Glass Physics and Chemistry

, Volume 40, Issue 5, pp 473–485 | Cite as

The results of application of Maxwell’s equations in glass science

  • S. V. Nemilov


Results of the application of Maxwell’s equations to describe mechanical and electrical relaxations in inorganic glasses and their melts prove the validity of the theoretical treatment of the processes within the context of continuum approximation. The relaxation properties of melts and glasses are predetermined by instantaneous modulus of elasticity (shear modulus), which adequately describes the response of the environment to local excitations related to a particle’s (atoms and ions) passage through potential barriers and the values of these barriers. The following points have been proposed: (1) generalized description of ionic conductivity of glass at a constant voltage and that of its mechanical losses, and (2) a novel equation quantitatively relating viscosity at a glass transition temperature, instantaneous shear modulus, and cooling rate of the melt. These results are proved by the experiments without introduction of any fitted constants and do not need any structural constraints imposed on the material. A new equation was obtained making it possible to calculate the sizes of atoms involved in individual viscous flow events, which is also valid without fitted constants, but only for inorganic substances with a spatial network of chemical bonds. It was shown that Maxwell’s equations and relations obtained using them are prospective for the creation of a unified theory of transport and the relaxation properties of glass and melts.


Maxwell’s equations moduli of elasticity viscosity internal friction ionic conductivity glass transition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Maxwell, J.C., On the dynamical theory of gases, Philos. Trans., 1867, vol. 157, pp. 49–88.CrossRefGoogle Scholar
  2. 2.
    Vinogradov, G.V. and Malkin, A.Ya., Reologiya polimerov (Rheology of Polymers), Moscow: Khimiya, 1977.Google Scholar
  3. 3.
    Nemilov, S.V., Interrelation between shear modulus and the molecular parameters of viscous flow for glass forming liquids, J. Non-Cryst. Solids, 2006, vol. 352, nos. 26–27, pp. 2715–2725.CrossRefGoogle Scholar
  4. 4.
    Maxwell, J.C., A Treatise on Electricity and Magnetism, Oxford: Clarendon, 1891, vol. 1, 3d ed.Google Scholar
  5. 5.
    Stratton, J.A., Electromagnetic Theory, New York: McGraw-Hill, 1941.Google Scholar
  6. 6.
    Nemilov, S.V., The review of possible interrelations between ionic conductivity, internal friction, and the viscosity of glasses and glass forming melts within the framework of Maxwell equations, J. Non-Cryst. Solids, 2011, vol. 357, no. 4, pp. 1243–1263.CrossRefGoogle Scholar
  7. 7.
    Nemilov, S.V., Maxwell equation for conductivity of dielectrics as the basis of direct relationship of ionic electrical conductivity and mechanical losses in glasses: New problems of physical chemistry of glass, Glass Phys. Chem., 2012, vol. 38, no. 1, pp. 27–40.CrossRefGoogle Scholar
  8. 8.
    Zdaniewsky, W.A., Rindone, G.E., and Day, D.E., The internal friction of glasses, J. Mater. Sci., 1979, vol. 14, pp. 763–775.Google Scholar
  9. 9.
    Andreev, I.V., Balashov, Yu.S., and Ivanov, N.V., High-temperature internal friction of some stabilized oxide glasses, Fiz. Khim. Stekla, 1981, vol. 7, no. 3, pp. 371–374.Google Scholar
  10. 10.
    Nemilov, S.V., Ageing kinetics and internal friction of oxide glasses, Glass Sci. Technol., 2005, vol. 78, no. 6, pp. 269–278.Google Scholar
  11. 11.
    Nemilov, S.V., Structural relaxation in oxide glasses at room temperature, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol., Part B, 2007, vol. 48, no. 4, pp. 291–295.Google Scholar
  12. 12.
    Nemilov, S.V., Relaxation processes in inorganic melts and glasses: An elastic continuum model as a promising basis for the description of the viscosity and electrical conductivity, Glass Phys. Chem., 2010, vol. 36, no. 3, pp. 253–285.CrossRefGoogle Scholar
  13. 13.
    MDL®SciGlass-7.8, Shrewsbury, Massachusetts, United States: Institute of Theoretical Chemistry, 2012.Google Scholar
  14. 14.
    Rötger, H., Elastische Nachwirkung durch Wärmediffusion (thermische Reibung) und Materiediffusion (eigentliche innere Reibung) bei periodischem und aperiodischem Vorgang, Glastech. Ber., 1941, no. 6, SS. 185–216.Google Scholar
  15. 15.
    Higgins, T.J., Macedo, P.B., and Volterra, V., Mechanical and ionic relaxation in Na2O · 3SiO2 glass, J. Am. Ceram. Soc., 1972, vol. 55, no. 10, pp. 488–491.CrossRefGoogle Scholar
  16. 16.
    Provenzano, V., Boesch, L.P., Volterra, V., Moynihan, C.T., and Macedo, P.B., Electrical relaxation in Na2O · 3SiO2 glass, J. Am. Ceram. Soc., 1972, vol. 55, no. 10, pp. 492–496.CrossRefGoogle Scholar
  17. 17.
    Knödler, D., Stiller, O., and Dietrich, W., Dynamic structure factor and acoustic attenuation in disordered solid electrolytes, Philos. Mag. B, 1995, vol. 71, no. 4, pp. 661–667.CrossRefGoogle Scholar
  18. 18.
    Roling, B., Happe, A., Ingram, M.D., and Funke, K., Interrelation between different mixed cation effects in the electrical conductivity and mechanical loss spectra of ion conducting glasses, J. Phys. Chem. B, 1999, vol. 103, no. 20, pp. 4122–4127.CrossRefGoogle Scholar
  19. 19.
    Vol’kenshtein, M.V. and Ptitsyn, O.B., The relaxation theory of glass transition, Dokl. Akad. Nauk SSSR, 1955, vol. 103, no. 5, pp. 795–798.Google Scholar
  20. 20.
    Vol’kenshtein, M.V. and Ptitsyn, O.B., The relaxation theory of glass transition: I. Solution of the basic equation and its investigation, Zh. Tekh. Fiz., 1956, vol. 26, no. 10, pp. 2204–2222.Google Scholar
  21. 21.
    Nemilov, S.V., Maxwell equation and classical theories of glass transition as a basis for direct calculation of viscosity at glass transition temperature, Glass Phys. Chem., 2013, vol. 39, no. 6, pp. 609–623.CrossRefGoogle Scholar
  22. 22.
    Leontovich, M.A., Comments to the theory of sound absorption in gases, Zh. Eksp. Teor. Fiz., 1936, vol. 6, no. 6, pp. 561–576.Google Scholar
  23. 23.
    Mandel’shtam, L.I. and Leontovich, M.A., On the theory of sound absorption in liquids, Zh. Eksp. Teor. Fiz., 1937, vol. 7, no. 3, pp. 438–449.Google Scholar
  24. 24.
    Nemilov, S.V., Interrelation between the velocity of sound propagation, mass, and energy of the chemical interaction, Dokl. Akad. Nauk SSSR, 1968, vol. 181, no. 6, pp. 1427–1429.Google Scholar
  25. 25.
    Nemilov, S.V., Kinetics of elementary processes in the condensed state: II. Shear relaxation and the equation of state of solids, Zh. Fiz. Khim., 1968, vol. 42, no. 6, pp. 1391–1396.Google Scholar
  26. 26.
    Dushman, S., Theory of unimolecular reaction velocities, J. Franklin Inst., 1920, vol. 189, no. 4, pp. 515–518.CrossRefGoogle Scholar
  27. 27.
    Polanyi, M. and Wigner, E., Über die Interferenz von Eigenschwingungen als Ursache von Energieschwankungen und chemischer Umsetzungen, Z. Phys. Chem., Abt. A, 1928, vol. 139A, SS. 439–452.Google Scholar
  28. 28.
    Hanggi, P., Talkner, P., and Borkovec, M., Reactionrate theory: Fifty years after Kramers, Rev. Mod. Phys., 1990, vol. 62, no. 2, pp. 251–341.CrossRefGoogle Scholar
  29. 29.
    Glasstone, S., Laidler, K.J., and Eyring, H., The Theory of Rate Processes: The Kinetics of Chemical Reactions, Viscosity, Diffusion, and Electrochemical Phenomena, New York: McGraw-Hill, 1941. Translated under the title Teoriya absolyutnykh skorostei reaktsii, Moscow: Inostrannaya Literatura, 1948.Google Scholar
  30. 30.
    Goodier, N.J., Slow viscous flow and elastic deformation, Philos. Mag., 1936, vol. 22, no. 22, pp. 678–681.Google Scholar
  31. 31.
    Einstein, A., Eine neue Bestimmung der Molekülardimensionen, Ann. Phys., 1906, vol. 19, no. 3, SS. 289–306.CrossRefGoogle Scholar
  32. 32.
    Myuller, R.L., The valence theory of viscosity and fluidity in the critical temperature region for high-melting glass-forming materials, Zh. Prikl. Khim. (St. Petersburg), 1955, vol. 28, no. 10, pp. 1077–1087.Google Scholar
  33. 33.
    Nemilov, S.V., Thermodynamic and Kinetic Aspects of the Vitreous State, Boca Raton, Florida, United States: CRC Press, 1995.Google Scholar
  34. 34.
    Dyre, J.C., The glass transition and elastic models of glass-forming liquids, Rev. Mod. Phys., 2006, vol. 78, pp. 953–972.CrossRefGoogle Scholar
  35. 35.
    Nemilov, S.V., Romanova, N.V., and Krylova, L.A., Kinetics of elementary processes in the condensed state: V. The volume of units activated in the viscous flow of silicate glasses, Zh. Fiz. Khim., 1969, vol. 43, no. 8, pp. 2131–2134.Google Scholar
  36. 36.
    Nemilov, S.V., Opticheskoe materialovedenie: Fizicheskaya khimiya stekla (Optical Materials Science: Physical Chemistry of Glass), St. Petersburg: St. Petersburg National Research University of Information Technologies, Mechanics, and Optics, 2009.Google Scholar
  37. 37.
    Littleton, J.T., Critical temperatures in silicate glasses, Ind. Eng. Chem., 1933, vol. 25, no. 7, pp. 748755.CrossRefGoogle Scholar
  38. 38.
    Nemilov, S.V., Kinetics of elementary processes in the condensed state: VIII. Ionic conduction in glass as the process occurring in an elastic medium, Zh. Fiz. Khim., 1973, vol. 47, no. 6, pp. 1479–1485.Google Scholar
  39. 39.
    Anderson, O.L. and Stewart, D.A., Calculation of activation energy of ionic conductivity in silica glasses by classical methods, J. Am. Ceram. Soc., 1954, vol. 37, no. 12, pp. 573–580.CrossRefGoogle Scholar
  40. 40.
    Osipov, A.A. and Osipova, L.M., Structure of glasses and melts in the Na2O-B2O3 system from high-temperature Raman spectroscopic data: I. Influence of temperature on the local structure of glasses and melts, Glass Phys. Chem., 2009, vol. 35, no. 2, pp. 153–166.CrossRefGoogle Scholar
  41. 41.
    Vollmayer, K., Kob, W., and Binder, K., How do the properties of a glass depend on the cooling rate? A computer simulation study of a Lennard-Jones system, J. Chem. Phys., 1996, vol. 105, no. 11, pp. 4714–4728.CrossRefGoogle Scholar
  42. 42.
    Mauro, J.C., Allan, D.C., and Potuzak, M., Nonequilibrium viscosity of glass, Phys. Rev. B: Condens. Matter, 2009, vol. 80, no. 9, p. 094204 (18 pages).CrossRefGoogle Scholar
  43. 43.
    Nemilov, S.V., Structural aspect of possible interrelation between fragility (length) of glass forming melts and Poisson’s ratio of glasses, J. Non-Cryst. Solids, 2007, vol. 353, nos. 5254, pp. 46134632.Google Scholar
  44. 44.
    Trinastic, J.P., Hamdan, R., Wu, Y., Zhang, L., and Hai-Ping Chenga, Unified interatomic potential and energy barrier distributions for amorphous oxides, J. Chem. Phys., 2013, vol. 139, no. 15, p. 154506.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.ITMO UniversitySt. PetersburgRussia

Personalised recommendations