A new approach to the mean field theory for nematic liquid crystals

Abstract

We have developed a new method to calculate the properties of the nematic liquid crystals (NLC). The new method involves the separation of the NLC molecules into two groups; those on a chain embedded in the liquid crystal and the rest. The interactions between the nearest neighbor molecules on the chain are treated exactly while the interaction between a molecule on the string and remaining molecules is treated via a mean field approach. We have calculated the partition function to the order 0(/β3) for the molecules on the chain using the cumulant expansion. Using the standard conditions for a nematic-isotropic (NI) transition to occur, we obtain the values of the interaction energies needed to fit the published data on the NI transitions in the homologous series of NLCs p,p′-di-n-alkoxyazobenzene. We find that the values of the strength of the microscopic interaction between the molecules (J) exhibit an even-odd dependence on the number of (CH2) groups in the tails of the molecules in this series. The values of A (the strength of the mean field interaction) do not exhibit an even-odd effect.