ScienceAsia 33 (2007): 321-327 |doi: 10.2306/scienceasia1513-1874.2007.33.321

A New Approach to the Mean Field Theory for Nematic Liquid Crystals

Saman Mongkolsakulvong^a and I Ming Tang^b*

 
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 NLC’s 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.

KEYWORDS: Nematic liquid crystal/mean-field theory, order parameter, cumulant expansion, p,p′-di-nalkoxyazobenzene.

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^a Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand.
^b Department of Physics, Faculty of Science, Mahidol University, Bangkok, 10400 Thailand.

* Corresponding author, E-mail: scimt@mahidol.ac.th

Received 28 Apr 2006, Accepted 26 Mar 2007