Water and Ice Dielectric Spectra Scaling at 0 {\deg}C

Dielectric spectra (10^4-10^11 Hz) of water and ice at 0 {\deg}C are considered in terms of proton conductivity and compared to each other. In this picture, the Debye relaxations, centered at 1/{\tau}_W ~ 20 GHz (in water) and 1/{\tau}_I ~ 5 kHz (in ice), are seen as manifestations of diffusion of separated charges in the form of H3O+ and OH- ions. The charge separation results from the self-dissociation of H2O molecules, and is accompanied by recombination in order to maintain the equilibrium concentration, N. The charge recombination is a diffusion-controlled process with characteristic lifetimes of {\tau}_W and {\tau}_I, for water and ice respectively. The static permittivity, {\epsilon}(0), is solely determined by N. Both, N and {\epsilon}(0), are roughly constant at the water-ice phase transition, and both increase, due to a slowing down of the diffusion rate, as the temperature is lowered. The transformation of the broadband dielectric spectra at 0 {\deg}C with the drastic change from {\tau}_W to {\tau}_I is mainly due to an abrupt (by 0.4 eV) change of the activation energy of the charge diffusion.