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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, $1/τ_{2}$, while the dc conductivity is a manifestation of the diffusion with a much slower recombination rate, $1/τ_{1}$. Applying a simple model based on Brownian-like diffusion, we find $τ_{2} \simeq 10^{-11}$ s and $τ_{1} \simeq 10^{-6}$ 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, $τ_{0} \simeq 10^{-9}$ 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.