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2 Structure of electrified interface

2 Structure of electrified interface. 1. The electrical double layer 2. The Gibbs adsorption isotherm 3. Electrocapillary equation 4. Electrosorption phenomena 5. Electrical model of the interface. 2.1 The electrical double layer. Historical milestones

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2 Structure of electrified interface

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  1. 2 Structure of electrified interface 1. The electrical double layer 2. The Gibbs adsorption isotherm 3. Electrocapillary equation 4. Electrosorption phenomena 5. Electrical model of the interface

  2. 2.1 The electrical double layer • Historical milestones • The concept electrical double layer Quincke – 1862 • Concept of two parallel layers of opposite charges Helmholtz 1879 and • Stern 1924 • Concept of diffuse layer Gouy 1910; Chapman 1913 • Modern model Grahame 1947

  3. Presently accepted model of the electrical double layer

  4. 2.2 Gibbs adsorption isotherm Definitions a G – total Gibbs function of the system Ga,Gb,Gs - Gibbsfunctions of phases a,b,s s Gibbs function of the surface phase s: Gs= G – { Ga + Gb } b

  5. Gibbs Model of the interface

  6. The amount of species j in the surface phase: njs = nj – { nja + njb} Gibbs surface excess Gj Gj = njs/A A – surface area

  7. Gibbs adsorption isotherm Change in G brought about by changes in T,p, A and nj dG=-SdT + Vdp + gdA + Smjdnj – surface energy – work needed to create a unit area by cleavage - chemical potential dGa =-SadT + Vadp + + Smjdnja dGb =-SbdT + Vbdp + + Smjdnjb and dGs = dG – {dGa + dGb}= SsdT + gdA + + Smjdnjs

  8. Derivation of the Gibbs adsorption isotherm dGs = -SsdT + gdA + + Smjdnjs Integrate this expression at costant T and p Gs = Ag + Smjnjs Differentiate Gs dGs = Adg + gdA + Snjsdmj + Smjdnjs The first and the last equations are valid if: Adg + Snjsdmj = 0 or dg = - Gjdmj

  9. Gibbs model of the interface - Summary

  10. 2.3 The electrocapillary equation Cu’ Ag AgCl KCl, H2O,L Hg Cu’’

  11. sM = F(GHg - Ge) +

  12. Lippmann equation

  13. Differential capacity of the interface

  14. Capacity of the diffuse layer Thickness of the diffuse layer

  15. 2.4 Electrosorption phenomena

  16. 2.5 Electrical properties of the interface In the most simple case – ideally polarizable electrode the electrochemical cell can be represented by a simple RC circuit

  17. Implication – electrochemical cell has a time constant that imposes restriction on investigations of fast electrode process Time needed for the potential across the interface to reach The applied value : Ec - potential across the interface E - potential applied from an external generator

  18. Time constant of the cell t = RuCd Typical values Ru=50W; C=2mF gives t=100ms

  19. Current flowing in the absence of a redox reaction – nonfaradaic current In the presence of a redox reaction – faradaic impedance is connected in parallel to the double layer capacitance. The scheme of the cell is: The overall current flowing through the cell is : i = if + inf Only the faradaic current –if contains analytical or kinetic information

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