Surface Migration of Water Molecules in Ice

Abstract

This paper continues the discussion of data given in a previous paper on the second term in the ``local conductivity'' of ice. It is inferred that the H₂O molecules in internal surfaces are engaged in a special kind of random walk, in which the molecule is always attached to the surface by one chemical bond. This is described as bipedal random walk. It occurs with an activation energy of 5.2 kcal/mole (0.23‐electron volt per molecule). On the other hand, molecules which jump up into field‐free space and return to the surface have to acquire an energy of 11.5 kcal/mole (0.5 ev/molecule). The ratio of the corresponding Boltzmann factors is about 10⁻⁵ at 0°C and about 10⁻⁸ at −100°C; this implies that the dominant mode of diffusion in internal surfaces in ice is bipedal random walk. The migration of a water molecule on an ice surface is a special type of diffusion process. The general formulas of the theory of stochastic processes and diffusion become available for the description of the diffusion of water molecules in a surface if the appropriate expression for the diffusion constant D is substituted in the formulas. A new procedure is used to calculate D from the Einstein relation. Instead of using the direct‐current conductivity, the second term of the local conductivity is used. The expression for the diffusion constant derived from the model for local conductivity is D_L=3.5×10⁻⁴ exp(−5.2×10³/RT) cm²/sec, where the activation energy 5.2×10³ cal/mole, is derived from the second term in the local conductivity of ice. This leads to a rather explicit model of the diffusion process: it may be described as bipedal random walk of the water molecule by the breaking of one bond at a time with an activation energy of 0.23‐electron volt associated with each step. It is pointed out also that the water molecule on an internal surface has a polarizability characteristic of the surface structure.