3.5 Protonic Transport as a Fundamental Mechanism of the Dielectric…
127
The proposed model is a single formula (3.12) instead of the two relaxations
and four oscillators, commonly used for the same spectral region [46, 47]. The
number of parameters is reduced from 3×6 = 18 to 6. Each parameter has a clear
physical meaning. The model explains not only the polarization mechanism, but
also DC conductivity. This is a distinctive feature of the model compared to existing
models [20, 48, 49]. In addition, it treats ice and water on the same footing. These
three advantages extend the range of the validity of the model.
We analyzed ice and water dielectric responses in an external electric field on
the same footing. We introduced a phenomenological model based on an analogy
between ionic conductors, ice and water. The model shows good agreement with
experimental data over fourteen orders in frequency magnitude, predicts the general
trend of the temperature dependence of the static dielectric constant, and is useful for
experimental data approximations. According to this model, ice and water conduct
electricity by the interaction of excess protons and proton holes. No other defects,
except short-living H 3 O
+ and OH
− ions, are required for the dielectric-spectra interpretation from DC up to terahertz. The model sheds new light on the electrical properties of water, which were not fully accounted for by previous models [20, 50]. It
also provides a simple means for analytical ice and water dielectric data approximation under a wide range of thermodynamic conditions within an extended frequency
range, up to 10
13 Hz.
References
1. K. Steffen, S.V. Nghiem, R. Huff, G. Neumann, The melt anomaly of 2002 on the Greenland
Ice Sheet from active and passive microwave satellite observations. Geophys. Res. Lett. 31,
L20402–5 (2004)
2. V.F. Petrenko, R.W. Whitworth, Physics of Ice (University Press, Oxford, 1999)
3. V.G. Artemov, A unified mechanism for ice and water electrical conductivity from direct current
to terahertz. Phys. Chem. Chem. Phys. 21, 8067–8072 (2019)
4. P.V. Hobbs, Ice Physics (Clarendon Press, Oxford, 1974)
5. A. von Hippel, The dielectric relaxation spectra of water, ice, and aqueous solutions, and their
interpret at ion 1. Critical survey of the status-quo for water. IEEE Tnans. Electr. Insul. 23,
801–816 (1988)
6. I. Takei, Physics and Chemistry of Ice, in Proceedings of the 11th International Conference on
the Physics and Chemistry of Ice ed. by Kuhs WF, vol 430 (2007)
7. S.G. Warren, R.E. Brandt, Optical constants of ice from the ultraviolet to the microwave: a
revised compilation. J. Geoph. Res. 113, 10–D14220 (2008)
8. T. Matsuoka, S. Fujita, S. Mae, Effect of temperature on dielectric properties of ice in the range
5–39 GHz. J. Appl. Phys. 80, 5884–5890 (1996)
9. D.C. Elton, M. Fernandez-Serra, The hydrogen-bond network of water supports propagating
optical phonon-like modes. Natl. Commun. 7, 10193–8 (2016)
10. D.D. Klug, E. Whalley, Origin of the high-frequency transkational bands of ice I. J. Claciol.
21, 55–63 (1978)
11. G.E. Walrafen, Raman spectrum of water: transverse and longitudinal acoustic modes below
≈ 300 cm −1 and optic modes above ≈ 300 cm −1 . J. Phys. Chem. 94, 2237–2239 (1990)
12. K. Abe, T. Shigenari, Raman spectra of proton ordered phase XI of ICE I. Translational vibrations below 350 cm −1 . J. Chem. Phys. 134, 104506–11 (2011)
127
The proposed model is a single formula (3.12) instead of the two relaxations
and four oscillators, commonly used for the same spectral region [46, 47]. The
number of parameters is reduced from 3×6 = 18 to 6. Each parameter has a clear
physical meaning. The model explains not only the polarization mechanism, but
also DC conductivity. This is a distinctive feature of the model compared to existing
models [20, 48, 49]. In addition, it treats ice and water on the same footing. These
three advantages extend the range of the validity of the model.
We analyzed ice and water dielectric responses in an external electric field on
the same footing. We introduced a phenomenological model based on an analogy
between ionic conductors, ice and water. The model shows good agreement with
experimental data over fourteen orders in frequency magnitude, predicts the general
trend of the temperature dependence of the static dielectric constant, and is useful for
experimental data approximations. According to this model, ice and water conduct
electricity by the interaction of excess protons and proton holes. No other defects,
except short-living H 3 O
+ and OH
− ions, are required for the dielectric-spectra interpretation from DC up to terahertz. The model sheds new light on the electrical properties of water, which were not fully accounted for by previous models [20, 50]. It
also provides a simple means for analytical ice and water dielectric data approximation under a wide range of thermodynamic conditions within an extended frequency
range, up to 10
13 Hz.
References
1. K. Steffen, S.V. Nghiem, R. Huff, G. Neumann, The melt anomaly of 2002 on the Greenland
Ice Sheet from active and passive microwave satellite observations. Geophys. Res. Lett. 31,
L20402–5 (2004)
2. V.F. Petrenko, R.W. Whitworth, Physics of Ice (University Press, Oxford, 1999)
3. V.G. Artemov, A unified mechanism for ice and water electrical conductivity from direct current
to terahertz. Phys. Chem. Chem. Phys. 21, 8067–8072 (2019)
4. P.V. Hobbs, Ice Physics (Clarendon Press, Oxford, 1974)
5. A. von Hippel, The dielectric relaxation spectra of water, ice, and aqueous solutions, and their
interpret at ion 1. Critical survey of the status-quo for water. IEEE Tnans. Electr. Insul. 23,
801–816 (1988)
6. I. Takei, Physics and Chemistry of Ice, in Proceedings of the 11th International Conference on
the Physics and Chemistry of Ice ed. by Kuhs WF, vol 430 (2007)
7. S.G. Warren, R.E. Brandt, Optical constants of ice from the ultraviolet to the microwave: a
revised compilation. J. Geoph. Res. 113, 10–D14220 (2008)
8. T. Matsuoka, S. Fujita, S. Mae, Effect of temperature on dielectric properties of ice in the range
5–39 GHz. J. Appl. Phys. 80, 5884–5890 (1996)
9. D.C. Elton, M. Fernandez-Serra, The hydrogen-bond network of water supports propagating
optical phonon-like modes. Natl. Commun. 7, 10193–8 (2016)
10. D.D. Klug, E. Whalley, Origin of the high-frequency transkational bands of ice I. J. Claciol.
21, 55–63 (1978)
11. G.E. Walrafen, Raman spectrum of water: transverse and longitudinal acoustic modes below
≈ 300 cm −1 and optic modes above ≈ 300 cm −1 . J. Phys. Chem. 94, 2237–2239 (1990)
12. K. Abe, T. Shigenari, Raman spectra of proton ordered phase XI of ICE I. Translational vibrations below 350 cm −1 . J. Chem. Phys. 134, 104506–11 (2011)