On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Modifications to the traditional Onsager theory for modeling isotropic-nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee-Parsons resummation term. The Lee-Parsons resummation term uses the Carnahan-Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager's original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee-Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state.

Automated summary

Modifications to the traditional Onsager theory for modeling isotropic-nematic phase transitions in hard prolate spheroidal systems were presented, involving updates to the Lee-Parsons resummation term for more accurate calculation of excluded volumes. These modifications lead to a better match between theoretical and simulation results by dividing the excluded volume by six instead of eight in the original Lee-Parsons resummation term. These modifications were also applied to binary mixtures of hard prolate spheroids using the BMCSL equation of state.