W’+  i dn i §2.1 Interfacial potential and Electrode Potential For electrochemical system, the useful work is: W’ = z i e  Under constant temperature and pressure, for process A  B: 1) Electrochemical potential

24. Electrochemical potential 1) Definition: z i is the charge on species i, , the inner potential, is the potential of phase . In electrochemical system, problems should be considered using electrochemical potential instead of chemical potential.

25. 2) Properties: 1) If z = 0 (species uncharged) 2) for a pure phase at unit activity 3) for species i in equilibrium between  and . 3) Effect on reactions 1) Reactions in a single phase:  is constant, no effect 2) Reactions involving two phases: a) without charge transfer: no effect b) with charge transfer: strong effect

26. 2) Inner, outer and surface potential (1) Potential in vacuum: the potential of certain point is the work done by transfer unite positive charge from infinite to this point. (Only coulomb force is concerned).  - strength of electric field

27. This process can be divided into two separated steps.  Vacuum, infinite charged sphere + + + + Electrochemical reaction can be simplified as the transfer of electron from species in solution to inner part of an electrode. e e e W 2 +   10 -6 ~ 10 -7 m W1W1 (2) Potential of solid phase

28. The work (W 1 ) done by moving a test charge from infinite to 10 -6 ~ 10 -7 m vicinity to the solid surface (only related to long-distance force) is outer potential. Outer potential also termed as Volta Potential (  ) is the potential measured just outside a phase.  10 -6 ~ 10 -7 m W1W1 Moving unit charge from vicinity (10 –6 ~10 -7 m) into inner of the sphere overcomes surface potential (  ). Short-distance force takes effect. W 2 +  W2W2 For hollow ball,  can be excluded.  arises due to the change in environment experienced by the charge (redistribution of charges and dipoles at the interface) (3) Inner, outer and surface potential

29. W2W2  10 -6 ~ 10 -7 m W1W1 The total work done for moving unit charge to inner of the charged sphere is W 1 + W 2  = (W 1 + W 2 ) / z e 0 =  +  The electrostatic potential within a phase termed the Galvani potential or inner potential (  ). If short-distance interaction, i.e., chemical interaction, is taken into consideration, the total energy change during moving unite test charge from infinite to inside the sphere:

30. inner hollow 10 -6 ~10 -7 infinite distance workfunction

31. the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surfaceenergyelectron voltselectron or energy needed to move an electron from the Fermi energy level into vacuum.Fermi energy (4) Work function and surface potential

32. For two conductors contacting with each other at equilibrium, their electrochemical potential is equal.   3) Measurability of inner potential = (1) potential difference

33. different metal with different Therefore

34. Conclusion No potential difference between well contacting metals can be detected   Galvanic and voltaic potential can not be measured using voltmeter.

35. If electrons can not exchange freely among the pile, i.e., poor electrical conducting between phases. n 1 Fermi level n 1 1’1’ (2) Measurement of inner potential difference

36. Knowing  V ,     can be only measured when (3) Correct connection n 1 Fermi level 1’1’

37. Consider the cell: Cu|Cu 2+ || Zn 2+ | Zn/Cu’ I S1S1 S2S2 III’ For homogeneous solution without liquid junction potential the potential between I and II depends on outer potential difference between metal and solution. (4) Analysis of real system

38. Using reference with the same The value of I  S  is unmeasurable but the change of is [  ( I  S  )] can be measured. the exact value  of unknown electrode can not be detected. absolute potential

39. Chapter 2 Electrode/electrolyte interface: structure and properties

40. Cu Zn Zn 2+ e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- 1) Transfer of electrons 2.4 origination of surface potential

41. Cu Cu 2+ Cu 2+ (aq) Cu Cu 2+ e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- 2) Transfer of charged species

42. AgI I¯I¯ I¯I¯ I¯I¯ I¯I¯ I¯I¯ I¯I¯ I¯I¯ + + + + + + + 3) Unequal dissolution / ionization +

43. I¯I¯ I¯I¯ I¯I¯ I¯I¯ I¯I¯ I¯I¯ I¯I¯ + + + + + + + 4) specific adsorption of ions

44. 5) orientation of dipole molecules – – – – ++ + + + + + + + – + – + – + – + – – – – – – – – – – Electron atmosphere

45. 6) Liquid-liquid interfacial charge KClHCl H+H+ K+K+ KCl HCl H+H+ H+H+ H+H+ H+H+ Cl - Different transference number

46. 1), 2), 3) and 6): interphase potential 4), 5) surface potential. 1) Transfer of electron 2) Transfer of charged species 3) Unequal dissolution 4) specific adsorption of ions 5) orientation of dipole molecules 6) liquid-liquid interfacial charge

47. Cu Cu 2+ e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- Electric double layer – + + + + + + + – – – – – – capacitor Holmholtz double layer (1853) Electroneutrality: q m = -q s

48. 2.5 Ideal polarizable electrode and Ideal non- polarizable electrode i charge i ec equivalent circuit i = i ch + i ec Charge of electric double layer Electrochemical rxn Faradaic process and non-Faradaic process

49. an electrode at which no charge transfer across the metal-solution interface occur regardless of the potential imposed by an outside source of voltage. ideal polarizable electrode no electrochemical current: i = i ch E I 0

50. Virtual ideal polarizable electrode Hg electrode in KCl aqueous solution: no reaction takes place between +0.1 ~ -1.6 V K + + 1e  = K 2Hg + 2Cl - - 2e - = Hg 2 Cl 2 +0.1 V -1.6 V Electrode Solution Hg

51. an electrode whose potential does not change upon passage of current (electrode with fixed potential) ideal non-polarizable electrode no charge current: i = i ec E I 0 Virtual nonpolarizable electrode Ag(s)|AgCl(s)|Cl  (aq.) Ag(s) + Cl   AgCl(s) + 1e 

52. For measuring the electrode/electrolyte interface, which kind of electrode is preferred, ideal polarizable electrode or ideal non- polarizable electrode?

53. 2.6 interfacial structure surface charge-dependence of surface tension: 1) Why does surface tension change with increasing of surface charge density? 2) Through which way can we notice the change of surface tension? Experimental methods: 1) electrocapillary curve measurement 2) differential capacitance measurement

54. interface Interphase Interfacial region   S S’ a a’ b b’ The Gibbs adsorption isotherm When T is fixed

55. Integration gives Gibbs adsorption isotherm

56. When the composition of solution keeps constant Lippman equation Electrocapillary curve measurement

57. Electrocapillary curves for mercury and different electrolytes at 18 o C. Zero charge potential:  0 (  pzc: potential at which the electrode has zero charge) Electrocapillary curve

58. Theoretical deduction of

59. Differential capacitance RsRs R ct C dl Differential capacitance

60. capacitor – + + + + + – – – – The double layer capacitance can be measured with ease using electrochemical impedance spectroscopy (EIS) through data fitting process. Measurement of interfacial capacitance

61. Integration of capacitance for charge density Differential capacitance curves C d = C(  )

62. KF K 2 SO 4 KCl KBr KI 0.4 0.8 1.2 1.60.0  / V C d /  F·cm -2 20 40 60 Dependence of differential capacitance on potential of different electrolytes. Differential capacitance curves

63. NaF Na 2 SO 4 KI 0.0 -0.4 -0.8 -1.20.4  / V q /  C·cm -2 4 0 8 12 -4 -8 -12 Charge density on potential

64. differential capacitance curves for an Hg electrode in NaF aqueous solution Dependence of differential capacitance on concentration Potential-dependent Concentration-dependent Minimum capacitance at potential of zero charge (E pzc ) 36  F cm -2 ; 18  F cm -2 ;

65. Surface excess         ++  qqsqs c0c0

66. For any electrolyte For R.E. in equilibrium with cation

67. KF 0.0 -0.4 -0.8 -1.20.4  / V q /  C·cm -2 -2 0 -4 -6 2 4 6 KAc KCl KBr KF KAc KCl KBr Anion excess cation excess Surface excess curves

68. Electrode possesses a charge density resulted from excess charge at the electrode surface (q m ), this must be balanced by an excess charge in the electrolyte (-q s ) 2.7 Models for electric double layer 1) Helmholtz model (1853) 0 d E

69. q charge on electrode (in Coulomb)

70. 2) Gouy-Chappman layer (1910, 1913) Charge on the electrode is confined to surface but same is not true for the solution. Due to interplay between electrostatic forces and thermal randomizing force particularly at low concentrations, it may take a finite thickness to accumulate necessary counter charge in solution. 0 d E Plane of shear

71. Boltzmann distribution Poisson equation Gouy and Chapman quantitatively described the charge stored in the diffuse layer, q d (per unit area of electrode:)

72. Integrate from x = d to x = 

73. For 1:1 electrolyte For Z:Z electrolyte

74. Experimentally, it is easier to measure the differential capacitance: Hyperbolic functions

75. For a 1:1 electrolyte at 25 o C in water, the predicted capacitance from Gouy-Chapman Theory. 1) Minimum in capacitance at the potential of zero charge 2) dependence of C d on concentration 2) Gouy-Chappman layer (1910, 1913)

76. 3) Stern double layer (1924) Combination of Helmholtz and Guoy-Chapman Models The potential drop may be broken into 2:

77. Inner layer + diffuse layer This may be seen as 2 capacitors in series: C i : inner layer capacitance C d : diffuse layer capacitance-given by Gouy-Chapman CiCi CdCd MS

78. Total capacitance (C t ) dominated by the smaller of the two. CiCi CdCd MS At low c 0 At high c 0 C d dominant C i dominant C d  C t C i  C t

79. Discussion: When c 0 and  are very small Stern equation for double layer

80. Discussion: When c 0 and  are very large C d plays a role at low potential near to the p. z. c.

81. Fitting result of Stern Model. Fitting of Gouy-Chapman model to the experimental results

82. 4) Gramham Model-specific adsorption 0 d E Triple layer Specifically adsorbed anions Helmholtz (inner / outer) plane