The Dipolar Correlation Factor of Ice VI

• Published in: Journal of Glaciology
• Main Authors: Johari, G. P., Whalley, E.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1978
• Subjects: Earth-Surface Processes; Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000033815; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000033815

Abstract The dipole moment μ of an H 2 O molecule in the orientationally disordered ices is greater than the moment of an isolated molecule, 1.84 D, due to two factors: (i) the mutual polarization of molecules, and (ii) the short-range average correlation of the dipole vectors, if the molecules are able to reorient. The magnitude of the average enhancement is given by Kirkwood's equation, 1 where ϵ 0 and ϵ ∞ are respectively the limiting low- and high-frequency relative permittivity of orientational polarization, N is the number density of dipoles, k is the Boltzmann constant and T is the temperature. The dipolar correlation factor g is defined by, 2 where μ i and μ j are the dipole moments of molecules i and j in a spherical region of radius r immersed in a larger spherical region of radius R and the angular brackets indicate average over all molecules i and all their orientations. In view of the defects, vacancies, imperfections, etc., in ice, it is not certain if the limits in Equation (2) have any experimental significance. However, an approximate value of g can be calculated by taking molecules up to the second co-ordination shell. The theoretical value of g for polycrystalline ice VI which is fully disordered (within the restrictions of ice rules) has been calculated by taking molecules up to the second nearest neighbours, in both the dendritic and non-dendritic models. The calculations were done for two kinds of molecules, I and II, having multiplicities 2 and 8 respectively, in the tetragonal unit cell in space group P4 2 / nmc , and, through the use of symmetry, keeping to a minimum the number of scalar products. In both the dendritic and non-dendritic, models, g I is 10%, or more, greater than g II and the appropriately weighted values of g are 2.342 in the former and 2.065 in the latter model. The effect of ring closure is, therefore, to reduce the value of g by 13%. The limiting high temperature experimental value of g from Equation (1), using Onsager's theory for the enhancement of the dipole moment ...