Optical anisotropies of alkylcyanobicyclohexyls and related compounds

Abstract

Mean-square optical anisotropies, γ², of cyanocyclohexane, bicyclohexyl, and the trans-4-cyano-trans-4′-n-alkylbicyclohexyls, NC—C₆H₁₀—C₆H₁₀—C_mH_2m+1, with m= 2, 5 and 7, have been determined from depolarized Rayleigh light-scattering measurements conducted on dilute solutions in carbon tetrachloride. The results are treated on the basis of additive contributions of group anisotropies: Γ_CC=Δα_CC– 2Δα_CH and Γ_CCN=Δα_CCN–Δα_CH, where the Δα denote the anisotropies of the polarizabilities of the indicated bonds. Diverse conformations of the bicyclohexyl system are taken into account. The value Γ′_CC= 0.68 ų required for bonds comprising this group appreciably exceeds the value of Γ_CC= 0.53 Å for the n-alkanes and presumably for the alkyl chains. Similarly, Γ_CCN= 3.3 ų is required for the cyano group attached to bicyclohexyl, compared with 2.15 ų for the same group in acyclic nitriles and in cyanocyclohexane. These differences appear to be due to inductive effects that are known to impair a simple additive scheme. Contributions of members of the alkyl chain beyond the first to the tensor â representing the anisotropy of the polarizability virtually vanish when averaged over the configuration of the chain. Hence, properties such as the electric birefringence should be independent of the length of the alkyl chain under conditions that allow the latter to be in a random configuration. The quadratic tensor invariant, γ²=Tr(ââ), should increase gradually with chain length. The relatively large alternating effects in the values of γ² for odd and even values of m are explained by the persistence of correlations in the directions of successive bonds of the alkyl chain. The effect of a departure of the principal axis of the polarizability tensor from the major geometric axis of the molecule is illustrated and its relevance to the anisotropic dispersion forces operative in liquid crystals is pointed out. The orientation-dependent energy attributable to the anisotropy of the polarizability is much smaller than would be required by the observed nematic–isotropic transition temperatures. This suggests that the large dipole moment of the molecules may be responsible for the nematic stability of the cyanobicyclohexyls.