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

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.