On the orientational distribution functions in de Vries-type smectic liquid crystals

In de Vries smectic liquid crystals, the transition from the orthogonal smectic A (SmA) to the tilted smectic C (SmC) phase occurs with essentially no decrease in smectic layer thickness. This unusual behaviour is commonly explained assuming a \u27hollow-cone\u27 or \u27volcano-like\u27 orientational distribution function (ODF) of rod-like molecules in SmA and the transition to SmC being a pure disorder-order transition in the molecular tilt directions. However, even after 20 years of extensive investigations, the experimental confirmation of this ad hoc model is still inconclusive. While optical and electro-optic studies of many de Vries smectics can be readily explained with the hollow-cone model, X-ray diffraction (XRD) studies as well as many polarised Raman spectroscopy (PRS) studies support a broad Maier-Saupe distribution of a sugarloaf-like shape. We review and summarise X-ray, electro-optic and PRS results on the ODFs in the SmA phases of materials claimed to be of the de Vries type and discuss how seemingly contradicting findings can be true at the same time. In molecules where the core is far from collinear with the long molecular axis, the cores may exhibit a volcano ODF while the molecular axes exhibit a sugarloaf ODF