Thermodynamic analysis of the low frequency relaxation time in the smectic A and C phases of a liquid crystal

Pressure-temperature-volume (pVT) measurements were carried out on 2-(4-hexyloxyphenyl)-5-octyl-pyrimidine, a substance exhibiting nematic and smectic A and C polymorphism. Analysis of the longitudinal relaxation times obtained recently for elevated pressures Czub et al., Z. Naturforsch. A: Phys. Sci. 58, 333 (2003)] was performed for isobaric, isothermal, and isochoric conditions within the two smectic phases. Several relationships linking the dynamical and thermodynamical quantities, derived recently for isotropic glass formers Roland et al. Rep. Prog. Phys. 68, 1405 (2005)], were found to hold for the liquid crystal, revealing a striking similarity of behaviors for these two types of materials. The parameter gamma characterizing the steepness of the interaction potential was derived in different ways. It is interesting that the liquid crystal gives relaxation time versus TV(-gamma) plots that are linear, unlike results for glass formers, implying that the dynamics of the former is thermally activated.