The use of chebyshev polynomials orthogonal on a finite arbitrary system of points for interpolating changes in nematic-isotropic liquid phase transition temperatures in homologous series |
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Authors: | Averyanov E M |
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Institution: | 1.Kirenskii Institute of Physics, Siberian Division, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia ; |
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Abstract: | Chebyshev polynomials Ψ
q
(x) orthogonal on a finite arbitrary system of points x
i
(i = 1−N) are used to interpolate changes in nematic-isotropic liquid phase transition temperatures t
c(x) in homologous series of liquid crystals (x = 1/n, where n is the number of the homologue). The expansion of the t
c(x) function into a series in Ψ
q
(x) polynomials was found to be very effective. Already at q ≤ 3, this series describes the known types of the t
c(x) dependences with high accuracy and very small root-mean-square deviations for mesogenic molecules of various chemical structures and dimensions. The dependence of the limiting t
l
= t
c(0) value on the form of X-shaped molecules and linear dimensions of N-mers with N rigid aromatic fragments linked with each other by flexible spacer chains was studied. |
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Keywords: | |
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