Molecular theory of dendritic liquid crystals: self-organisation and phase transitions

We present tractable molecular theory descriptions of liquid crystalline dendrimers based on clearly defined approximations and in terms of the dominant interactions underlying the self-organisation of these large and complex supermolecular entities. We formulate the configurational partition function for dendrimers, taking explicit account of their conformations and segmental interactions. Two approximate schemes are presented: the first is based on the effective interactions of the dendrimers as a whole while the second scheme is based on the interactions among the mesogenic units contained in the dendrimers. Results of lattice calculations for phase transitions in the context of the first scheme are presented and they show that the minimal inclusion of shape anisotropy and of sub-molecular partitioning into chemically distinct parts is sufficient to reproduce the variety of phases and phase sequences observed experimentally and provides insights into the conformational aspect of these transitions. In the second scheme, the description of the dendromesogenic system reduces to that of an ensemble of mesogenic dimers. This scheme can be readily extended to the description liquid crystalline oligomers and polymers consisting of mesogenic units connected by flexible spacers in various architectures. It thus provides a unified approach for treating mesomorphic phase transitions of supermolecular and macromolecular systems that can be built by connecting the same submolecular units in topologically different ways.