Crossover Temperature To for Uniaxial Calamitic Nematic Mixture

Abstract
The crossover temperature То corresponds to the minimum point at the dependence n_o(T) of the ordinary refractive index for uniaxial liquid crystal. The temperature dependences of the extraordinary refractive index n_e(T) and the birefringence Δn(T) = n_e – n_o have no peculiarities at this point. For uniaxial nematic mesogen, the coefficients of the function Δn(T) = Δn₀(1 – Т/T₁)^β and the value ΔТ_о = T₁ – Т_о are of practical interest. The use of nematic mixtures makes it possible to vary these parameters in order to optimize operating characteristics of material. This work is devoted to determining the parameters ΔТ_о and β for calamitic nematic mixture consisting of different calamitic nematics of sort α with known parameters {p_α} = {ΔT_{o_α}, β_α; , B₁^(α)}, where B₁^(α)= d_α/dT, _α = (n_e + 2n_o)_α/3. The values ΔT_o and β are shown to depend on the volume fractions φ_α of the mixed components and parameters {p_α}. The equation for determining ΔT_o was derived and its solutions were found for three binary nematic mixtures with different sets {{p_α}. Nonlinear dependences ΔT_o(φ_α) and β(φ_α) for these mixtures were studied.

Keywords: liquid crystalline mixtures, crossover temperature To