Multiple Protonic Kinetic Energy Band Models of Melted Ice Periodic Lattice for Pure Liquid Water

Existence of long-range order in fluid water under numerous daily conditions led us to extend the 1933 Bernal-Fowler Hexagonally Close Packed (HCP) crystalline ice lattice to model pure liquid water as Melted Ice. The 8 protons in the primitive unit cells (PUC) of the HCP lattice vibrate about their lattice positions, jump among the 16 possible proton sites, half empty and half occupied in the PUC and transport among the PUC's. Propagating and localized proton vibrations are respectively the Protonic Fermions and Bosons, described by the Bloch and Wannier eigenfunctions, which are perturbed to form localized states (protonic traps) by rare random localizations. The eigenvalues of the frozen periodic lattice give the kinetic energy-band landscapes of the protonic Fermions and Bosons, while the long-range order in fluid water led us to model the proton transport by our 3-step (A, B, C) collision dynamics (DDGRT). The observed 3 thermal activation energies of pH and positive and negative ion electrical mobilities, are in excellent agreement with Slinky Toy Model of the proton vibration frequencies of dilute vapor water, providing the existence proof for this new two-phase approach to model liquid water, employing ice lattice and random distribution of water molecules in vapor.