Nematic-nematic phase separation in binary mixtures of thick and thin hard rods

Results from Onsager-like theories

S. Varga, Kirstin Purdy, Amparo Galindo, Seth Fraden, George Jackson

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

The fundamental nature of the nematic-nematic (N-N) 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 (D1 D2), but equal length (L1=L2=L). 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 N-N demixing; only a single region of N-N coexistence bounded at lower pressures (densities) by a N-N 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 (d=D2 D1) where the N-N phase coexistence is closed off by a critical point at lower pressure. A second region of N-N coexistence can be found at even lower pressures for certain values of the parameters; this region is bounded by an "upper" N-N critical point. The two N-N coexistence regions can also merge to give a single region of N-N 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 N-N 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 N-N phase behavior obtained using the Parsons-Lee approach substantially deviates from that with the Onsager theory for the N-N transition due to the nonvanishing third and higher order virial coefficients. We also provide a detailed discussion of the N-N 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.

Original languageEnglish
Article number051704
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume72
Issue number5
DOIs
Publication statusPublished - Nov 2005

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Binary Mixtures
Phase Separation
binary mixtures
critical point
rods
low pressure
virial coefficients
aspect ratio
equations of state
Critical point
Coexistence
approximation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Nematic-nematic phase separation in binary mixtures of thick and thin hard rods : Results from Onsager-like theories. / Varga, S.; Purdy, Kirstin; Galindo, Amparo; Fraden, Seth; Jackson, George.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 72, No. 5, 051704, 11.2005.

Research output: Contribution to journalArticle

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