Proton Electrodynamics in Liquid Water

The dielectric spectrum of liquid water, ${10}^4-{10}^{11}$ Hz, is interpreted in terms of diffusion of charges, formed as a result of self-ionization of H${}_2$O molecules. This approach explains the Debye relaxation and the dc conductivity as two manifestations of this diffusion. The Debye relaxation is due to the charge diffusion with a fast recombination rate, $1\mathrm{/}{\tau }_2$, while the dc conductivity is a manifestation of the diffusion with a much slower recombination rate, $1\mathrm{/}{\tau }_1$. Applying a simple model based on Brownian-like diffusion, we find ${\tau }_2\simeq {10}^{-11}$ s and ${\tau }_1\simeq {10}^{-6}$ s, and the concentrations of the charge carriers, involved in each of the two processes, $N_2\simeq 5\times {10}^{26}$ m${}^{-3}$ and $N_1\simeq {10}^{14}$ m${}^{-3}$. Further, we relate $N_2$ and $N_1$ to the total concentration of H${}_3$O${}^{+}$–OH${}^{-}$ pairs and to the pH index, respectively, and find the lifetime of a single water molecule, $\tau_{0} \simeq 10^{-9}$ s. Finally, we show that the high permittivity of water results mostly from flickering of separated charges, rather than from reorientations of intact molecular dipoles.