Nematic-isotropic interface of some members of the homologous series of 4-cyano-4′-($n$-alkyl)biphenyl liquid crystals

The properties of the nematic-isotropic interface of some members of the homologous series of 4-cyano-4′-($n$-alkyl)biphenyl liquid crystals [$n$-pentyl (5CB), $n$-hexyl (6CB), $n$-heptyl (7CB), and $n$-octyl (8CB)] are studied by optical reflectometry. The thickness of the interface is obtained by measuring the ratio of the actual reflected intensity to the value expected for a sharp interface. We find an effective thickness of order 400 Å in 5CB, 7CB, and 8CB, and of order 750 Å in 6CB. As shown by some authors, the effective thickness $L$ is related to the superposition of two different contributions: an intrinsic diffuse profile due to density and order-parameter variations across the interface and an apparent diffuse profile of the interface due to surface capillary waves. Both of these contributions are accounted by us in our theoretical analysis. The intrinsic thickness is obtained in a satisfactory agreement with the predictions of the Landau—de Gennes theory. The easy polar angle is obtained by measuring the intensity anisotropy for the reflected extraordinary and ordinary waves. In all these samples the director is found to be tilted with respect to the vertical axis with a tilt angle which ranges from 48.5° in 8CB to 64.5° in 6CB. The anchoring energy coefficient $W$ at the interface is obtained by applying an orienting torque by means of a horizontal magnetic field and by measuring the corresponding variation of the surface polar angle. We find $W$ ranges from 0.84 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$ ${\mathrm{rad}}^2$ in 6CB to 8.5 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$ ${\mathrm{rad}}^2$ in 8CB. The experimental results are discussed in terms of the Landau—de Gennes expansion of the free energy and of the Parsons theory of the surface tension. All the phenomenological coefficients of this latter theory are obtained for the first time.