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)

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

GROTTHUSS MECHANISM 1806 PROTONS EXIST IN WATER AS HYDRONIUM Lituanian born in Dresden 1822 committed suicide- studied in Polytechnique (Vauquelin) CONDUCTION MECHANISMS

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

Water Structure Rotational invariance broken by hydrogen bonding

Ice H Bonds Crystalline Fields Break Rotational Symmetry

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.

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

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, 952-958 (2006)

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

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 1985 greatest condensed matter physcisits –Polaron, ferrro., imprisonment of resonance radiation, electron-phonon interaction Hydronium is hydrated (aqueous polaron) ABOUT WHAT WE NEED!!