The effect of compression on the Frank constants of two nematic liquid crystals

Abstract

Along lines in the phase diagram of a nematic liquid crystal on which its order parameter (i.e. the degree of alignment of its molecules) is constant, the Frank stiffness constants are expected to increase with pressure. We have sought evidence for this by studying, using an orthodox optical method, a magnetic Fréedericksz transition in thin films of two alkyl cyanobiphenyl compounds inside pressure vessels; our measurements on 5CB extended to 2kbar and on 6CB to 0.5 kbar. To analyse our data we need to know, though not with great precision, the ordinary refractive index of the nematic, n ₀, for each pressure and temperature. We therefore made supplementary measurements of refractive index on 5CB and 6CB (and incidentally on 7CB and 8CB as well) at pressures up to 2.5 kbar. Given n ₀ we can deduce the extraordinary refractive index n _e from our observations on the Fréedericksz transition. Hence we can deduce values for the quantity σ(= 3(n _e ² - n ₀ ²)/(n _e ² + 2n₀ ² - 3)), which we take to be proportional to the order parameter. As for the anisotropy in the magnetic susceptibility, which is also involved in the analysis, we make the assumption that along lines in the phase diagram for which S is constant the anisotropy per unit mass, Δχ^(m), is constant too, despite the biaxiality effects which are known to prevent Δχ^(m)/σ from being quite independent of temperature at atmospheric pressure. Our results suggest that for 5CB the effect of compression on both the bend constant, K ₃, and the splay constant, K ₁, is about half as great as would be predicted by Maier-Saupe theory in its simplest form. Alternative theories which could be used to explain the difference are outlined in the final section, but we have no explanation for what we observe for 6CB, where the effect of compression seems to be significantly smaller still—too small, indeed, to be detected.