Demixed and ordered phases in hard-rod mixtures

Abstract

We analyse demixing and ordering transitions in systems of hard cylindrical particles. The second virial approximation of Onsager and a bifurcation analysis, as introduced by Koda and Kimura, are used to evaluate the free energies, pressures, and density distribution functions in mixtures of equally long but differently wide cylinders. The spatial density distribution along the one relevant coordinate is of particular importance as it provides more detailed information concerning the nature of the phase transition than the bare bifurcation diagnosis. Detailed results are given for the nematic–nematic spinodal and the nematic–smectic transitions. Allowing for the absence of an isotropic phase, our results are in good qualitative agreement with those for freely orienting rods reported previously, and indicate a complex sequence of phase diagrams as the diameter dissimilarity of the two components is increased, with upper and lower critical points bounding nematic and smectic demixing regions. However, experimental results on colloidal rods show that nematic demixing occurs at a diameter ratio much smaller than ours or those for freely rotating fluids, indicating that Onsager-type theories may be insufficient to reproduce this phenomenon in a quantitative manner and, consequently, that more sophisticated approaches, presumably incorporating particle flexibility and additional interactions, are required.

Keywords:

• liquid crystals
• Onsager approximation
• smectic ordering
• demixing

Acknowledgements

SV, AG and FV would like to thank financial support from the Austrian–Hungarian Action Foundation (grant number 68öu1). Support from the Hungarian–Spanish (HH2006-2005) and Austrian–Spanish (HU2006-0006) Integrated Actions Programmes, and grants S-0505/ESP-0299 from the Comunidad Autónoma de Madrid, and FIS2005-05243-C02-01, FIS2005-05243-C02-02, and FIS2007-65869-C03-01 from the Ministerio de Educación y Ciencia of Spain, are also acknowledged.