Percolation Model for Proton Immobility in Ice

Abstract

A simple Ising model and a statistical theory of gel formation in a polymer matrix were combined to explain the effect of temperature on the mobility of protons in ice. Cowin et al observed that protons in ice bulk were immobile at temperatures below 190 K, and suddenly become mobile at temperatures above 190 K (Nature 398, 405 (1999)). We proposed here that the transport of protons is controlled by a percolation mechanism. The proton transport is facilitated by the occurrence of easily reoriented water molecules in the ice bulk. The fraction of this molecule depends on temperature and was calculated using a simple Ising model. The formation of network of these molecules which provides pathways for proton transport was calculated using a statistical theory of gel formation in a polymeric system. Our model succeeded to reproduce the variation of potential difference between the ice film surfaces with respect to temperature as observed by Cowin et al based on a soft landing experiment.