1. Lecture 11 Electron Transfer Theories - The Theory of Markus -
Reference.
R. Memming, Semiconductor Electrochemistry, Wiley-VCH, 2000 (e-book)
A.J. Bard and L.R. Faulkner, Electrochemical Methods: Fundamentals and Applications, Wiley, 2001
J. O’M. Bockris, A.K.N. Reddy, and M. Gamboa-Aldeco, Modern Electrochemistry, Kluwer Academic/Plenum Publishers, 2000
Lecture note

2. Structure of the Interface
At equilibrium, the charges or molecules will be redistributed to have a constant (electro)chemical potential (or Fermi energy)
 Built-in Charges in
1. Electrolyte
IHP
OHP
Diffuse layer
2. Electrode
Free carriers for metals
Space charges for SC

3. Structure of the Interface
Metal-electrolyte interface
Semiconductor-electrolyte interface

4. Band Bending of a Semiconductor
n-type Semiconductor
p-type Semiconductor

5. Band Bending of a Semiconductor with Bias
cathodic
anodic
Negative bias: accumulation
Small bias:
depletion
Positive bias:
inversion

6. Flat Band Potential

7. Band Edge Positions of Semiconductors

8. Semiconductor-Electrolyte Interface
Charge distribution in a semiconductor and electrolyte
Potential drop in a semiconductor
Flatband potential (vs. pH)
Band edge pinning

9. OK.
We know charge distribution and band bending of a semiconductor in contact with an electrolyte. We also know how the bands of the semiconductor would change with application of an external bias.
Now we want to produce a chemical reaction at the interface, i.e., water reduction or water oxidation, by injecting electrons or holes into an electrolyte.
How would this happen?
What physical and chemical aspects would you need to describe this reaction at the interface?
Markus theory (The 1992 Nobel Laureate in Chemistry)
Gerischer theory

11. The Marcus Theory

12. Electron Transfer in Self-Exchange Reaction
Let’s consider a simplest charge transfer reaction:
a single electron is transferred without forming or breaking a bond
A + A- = A- + A
Examples?
What is the free energy of the self-exchange reactions?

13. Previous Model The Franck-Condon Principle:
The positions of the nuclei are unchanged in the course of the electron transfer

14. The Marcus Model l: reorganization energy
The energy of the product with respect to its equilibrium state when its solvent coordinate is still the same as that of the reactant state
= the work required to distort the reactant (D,A) from its equilibrium coordinate to the equilibrium coordinate of the product without any electron transfer

17. The electron rate transfer rate constant ket
k : a transmission coefficient (from 0 to 1)
n : the frequency of nuclear motion through the transition state ( ~ s-1)
DG# : the Gibbs energy of activation
for self-exchange reactions.

18. Electron Transfer in Homogeneous Solutions
Let’s consider a simplest charge transfer reaction:
a single electron is transferred without forming or breaking a bond
D + A = D+ + A-,
D = electron donor and A = electron acceptor.
D + A  (D, A)  (D, A)#  (D+, A-)#  (D+, A-)  D+ + A-
Ro and Po = an encounter complex with D, A, D+, A- in their equilibrium configurations
R# and P# = the activated complexes

22. Inverted region

23. The Reorganization Energy
Reorganization energy l
Inner sphere reorganization：　
a redox chemical reaction that proceeds via a covalent linkage—a strong electronic interaction—between the oxidant and the reductant reactants.
Outer sphere reorganization:
an electron transfer (ET) event that occurs between chemical species that remain separate intact before, during, and after the ET event
[MnO4]- + [Mn*O4]2- → [MnO4]2- + [Mn*O4]-

24. Reorganization energy l
Inner sphere reorganization energy：　
Outer sphere reorganization energy :

25. The Reorganization Energy

26. Electron Transfer Processes at Electrodes

28. Next Meeting
The Gerischer Model