1. A POLARON VIEW OF PROTON MOBILITY IN WATER
P. Pincus
Physics and Materials Departments
UCSB
Learn about anomalous dynamics……my talk is a comic relief after drinking…….no bilogy but
 KIAS Workshop on Anomalous Dynamics in Biological Systems
September 2015 
Dan Hone (UCSB)
Yong-Seok Jho (APCTP)

2. Introduction Biology exists in water
Molecules that are both soluble and Self. assemble

3. GROTTHUSS MECHANISM 1806 PROTONS EXIST IN WATER AS HYDRONIUM
Lituanian born in Dresden committed suicide- studied in Polytechnique (Vauquelin)
CONDUCTION MECHANISMS

4. Outline Motivation Molecular Ideas Crystal Field Basins
"Hubbard" Model
The hydronium polaron

5. Water Structure
Rotational invariance broken by hydrogen bonding

6. Ice
H Bonds
Crystalline Fields Break Rotational Symmetry

7. Model- Basins Crystal field basins may be occupied by (0,1) protons.
Local Water Structure
Crystal field basins may be occupied by (0,1) protons.

8. Single Molecule Energies
2H2O OH- + H3O+
Take zero of energy to be one proton in one basin on one molecule

9. Hydrogen Bonds and the Hubbard Model
OH-
Treat basins as Fermion states
t is matrix element to transfer a proton from one basin to another associated with a nearest neighbor O- - t
This is a Hubbard model. Because of degeneracy….4 spots for two protons, the ground state is degenerate without long range order. Similar to low d system where fluctuations kill long range order.
H-bond energy ~ -t2/V ~ 5kBT
t ~ 10kBT Intermediate Coupling
H3O+
D. W. Hone and P. A. Pincus “A Lattice Model of Hydrophobic Interactions”, EPL 76, (2006)

10. Some Numbers BUT Diffusion Constant of water in water
Diffusion Constant of protons in water
Diffusion constant of HP model
DHP≈(t/h)a2 D
103 Too Big
BUT

11. Polarons Electronic Holstein Polaron
Distortion dressing increases effective mass or electronic hops out of self-consistent well (activated hopping)
Mass enhancement
Lattice distorts - Holstein died in greatest condensed matter physcisits –Polaron, ferrro., imprisonment of resonance radiation, electron-phonon interaction
Hydronium is hydrated (aqueous polaron)
ABOUT WHAT WE NEED!!