Single Protonic Phonon Absorption Limited Bipolar and Unipolar Trappy Proton Transport in Pure Liquid Water Modeled by Melted Ice Lattice

B. Jie, C. Sah
Xiamen University,

Keywords: protonic water physics, protonic phonons, melted ice lattice


We modeled (September 2013) the pure liquid water as a protonic semiconductor with melted ice lattice. It was based on the 1933 Bernal-Fowler ice model, with the hexagonal close packed (HCP) primitive unit cell containing four water molecules, which was proven by the 1935 Linus Pauling residual entropy theory to explain Giauque's 1932-1935 low temperature specific heat measurements. The electrical charge carrier concentration and mobility of the point-mass protons in pure water were modeled by us using the bipolar protonic energy band model of protons and prohols (proton-holes), analogous to the bipolar electronic energy band model of electrons and holes in electronic solids. Alternatively, pure water can also be modeled by the unipolar protonic energy band model with three positive point-mass protons, containing also the high concentration (twice many) dynamic protonic trapping centers. Bipolar and unipolar proton transports are rate-limited by proton detrapping at dynamic proton-trapping centers, involving the absorption of only one protonic phonon, while its inverse, proton trapping with the emission of one protonic phonon, has a much higher rate. Detrapping of a trapped proton, from the absorption of one protonic phonon, is characterized by a thermal activation energy, which is extracted from the experimental mobility versus temperature. Using the one-dimension Newtonian spring-mass model, the ratios of the thermal activation energies are computed from the four water molecules in one primitive cell, and they match the experimental activation energies, and they also match the experimental proton vibrational frequencies of isolated water molecules in vapor.