The average shapes of flexible mesogenic molecules On the choice of reference frame

Abstract

The flexibility of most mesogenic molecules creates a problem when we wish to consider their shape, especially as the anisotropy in this is often invoked to explain liquid-crystalline behaviour. It has been suggested that images constructed from the average positions of atoms in the molecule with superimposed ellipsoids representing the mean square displacements of the atoms could present one solution to the problem. However, the nature of the image necessarily depends on the choice of the reference frame set in the molecule. Here we show how the images change as the atoms used to define the reference frame move along a single heptyl chain attached to a mesogenic core in both the isotropic and nematic phases. The appearance of the images and how they change with phase and reference frame are discussed in general terms. In addition, the possible relationship between the images and the order parameters for axes set in the same reference frame as that used to construct the image is explored. The significance of the fluctuational ellipsoids is also considered although they appear only to influence the order parameters at second order.