Nematic-nematic phase separation in binary mixtures of thick and thin hard rods: results from Onsager-like theories.

The fundamental nature of the nematic-nematic phase separation in binary mixtures of rigid hard rods is analyzed within the Onsager second-virial theory and the extension of Parsons and Lee which includes a treatment of the higher-body contributions. The particles of each component are modeled as hard spherocylinders of different diameter , but equal length . In the case of a system which is restricted to be fully aligned (parallel rods), we provide an analytical solution for the spinodal boundary for the limit of stability of demixing; only a single region of coexistence bounded at lower pressures (densities) by a critical point is possible for such a system. The full numerical solution with the Parsons-Lee extension also indicates that, depending on the length of the particles, there is a range of values of the diameter ratio where the phase coexistence is closed off by a critical point at lower pressure. A second region of coexistence can be found at even lower pressures for certain values of the parameters; this region is bounded by an "upper" critical point. The two coexistence regions can also merge to give a single region of coexistence extending to very high pressure without a critical point. By including the higher-order contributions to the excluded volume (end effects) in the Onsager theory, we prove analytically that the existence of the lower critical point is a direct consequence of the finite size of the particles. A new analytical equation of state is derived for the nematic phase using the Gaussian approximation. In the case of Onsager limit (infinite aspect ratio), we show that the phase behavior obtained using the Parsons-Lee approach substantially deviates from that with the Onsager theory for the transition due to the nonvanishing third and higher order virial coefficients. We also provide a detailed discussion of the phase behavior of recent experimental results for mixtures of thin and thick rods of the same length, for which the Onsager and Parsons-Lee theories can provide a qualitative description.