Abstract
Half-quantum interpretation is proposed for the liquid-glass transition as the freezing of characteristic acoustic frequencies (degrees of freedom) that are related to the molecular mobility of delocalized excited kinetic units, namely, linear quantum oscillators. There exists a correlation between the energy quantum of an elementary excitation (atom delocalization energy) and the glass transition temperature, which is proportional to the characteristic Einstein temperature. By analogy with the Einstein theory of the heat capacity of solids, the temperature range of the concentration of excited atoms in an amorphous medium is divided into the following two regions: a high-temperature region with a linear temperature dependence of this concentration and a low-temperature region, where the concentration of excited atoms decreases exponentially to the limiting minimum value (about 3%). At this value, the viscosity increases to a critical value (about 1012 Pa s), which corresponds to the glass transition temperature, i.e., the temperature of freezing the mobility of excited kinetic units. The temperature dependence of the free activation energy of viscous flow in the glass transition range is specified by the temperature dependence of the relative number of excited atoms.
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References
M. I. Ojovan, Adv. Condens. Matter Phys. 2008, Article ID 817829 (2008).
Al. Al. Berlin, L. Rotenburg, and R. Baserst, Vysokomol. Soedin., Ser. A 35, 857 (1993).
D. S. Sanditov and G. M. Bartenev, Physical Properties of Disordered Structures (Nauka, Novosibirsk, 1982) [in Russian].
V. G. Rostiashvili, V. I. Irzhak, and B. A. Rozenberg, Vitrification of Polymers (Khimiya, Leningrad, 1987) [in Russian].
W. Götze, in Liquids, Freezing, and Glass Transition, Ed. by J. P. Hansen, D. Levesque, and J. Zinn-Justin (North-Holland, Amsterdam, The Netherlands, 1991; Nauka, Moscow, 1992).
J. H. Gibbs and E. A. Di Marzio, J. Chem. Phys. 28, 373 (1958).
M. I. Ozhovan, Zh. Éksp. Teor. Fiz. 130(5), 944 (2006) [JETP 103 (5), 819 (2006)].
H. Tanaka, J. Non-Cryst. Solids 351, 3371 (2005).
A. Yu. Pryadil’shchikov, A. T. Kosilov, A. V. Evteev, and E. V. Levchenko, Zh. Éksp. Teor. Fiz. 132(6), 1352 (2007) [JETP 105 (6), 1184 (2007)].
C. A. Angel, K. L. Ngai, G. B. Mckenna, P. E. McMillan, and S. W. Martin, J. Appl. Phys. 88, 3113 (2000).
K. L. Ngai and S. Capaccioli, J. Am. Ceram. Soc. 91, 709 (2008).
J. C. Dure, Rev. Mod. Phys. 78, 953 (2006).
J. Zarzycki, Glasses and the Vitreous State (Cambridge University Press, New York, 1982).
G. S. Grest and M. H. Cohen, Adv. Chem. Phys. 48, 455 (1981).
M. I. Klinger, Usp. Fiz. Nauk 152(4), 623 (1987) [Sov. Phys.—Usp. 30 (8), 699 (1987)].
I. V. Razumovskaya and G. M. Bartenev, in The Vitreous State: A Collection of Works (Nauka, Leningrad, 1971), p. 34 [in Russian].
D. S. Sanditov, Zh. Éksp. Teor. Fiz. 135(1), 108 (2009) [JETP 108 (1), 98 (2009)].
S. V. Nemilov, Fiz. Khim. Stekla 6, 257 (1980).
I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans and Green, London, 1954; Nauka, Novosibirsk, 1966).
S. V. Nemilov, Thermodynamic and Kinetic Aspects of the Vitreous State, (CRC Press, Boca Raton, Florida, United States, 1995).
S. V. Nemilov, Fiz. Khim. Stekla 4, 662 (1978).
R. L. Myuller, in The Vitreous State: A Collection of Works (Academy of Sciences of the Soviet Union, Moscow, 1960), p. 61 [in Russian].
R. L. Myuller, Zh. Prikl. Khim. (Leningrad) 28, 1077 (1955).
V. N. Filipovich, Fiz. Khim. Stekla 1, 256 (1975).
R. H. Doremus, Am. Ceram. Soc. Bull. 82, 59 (2003).
M. I. Ojovan, Pis’ma Zh. Éksp. Teor. Fiz. 79(2), 97 (2004) [JETP Lett. 79 (2), 85 (2004)].
D. S. Sanditov, Zh. Éksp. Teor. Fiz. 137(4), 767 (2010) [JETP 110 (4), 675 (2010)].
Ya. I. Frenkel’, in Proceedings of the Conference on Viscosity of Liquids and Colloidal Solutions, Institute of Mechanical Engineering, Moscow, Soviet Union, 1941 (Academy of Sciences of the Soviet Union, Moscow, 1944), Vol. 2, p. 24.
P. B. Macedo and T. A. Litovitz, J. Chem. Phys. 42, 245 (1965).
D. S. Sanditov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 2, 17 (1971).
SciGlass: Glass Property Database (Version 6.6) (Institute of Theoretical Chemistry, Shrewsbury, Massachusetts, United States, 2006).
D. S. Sanditov and A. A. Mashanov, Fiz. Khim. Stekla 36(1), 55 (2010) [Glass. Phys. Chem. 36 (1), 41 (2010)].
H. W. Leideeker, J. H. Simmons, T. A. Litovitz, and P. B. Macedo, J. Chem. Phys. 55, 2028 (1971).
D. S. Sanditov, Dokl. Akad. Nauk 390(1–3), 209 (2003) [Dokl. Phys. Chem. 390 (1–3), 122 (2003)].
J. D. Ferry, Viscoelastic Properties of Polymers (Inostrannaya Literatura, Moscow, 1963; Wiley, New York, 1980).
V. V. Tarasov, Problems of the Physics of Glass (Stro’izdat, Moscow, 1979) [in Russian].
S. C. Waterton, J. Soc. Glass Technol. 16, 244 (1932).
N. I. Shishkin, Zh. Tekh. Fiz. 26, 1461 (1956).
E. Jenckel, Z. Phys. Chem. 184, 309 (1939).
G. Meerlender, Rheol. Acta 6, 309 (1967).
F. Lindemann, Physica (Amsterdam) 7, 609 (1910).
B. D. Sanditov, M. V. Darmaev, D. S. Sanditov, and V. V. Mantatov, Deform. Razrushenie Mater. 4, 18 (2008).
V. N. Novikov and A. P. Sokolov, Nature (London) 431, 961 (2004).
D. S. Sanditov, A. A. Mashanov, B. D. Sanditov, and V. V. Mantatov, Fiz. Khim. Stekla 34(4), 512 (2008) [Glass Phys. Chem. 34 (4), 389 (2008)].
N. S. Andreev, N. A. Bokov, Fiz. Khim. Stekla 22(4), 407 (1996) [Glass Phys. Chem. 22 (4), 295 (1996)].
A. I. Olemskoĭ and A. V. Khomenko, Zh. Tekh. Fiz. 70(6), 10 (2000) [Tech. Phys. 45 (6), 672 (2000)].
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Original Russian Text © D.S. Sanditov, 2010, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2010, Vol. 138, No. 5, pp. 850–861.
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Sanditov, D.S. Liquid-glass transition as the freezing of characteristic acoustic frequencies. J. Exp. Theor. Phys. 111, 749–759 (2010). https://doi.org/10.1134/S1063776110110063
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DOI: https://doi.org/10.1134/S1063776110110063