Abstract
It is shown for liquid crystals of various chemical classes that the nematic-isotropic transition temperatures in homologous series of compounds undergoing enantiotropic transitions are described by secondorder inhomogeneous recurrent equations with constant coefficients: T(n + 2) = aT(n + 1) + bT(n) + c (n is the number of alkyl carbon atoms). Solutions of the corresponding differential equations as T(n) functions allow reproduction of the even-odd alternation of the clearing temperatures.
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Gray, G.W., Molecular Physics of Liquid Crystals, Luckhurst, G.R. and Gray, G.W., Eds., New York: Academic, 1979, ch. 1, p. 1.
Demus, D.J, Handbook of Liquid Crystals, Demus, D.J., Goodby, W., Gray, G.W., Spiess, H.-W., and Vill, V., London: Wiley, 1998, ch. VI, p. 133.
Grebenkin, M.F. and Ivashchenko, A.V., Zhidkokristallicheskie materialy (Liquid Crystalline Materials), Moscow: Khimiya, 1989.
Aver’yanov, E.M., Stericheskie effekty zamestitelei i mezomorfizm (Steric Effects of Substituents and Mesomorphism), Novosibirsk: Sib. Otd. Ross. Akad. Nauk, 2004.
de Jeu, W.H., Physical Properties of Liquid Crystalline Materials, New York: Gordon and Breach, 1980.
Chandrasekhar, S., Liquid Crystals, Cambridge: Cambridge Univ. Press, 1977, 2nd ed.
Demus, D., Demus, H., and Zaschke, H., Flussige Kristalle in Tabellen, Leipzig: Grundstoffindustrie, 1974, vols. I, II.
Bazarov, I.P. and Gevorkyan, E.V., Statisticheskaya fizika zhidkih kristallov (Statistical Physics of Liquid Crystals), Moscow: Mosk. Gos. Univ., 1992.
Knaak, L.E., Rosenberg, H.M., and Serve, M.P., Mol. Cryst. Liq. Cryst., 1972, vol. 17, no. 1, p. 171.
Thiemann, T. and Vill, V., Liq. Cryst., 1997, vol. 22, no. 4, p. 519.
Aver’yanov, E.M., Russ. J. Phys. Chem., 2006, vol. 80, no. 1, p. S123.
Pustyl’nik, E.I., Statisticheskie metody analiza i obrabotki nablyudenii (Statistical Methods of Analysis and Treatment of Observables), Moscow: Nauka, 1968.
Draper, N. R. and Smith, H., Applied Regression Analysis, New York: Wiley, 1966, 1st ed.
Zenkevich, I.G., Zh. Fiz. Khim., 2006, vol. 80, no. 10, p. 1841.
Zenkevich, I.G., Zh. Fiz. Khim., 2007, vol. 48, no. 6, p. 1072.
Zenkevich, I.G., Zh. Fiz. Khim., 2006, vol. 76, no. 11, p. 1816.
Marinichev, A.N. and Sokolova, E.P., Zhidkie kristally i ikh prakt. ispol’z., 2007, no. 1(19), p. 84.
Marple, S.L., Jr., Digital Spectral Analysis and Its Applications, Englewood Cliffs: Prentice Hall, 1987.
Arnold, H., Z. Phys. Chem. (Leipzig), 1964, vol. 226, p. 146.
Oweimreen, G.A. and Morsy, M.A., Thermochim. Acta, 2000, vol. 346, no. 1, p. 37.
Gray, G.W. and Mosley, A., J. Chem. Soc., Perkin. Trans. 2, 1976, p. 97.
Nagamine, T., Januszko, A., Ohta, K., Kaszynski, P., and Endo, Y., Liq. Cryst., 2005, vol. 32, no. 8, p. 985.
Emsley, J.W., Luckhurst, G.R., and Shilstone, G.N., Mol. Phys., 1984, vol. 53, no. 4, p. 1023.
Mironovskii, L.A., Modelirovanie raznostnyh uravnenii (Modeling Differential Equations), St. Petersburg: S.-Peterb. Gos. Univ. Aviats. Priborostr., 2004.
Emsley, J.W., Luckhurst, G.R., and Stockley, C.P., Proc. Roy. Soc. London, Ser. A, 1982, vol. 381, p. 117.
Vertogen, G. and de Jeu, W.H., Thermotropic Liquid Crystals, Fundamentals, Berlin: Springer, 1988.
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Original Russian Text © E.P. Sokolova, A.N. Marinichev, 2009, published in Zhurnal Obshchei Khimii, 2009, Vol. 79, No. 1, pp. 18–25.
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Sokolova, E.P., Marinichev, A.N. Description of the even-odd alternation of the clearing temperatures over homologous series of mesogens by second-order differential equations. Russ J Gen Chem 79, 16–23 (2009). https://doi.org/10.1134/S1070363209010034
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DOI: https://doi.org/10.1134/S1070363209010034