The mesogenic index: an empirical method for predicting polymeric liquid crystallinity

An empirical method for predicting the chemical compositions of random or partially ordered copolymers that exhibit mesophases was devised by the authors in 1989, while working on liquid crystal copolymer synthesis for BP Chemicals. A brief description of the method and its application to the chemical synthesis of amorphous thermotropic polyamides was given by the authors in a previous paper. Thermotropic polyimides were also synthesized by the authors as a result of the use of the predictive method. Subsequently, the method has been updated and applied to polycarbonates and polyimides. The new approach has been termed 'the mesogenic index' (MI) and has successfully been applied to 23 copolymer systems in which the critical compositions for mesophase formation have been established by means of varying constituent monomer concentrations. It is also consistent in predicting liquid crystalline behaviour in several hundred main-chain polymer systems containing amide, ester, carbonate, ether and urethane groups. It is inherent in the MI system that the mesogenic length is defined in terms of the number of monomer units for a given polymer class. From published work in the literature, it was first established that ester and amide groups need at least two and three aromatic rings in the mesogen respectively. Using these values to define mesogen length in polyester and polyamide copolymers, the condition MI > 10 has been determined for mesophase formation.. This rule has been applied to other linking groups, such as carbonate or imide, with the surprising result that the corresponding mesogen lengths for these condensation polymers are simple numbers. Moreover, the rule has been applied successfully to mixed systems, by simply averaging the contributions of the different groups to the mesogen length in strictly molar proportions. The mesogenic index is based upon summing functional group contributions towards rigidity and/or resonance stabilization of the mesogen. To the best of our knowledge, this is the first simple method to be published that successfully correlates chemical composition with mesophase formation.