Paranematic-to-nematic ordering of a binary mixture of rod-like liquid crystals confined in cylindrical nanochannels

We explore the optical birefringence of the nematic binary mixtures 6CB${}_{1-x}$7CB${}_x$ ($0\le x\le 1$) imbibed into parallel-aligned nanochannels of mesoporous alumina and silica membranes for channel radii of $3.4~\le~R~\le 21.0$ nm. The results are compared with the bulk behavior and analyzed with a Landau-de-Gennes model. Depending on the channel radius the nematic ordering in the cylindrical nanochannels evolves either discontinuously (subcritical regime, nematic ordering field $\sigma <1\mathrm{/}2$) or continuously (overcritical regime, $\sigma >1\mathrm{/}2$), but in both cases with a characteristic paranematic precursor behavior. The strength of the ordering field, imposed by the channel walls, and the magnitude of quenched disorder varies linearly with the mole fraction $x$ and scales inversely proportionally with $R$ for channel radii larger than 4 nm. The critical pore radius, $R_c$, separating a continuous from a discontinuous paranematic-to-nematic evolution, varies linearly with $x$ and differs negligibly between the silica and alumina membranes. We find no hints of preferred adsorption of one species at the channels walls. By contrast, a linear variation of the nematic-to-paranematic transition point $T_{\mathrm{P}\mathrm{N}}$ and of the nematic ordering field $\sigma$ vs. $x$ suggest that the binary mixtures of cyanobiphenyls 6CB and 7CB keep their homogeneous bulk stoichiometry also in nanoconfinement, at least for channel diameters larger than $\sim$7 nm.