Two Sublattice Model of Hydrogen Bonding at Finite Temperatures

Abstract

The high anisotropic proton conductivity in many hydrogen-bonded molecules (e.g. ice), has attracted a lot of theoretical interest^1–5. This unusualy high mobility of protons, also plays a role in interpreting certain biological processes^6,7. The transfer of protons in a hydrogen bonded system is done by ionic (to be considered here) and rotational defects along Bernal-Fowler filaments⁸. The effective potential that a hydrogen-bonded proton feels between two heavy ions can be described by a double well potential, with two equivalent equilibrium positions separated by a barrier. This provides a mechanism for the transfer of protons along the chain. As the basic hydrogen—bonded chain one considers a sequence of alternating heavy ions (OH ^– ions for ice) and protons but the heavy ion sublattice must not be thought of as a fixed substrate. The motion of the heavy ions along with their coupling to the protons is very important, as it is shown by experiments of the O — H distance as a function of the O — O distance in the O — H — —O systems⁹. For a realistic hydrogen bonding potential the relative displacement of neighbouring heavy ions changes the barrier height drastically.