Transcript PowerPoint

Lecture 11
Electron Transfer Theories
- The Theory of Markus Reference.
1. R. Memming, Semiconductor Electrochemistry, Wiley-VCH, 2000 (e-book)
2. A.J. Bard and L.R. Faulkner, Electrochemical Methods: Fundamentals and
Applications, Wiley, 2001
3. J. O’M. Bockris, A.K.N. Reddy, and M. Gamboa-Aldeco, Modern Electrochemistry,
Kluwer Academic/Plenum Publishers, 2000
Lecture note
http://les.kaist.ac.kr/B_Lecture
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
Structure of the Interface
Metal-electrolyte interface
Semiconductor-electrolyte interface
Band Bending of a Semiconductor
n-type Semiconductor
p-type Semiconductor
Band Bending of a Semiconductor with Bias
cathodic
anodic
Negative bias:
accumulation
Small bias:
depletion
Positive bias:
inversion
Flat Band Potential
Band Edge Positions of Semiconductors
Semiconductor-Electrolyte Interface
1. Charge distribution in a semiconductor and electrolyte
2. Potential drop in a semiconductor
3. Flatband potential (vs. pH)
4. Band edge pinning
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
The Marcus Theory
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?
Previous Model
The Franck-Condon Principle:
The positions of the nuclei are unchanged in the course of the electron transfer
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
The electron rate transfer rate constant ket
k et  kn exp( 
DG
kT
#
)
k : a transmission coefficient (from 0 to 1)
n : the frequency of nuclear motion through the transition state ( ~ 1012-1013 s-1)
DG# : the Gibbs energy of activation
DG
for self-exchange reactions.
#

l
4
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
Inverted region
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]-
Reorganization energy l
Inner sphere reorganization energy：
Outer sphere reorganization energy :
The Reorganization Energy
Electron Transfer Processes at Electrodes
Next Meeting
The Gerischer Model