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Studies of Water VI. One-Band, Two-Band and Three-Band, Trappy, Protonic, Semiconductor Lattice Models for Pure Liquid Water

Binbin Jie1, , Tianhui Jie2 and Chihtang Sah1, 3

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 Corresponding author: Binbin Jie, binjie@xmu.edu.cn

DOI: 10.1088/1674-4926/39/11/111001

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Abstract: This report adds three protonic semiconductor models to explain the " abnormally” high electrical conductivity of pure liquid water characterized by the three industrial consensus parameters, the ion product (or pH) and the two ion mobilities. Existence of long-range order in fluid water under numerous daily conditions led us to extend the 1933 Bernal-Fowler hexagonally close packed crystalline Ice Lattice to model liquid water as Melted Ice. Protonic kinetic energy band and bound (trap) pictures provide semiconductor-physics based new models of these three parameters. They are extrapolatable engineered-models for developing novel biological, chemical, electrical, mechanical and medical applications of liquid water.

Key words: solid and soft-fluid-liquid materials physics, pure water, point-mass positive proton and negative prohol, proton-ion product (pH) and mobilities, propagating-and-localized phonon scattering and detrapping-trapping of propagating-and-localized protons and prohols, Protonic Fermionic Bosons and Bosonic Fermions



[1]
Jie B B, Sah C T. Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water. J Semicond, 2017, 38(7): 071001 doi: 10.1088/1674-4926/38/7/071001
[2]
Sah C T. Fundamentals of Solid-State Electronics. 1010pp. 1991. World Scientific, Singapore. For A1G, see Preface. For electron-hole grtt models, see Section 360, Generation, Recombination, Trapping and Tunneling, and its subsection on p. 270−290
Fig. 1.  (Color online) Position space diagram of our 3-step (A, B, C) Collision Dynamics (DD Transport and GRT Kinetics: DDGRT − Drift, Diffusion, Generation, Recombination and Trapping) of point-mass protons in our Born-Von Karman Periodic Lattice Model of the melted ice for pure liquid water from the 1933 Bernal-Fowler Ice Model of Hexagonal Close Packed (hcp) Lattice. The Primitive Unit Cell (PUC), U, contains 4 water molecules in the hcp configuration with four tetrahedrally directed nearest neighbor Oxygen nuclei at 3 Angstroms (300 picometers) distance apart, and two trisector proton trapping sites at 100 pm from the nearest Oxygen nucleus. Only one of two proton trapping sites is occupied by or filled with a proton when water is frozen (T = 0°K) or KE(Kinetic Energy) = 0 meV. The 2-D plane view is the projection along the c-axis of the HCP Ice Lattice. The numerical values are the thermal activation energies and scattering energy changes of the protons and their corresponding absorbed or emitted phonon energies of the vibrating protons or oxygen nuclei.

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Fig. 2.  (Color online) Same as Fig. 1 except showing the route details of the phonon-assisted 3-step (A, B, C) trapping-limited diffusion-drift transport processes.

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Fig. 4.  The comparison table of three new protonic models for pure liquid water. (a) one-band unipolar model with two trap species and three trap energy levels, (b) two-band bipolar model with one trap species and three charge states, and (c) three-band bipolar model with no trap species. Different from the models in Fig. 3, these three models are with the charge neutrality from the mobile charges and trap charges, which leads to the inequality of mobile positive charge and mobile negative charge. Also, the phonon energies at the boiling temperature 100 °C are derived from the symmetrical stretching mode frequency of isolated water molecules based on the 1-D inverse bond length force constant assumption.

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Fig. 3.  Reproduce Fig. 5 of W5[1] for easy comparison with the following modification. The column labels for the activation energies E± and Eμ+, μ− were replaced by the corresponding protonic phonon energies. The energy coefficients were changed to the protonic phonon energies at the boiling temperature 100 °C. In addition, one column was replaced by the p+/p− column to indicate that the charge neutrality was not applied in W5[1] and the mobile charge ratio is set to be 1.

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[1]
Jie B B, Sah C T. Studies of Water V. Five Phonons in Protonic Semiconductor Lattice Model of Pure Liquid Water. J Semicond, 2017, 38(7): 071001 doi: 10.1088/1674-4926/38/7/071001
[2]
Sah C T. Fundamentals of Solid-State Electronics. 1010pp. 1991. World Scientific, Singapore. For A1G, see Preface. For electron-hole grtt models, see Section 360, Generation, Recombination, Trapping and Tunneling, and its subsection on p. 270−290

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    Received: 10 October 2018 Revised: Online: Uncorrected proof: 18 October 2018Accepted Manuscript: 22 October 2018Published: 01 November 2018

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      Article Navigation >  Journal of Semiconductors  > 2018  >  39(11): 111001
      Binbin Jie, Tianhui Jie, Chihtang Sah. Studies of Water VI. One-Band, Two-Band and Three-Band, Trappy, Protonic, Semiconductor Lattice Models for Pure Liquid Water[J]. Journal of Semiconductors, 2018, 39(11): 111001. doi: 10.1088/1674-4926/39/11/111001 ****B B Jie, T H Jie, C T Sah, Studies of Water VI. One-Band, Two-Band and Three-Band, Trappy, Protonic, Semiconductor Lattice Models for Pure Liquid Water[J]. J. Semicond., 2018, 39(11): 111001. doi: 10.1088/1674-4926/39/11/111001.
      Citation:
      Binbin Jie, Tianhui Jie, Chihtang Sah. Studies of Water VI. One-Band, Two-Band and Three-Band, Trappy, Protonic, Semiconductor Lattice Models for Pure Liquid Water[J]. Journal of Semiconductors, 2018, 39(11): 111001. doi: 10.1088/1674-4926/39/11/111001 ****
      B B Jie, T H Jie, C T Sah, Studies of Water VI. One-Band, Two-Band and Three-Band, Trappy, Protonic, Semiconductor Lattice Models for Pure Liquid Water[J]. J. Semicond., 2018, 39(11): 111001. doi: 10.1088/1674-4926/39/11/111001.
      shu

      Studies of Water VI. One-Band, Two-Band and Three-Band, Trappy, Protonic, Semiconductor Lattice Models for Pure Liquid Water

      DOI: 10.1088/1674-4926/39/11/111001
      • 1.

        Department of Physics, Xiamen University, Xiamen 361005, China

      • 2.

        Student Member, American Physical Society, US Institution applied

      • 3.

        Chinese Academy of Sciences, Beijing 100864, China

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      Our study of water began in earnest on the 7th of July, 2013 in order to give a presentation on Friday, the 13th of September, 2013, at the Sah Pen-Tung 111th Anniversary Memorial Symposium of the 2013 Fall National Meeting of the Chinese Physical Society, held for the first time at Xiamen University, China, during September 12 to 15, 2013. The first three of our written reports were published in the December 2013, February 2014 and April 2014 issues of this journal. Our 4th written report giving the first experimental verification of our model for the characterization parameter of pure water at thermodynamic equilibrium, the “ion product” (pH), was published in the April 2016 issue of the Chinese Journal of Chemical Physics, which was based on our 5th verbal report, presented at the 2015 (San Antonio, Texas) March Meeting of the American Physical Society (APS). Our 5th written report published in the July 2017 issue of this journal was based on our 6th and 7th presentations at the APS March Meetings in 2016 (New Orleans) and 2017 (Washington DC) and also based on our two seminars presented at 2016 General Assembly of the Chinese Academy of Sciences (CAS) in Beijing on June 2 and 3, as well as our tutorial lectures presented on August 6, 2016, at the 10th Summer School in Theoretical Physics funded by the National Natural Science Foundation of China, on Soft Materials Physics, hosted by the Physics Department of Xiamen University, China, during August 1 to 14, 2016. These were described in our 5th written report published in the July 2017 issue of this journal[1]. This 6th written report is based on our 8th presentations at the 2018 (Anaheim) APS March Meeting and 4 invited 2-hour seminars presented at 3 CAS Research Institutes (Beijing, Dalian and Shanghai) during and after CAS’ 19th General Assembly (May 28 thru June 1, 2018) in Beijing, and one Seminar (June 6) at the College of Physical Science and Technology of Xiamen University. Slides and talkscripts can be provided upon request by email.

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      • Corresponding author: binjie@xmu.edu.cn
      • Received Date: 2018-10-10
      • Published Date: 2018-11-01

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