ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa


Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2017, Vol. 14, No. 3, pp. 255-270

Attenuation coefficient and dielectric permittivity of supercooled volume water in the temperature range 0…–90 °C at frequencies 11…140 GHz

G.S. Bordonskiy 1 , A.O. Orlov 1 , Yu.B. Khapin 2 
1 Institute of Natural Resources, Ecology and Cryology SB RAS, Chita, Russia
2 Space Research Institute RAS, Moscow, Russia
Accepted: 27.01.2017
DOI: 10.21046/2070-7401-2017-14-3-255-270
While solving the problems of microwave radiation transferring in atmosphere aerosols, frozen earth covers and other natural and artificial dispersive media, it is essential to know dielectric parameters of supercooled volume water. Microwave properties of water have been well studied at positive temperatures, however, there are few works focused on supercooled water. Measurements of dielectric permittivity have been taken only at the temperature to 18 °C at maximum frequency of 9.61 GHz.
At the same time, there is a need in exact knowledge of electromagnetic water loss at lower temperatures and in a wide frequency range. It is especially required for a millimeter range where one can observe maximum specific attenuation of electromagnetic radiation. The main difficulty in such measurements is getting enough quantity of supercooled volume water for measurements at temperatures from –20 °C to –42 °C.
In the present study, we used wet nanoporous silicate materials, i.e. silica gels with average pore diameter 6–9 nm for deep supercooling when measuring dielectric water parameters over a frequency interval of 11…140 GHz. Under certain conditions, it is possible to supercool water to a temperature of –90 °C which would be close to volume water according to its physical characteristics.
The measurements made revealed a property unknown before, i.e. presence of some significant redundant losses at the temperatures below –30 °C as compared to the data from well-known models. For mathematical description of an imaginary part of relative dielectric permittivity, an additional summand represented as a sum of two Gaussian functions was introduced. One of them has an extremum close to –45 °C, another one has an extremum at
–60…–80 °C. Additional attenuation at –45 °C is supposed to be connected with the second critical water point which has been found before when using computer simulation and below this temperature at –60…–80 °C determined by the solid matrix properties and ferroelectric ice “0”.
Keywords: supercooled water, microwaves, dielectric properties, nanoporous media, second critical point of water, ferroelectric ice “0”
Full text


  1. Antonov A.S., Batenin V.M., Vinogradov A.P., Elektrofizicheskie svoistva perkolyatsionnykh sistem (Electrophysical properties of percolation systems), Moscow: In-t vysok. temperatur, 1990, 117 p.
  2. Bakhtina E.Yu., Eshevskii O.Yu., Il'in V.A., Korzhavchikov M.A., Frolov A.V., Osobennosti fazovykh perekhodov v plenkakh svyazannoi vody na poverkhnosti granits dispersnykh sistem (Features of phase transitions in the films of bound water on the surface of dispersed systems borders), Kondensirovannye sredy i mezhfaznye granitsy, 2001, Vol. 3, No. 2, pp. 136–142.
  3. Benzar' V.K., Tekhnika SVCh-vlagometrii (Technique microwave moisture metering), Minsk: Vysshaya shkola, 1974, 350 p.
  4. Bobrov P.P., Maslennikov N.M., Sologubova T.A., Etkin B.C., Issledovanie dielektricheskikh kharakteristik pochv v oblasti perekhoda vlagi iz svobodnoi v svyazannuyu na sverkhvysokikh chastotakh (Investigation of dielectric properties of soil at microwave frequencies in the transition of water from free to bound), DAN SSSR, 1989, Vol. 304, No. 5, pp. 1116–1119.
  5. Bordonskii G.S., Krylov S.D., Strukturnye prevrashcheniya pereokhlazhdennoi vody v nanoporakh po dannym o pogloshchenii mikrovolnovogo izlucheniya (Structural transformations of supercooled water in nanopores, studied by microwave radiation), Zhurnal fizicheskoi khimii, 2012, Vol. 86, No. 11, pp. 1806–1812.
  6. Bordonskii G.C., Orlov A.O., Shchegrina K.A., Dielektricheskie poteri v pereokhlazhdennoi porovoi vode na chastote 34 GGts (Electromagnetic losses of supercooled pore water at 34 GHz), Izvestiya vuzov. Radiofizika, 2016, Vol. 59, No. 10, pp. 906–915.
  7. Bordonskii G.S., Dielektricheskie poteri presnogo l'da na SVCh (Dielectric loss freshwater ice at microwave frequencies), Radiotekhnika i elektronika, 1995, No. 11, pp. 1620–1622.
  8. Bordonskii G.S., Orlov A.O., Perkolyatsionnyi mekhanizm zavisimosti dielektricheskoi pronitsaemosti melkodispersnykh sred (Percolation effect of change moisture dependence on dielectric permittivity of dispersed media), Issledovanie Zemli iz kosmosa, 2011, No. 4, pp. 12–18.
  9. Bordonskii G.S., Filippova T.G., Vliyanie perkolyatsii na dielektricheskie svoistva merzlykh dispersnykh sred (Influence percolation on the dielectric properties of the dispersion medium frozen), Kondensirovannye sredy i mezhfaznye granitsy, 2002, Vol. 4, No. 1, pp. 21–26.
  10. Vinogradov A.P., Elektrodinamika kompozitnykh materialov (Electrodynamics of composite materials), Moscow: Editorial URSS, 2001, 208 p.
  11. Ershov E.D., Vlagoperenos i kriogennye tekstury v dispersnykh porodakh (The moisture transfer and cryogenic textures in dispersed rocks), Moscow: Izd-vo MGU, 1979, 214 p.
  12. Il'in V.A., Slobodchikova S.V., Etkin V.S., Laboratornye issledovaniya dielektricheskoi pronitsaemosti merzlykh peschanykh pochv (Laboratory investigations of the dielectric constant of frozen sandy soil), Radiotekhnika i elektronika, 1993, Vol. 38, No. 6. pp. 1036–1041.
  13. Kask N.E., Perkolyatsiya i perekhod “metall-nemetall” pri lazernom isparenii kondensirovannykh sred (Percolation and transition “metal-nonmetal” during laser evaporation of condensed matter), Pis'ma v ZhETF, 1994, Vol. 60, No. 3. pp. 204–208.
  14. Kutuza B.G., Danilychev M.V., Yakovlev O.I., Sputnikovyi monitoring Zemli: Mikrovolnovaya radiometriya atmosfery i poverkhnosti (Remote sensing of the Earth: Microwave radiometry of the atmosphere and surface), Moscow: LENAND, 2016, 336 p.
  15. Orlov A.O., Issledovanie mikrovolnovykh svoistv pereokhlazhdennoi vody v poristykh sredakh na chastotakh 34 i 94 GGts (Study of microwave properties of supercooled water in porous media at frequencies of 34 and 94 GHz), Vestnik ZabGU, 2016, Vol. 22, No. 8, pp. 14–20.
  16. Parfenov V.A., Kirik S.D., Poluchenie mezostrukturirovannykh silikatnykh materialov s kontroliruemymi razmerami por v prisutstvii tsetildimetilamina (Preparation mesostructured silicate materials with controlled pore sizes in the presence tsetildimetilamina), Trudy V Staverovskikh chtenii. Ul'trapresnye poroshki, nanostruktury, materialy: poluchenie, svoistva, primenenie (Proc. Conf. V Staverovskie Reading. Ultrafresh Powders, Nanostructures Materials: Preparation, Properties and Application), Krasnoyarsk, 2009, pp. 318–322.
  17. Khaken G., Sinergetika (Synergetics), Moscow: URSS: LENAND, 2015, 880 p.
  18. Sharkov E.A., Radioteplovoe distantsionnoe zondirovanie Zemli: fizicheskie osnovy: (Passive Microwave Remote Sensing of the Earth: Physical Foundations), Moscow: IKI RAN, 2014, 544 p.
  19. Shklovskii B.I., Efros A.L., Elektronnye svoistva legirovannykh poluprovodnikov (The electronic properties of doped semiconductors), Moscow: Nauka, 1970, 416 p.
  20. Angell C.A., Oguni M., Sichina W.J., Heat capacity of water at extremes of supercooling and superheating, J. Phys. Chem., 1982, Vol. 86. No. 6. pp. 998–1002.
  21. Anisimov M.A., Cold and supercooled water: a novel supercritical-fluid solvent, Russian Journal of Physical Chemistry B, 2012, Vol. 6, No. 8, pp. 861–867.
  22. Bertolini D., Cassettari M., Salvetti G., The dielectric relaxation time of supercooled water, J. Chem. Phys., 1982, Vol. 76, No. 6, pp. 3285–3290.
  23. Caddedu M.P., Turner D.D., Evaluation of water permittivity models from ground-based observations of cold clouds at frequencies between 23 and 170 GHz, IEEE Trans. Geosc. Rem. Sens., 2011, Vol. 49, No. 8, pp. 2999–3008.
  24. Castrillon S.R.-V., Giovambattista N., Arsay I.A., Debenedetti P.G., Structure and energetics of thin film water, J. Phys. Chem. C., 2011, Vol. 115, pp. 4624–4635.
  25. Cerveny S., Mallamace F., Swenson J., Vogel M., Xu L., Confined water as model of supercooled water, Chem. Rev., 2016, Vol. 116, No. 13, pp. 7608–7625.
  26. Ellison W.J., Permittivity of pure water, at standard atmospheric pressure, over the frequency range 0–25THz and the temperature range 0–100°C, J. Chem. Phys. Ref. Data, 2007, Vol. 36, No. 1, pp. 1–18.
  27. Ellison W.J., English S.J., Lamkaouchi K., Balana A., Obligis E., Deblonde G., Hewison T.J., Bauer P., Kelly G., Eymard L., A comparison of ocean emissivity models using the Advanced Microwave Sounding Unit, the Special Sensor Microwave Imager, the TRMM Microwave Imager, and airborne radiometer observations, J. Geoph. Res., 2003, Vol. 108, No. D21, pp. 4663–4677.
  28. Fedichev P.O., Menshikov L.I., Bordonskiy G.S., Orlov A.O., Experimental evidence of the ferroelectric nature of the λ-point transition in liquid water, JETP Letters, 2011, Vol. 94, No. 5, pp. 401–405.
  29. Franzese G., Stanley H.E., The Widom line of supercooled water, J. Phys.: Condens. Matter, 2007, Vol. 19, pp. 205126/16.
  30. Hodge I.M., Angell C.A., The relative permittivity of supercooled water, J. Chem. Phys., 1978, Vol. 68, No. 4, pp. 1363–1367.
  31. Komarov V., Wang S., Tang J., Permittivity and measurements, Encyclopedia of RF and Microwave Engineering, K. Chang (ed.), 2005, J. Wiley & Sons, Inc., pp. 3693–3711.
  32. Korobeynikov S.M., Drozhzhin A.P., Furin G.G., Charalambakos V.P., Agoris D.P., Surface conductivity in liquid-solid interface due to image force, Proceedings of 2002 IEEE 14th International Conference on Dielectric Liquids. ICDL 2002, pp. 270–273.
  33. Korobeynikov S.M., Melekhov A.V., Soloveitchik Yu.G., Royak M.E., Agoris D.P., Pyrgioti E., Surface conductivity at the interface between ceramics and transformer oil, Journal of Physics D: Applied Physics, 2005, Vol. 38, No. 6, pp. 915–921.
  34. Limmer D.T., Chandler D., Phase diagram of supercooled water confined to hydrophilic nanopores, J. Chem. Phys., 2012, Vol. 137, pp. 044509/11.
  35. Meissner T., Wentz F.J., The complex dielectric constant of pure and sea water from microwave satellite observations, IEEE Trans. Geosci. Rem. Sens., 2004, Vol. 42, No. 9, pp. 1836–1849.
  36. Quigley D., Alfè D., Slater B., Communication: On the stability of ice 0, ice i, and Ih, The Journal of Chemical Physics, 2014, Vol. 141, Issue 16, p. 161102.
  37. Ronne C., Thrane L., Astrand P.-O., Wallqvist A., Mikkelsen K.V., Keiding S.R., Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation, J. Chem. Phys., 1997, Vol. 107, Issue 14, pp. 5319–5331.
  38. Rosenkranz P.W., A model for the complex dielectric constant of supercooled liquid water at microwave frequencies, IEEE Transactions on Geoscience and Remote Sensing, 2015, Vol. 53, Issue 3, pp. 1387–1393.
  39. Russo J., Romano F., Tanaka H., New metastable form of ice and its role in the homogeneous crystallization of water, Nature Materials, 2014, Vol. 13, Issue 7, pp. 733–739.
  40. Schreiber A., Kotelsen I., Findenegy G.H., Melting and freezing of water in ordered mesoporous silica materials, Phys. Chem. Chem. Phys., 2001, Vol. 3, pp. 1185–1195.
  41. Stanley H.E., Buldyrev S.V., Franzese G., Havlin S., Mallamace F., Kumar P., Plerou V., Preis T., Correlated randomness and switching phenomena, Physica A: Statistical Mechanics and its Applications, 2010, Vol. 389, Issue 15, pp. 2880–2893.
  42. Stogryn P.A., Bull H.T., Rubayi K., Iravanchy S., The microwave permittivity of sea and fresh water, Tech. Rep., 1995, GenCorp Aerojet, Azusa, Calif.
  43. Widom B., Some Topics in the Theory of Fluids, J. Chem. Phys., 1963, Vol. 39, pp. 2808–2812.
  44. Zelsmann H.R., Temperature dependence of the optical constants for liquid H2O and D2O in the far IR region, Journal of Molecular Structure, 1995, Vol. 350, No. 2, pp. 95–114.