Understanding the dependence of the transitional properties of liquid crystal dimers on their molecular geometry

The characteristic feature of liquid crystal dimers, in which two mesogenic groups are linked by a flexible spacer, is often thought to be the strong odd-even effect exhibited by their transitional properties. That is, the nematic-isotropic transition temperature and the entropy of transition are large for dimers with an even number of groups in the spacer in comparison with those for neighbouring dimers with an odd number of groups. However, the magnitude of the odd-even effect along a homologous series of dimers is found to depend strongly on the nature of the link between the mesogenic group and the spacer. This dependence is thought to originate in the variation of the molecular geometry with the linking group, a view which is supported by detailed molecular held theory calculations involving all of the conformational states. Here we are concerned with developing a more transparent understanding of this geometrical effect using a simple model of the dimers in which all of the conformational states are replaced by just two, a linear and a bent conformer. The model has been found to exhibit a strong odd-even effect as well as a nematic-nematic transition when the bond angle is tetrahedral. We have used this model to explore the dependence of the transitional properties of liquid crystal dimers on their geometry by varying the bond angle of the bent conformer. The behaviour predicted by the model for the nematic-isotropic transition is found to be in qualitative agreement with experiment. In addition, the nematic-nematic transition is observed to exhibit a critical behaviour as the bond angle is increased. At the other extreme, when the bond angle is reduced to its limiting value of 90 degrees there is a very strong first order transition between a discotic and a calamitic nematic.