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 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 Charge distribution in a semiconductor and electrolyte Potential drop in a semiconductor Flatband potential (vs. pH) 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 : 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 for self-exchange reactions.

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