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Double layer and adsorbtion

Double layer and adsorbtion. Sähkökemian peruseet KE-31.4100 Tanja Kallio t anja.kallio@aalto.fi C213. CH 5 – 5.2. Electrical double layer. x 2. x 1. 0. + . + . X = 0 interphase X = x 1 inner Helmholtz layer X = x 2 outer Helmholtz layer. + . +. + . + . -. +. + .

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Double layer and adsorbtion

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  1. Double layer and adsorbtion Sähkökemianperuseet KE-31.4100 Tanja Kallio tanja.kallio@aalto.fi C213 CH 5 – 5.2

  2. Electrical double layer x2 x1 0 + + X = 0 interphase X = x1 inner Helmholtz layer X = x2 outer Helmholtz layer + + + + - + + + + + + + + + + + + + + + + + - + + + + + + + + + + + + + + - + + + + - + + + + + + + + + +

  3. - - - - - - - OHL potential electrolyte metal x2 0 - - - - + + + + + + + + + Potential distribution at the interphase (1/3) distance from the interphase

  4. - - - - - + + + + + + + + - - OHL - - potential semiconductor - electrolyte - - - - x2 0 - - distance from the interphase - - Potential distribution at the interphase (2/3)

  5. - - - - - - - - - - - - - - + + + + + + + + + + + + + Potential distribution at the interphase (3/3) potential electrolyte II electrolyte I 0 distance from the interphase

  6. Gibbs adsorption isotherm (1/5) Phase a and b in contact. Differentials of Gibbs energies for this phases are phase a phase b For the whole system a new force g, surface tension, must be taking into account interfacial zone Let us consider a system at constant temperature and pressure and so the first two terms on the right-hand side can be omitted.

  7. Gibbs adsorption isotherm (2/5) By subtracting Gibbs energies of the phase a and b from that of the whole system Gibbs energy of the interphase, dGs,is obtained Surfaces at the interphase have either higher or lower number of species compared to the bulk phase. This difference is surface concentration or surface excess So dGscan be written (5.7)

  8. Gibbs adsorption isotherm (4/5) When a surface is formed between two phases via infinitesimal changes Gibbs energy of an interphase is obtained by integrating the previous equation Thus By differentiating (5.10)

  9. Gibbs adsorption isotherm (5/5) As equations (5.7) and (5.10) must be equivalent the sum of the last two term in eq (5.10) must be zero. When surface excess is given per surface unit where Gibbs adsorption isotherm

  10. Adsorption in diluted solution: relative surface excess Gibbs-Duhem equation is valid in bulk phase solvent Inserting the Gibbs-Duhemeq in the Gibbs adsorption isotherm relative surface excess s for diluted solution n1>>ni and thus

  11. The electrocapillary equation (1/3) RE WE Pt(s) | H2(g) | HCl(aq) | Hg(l) | Pt(s) Surface tension is obtained by applying Gibbs adsorption isotherm for the interphase between the Hg electrode and HCl electrolyte Excess charge density on the metal, sm, is Equal, but opposite, charge density, sl, resides on the solution side

  12. The electrocapillary equation (2/3) Combining the equations we obtain From the equilibriums at the interphases As the composition of the H2(g) in the RE does not change and thus, for the equilibrium reaction H2 2 H+ + 2 e– canbewritten Inserting electrochemical potentials in the above most eq and applying dG = -nFdEfor the last term we obtain

  13. The electrocapillary equation (3/3) Lippmann equation or electrocapillary equation Capacitance of the double layer is (compare to a planar capasitor) D.C. Grahame, Chem. Rev. 41 (1947) 441

  14. Adsorption of organic molecules D.C. Grahame, Chem. Rev. 41 (1947) 441

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