### 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 language | English |
---|---|

Article number | 051704 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 72 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 2005 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*72*(5), [051704]. https://doi.org/10.1103/PhysRevE.72.051704

**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.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 72, no. 5, 051704. https://doi.org/10.1103/PhysRevE.72.051704

}

TY - JOUR

T1 - Nematic-nematic phase separation in binary mixtures of thick and thin hard rods

T2 - Results from Onsager-like theories

AU - Varga, S.

AU - Purdy, Kirstin

AU - Galindo, Amparo

AU - Fraden, Seth

AU - Jackson, George

PY - 2005/11

Y1 - 2005/11

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevE.72.051704

DO - 10.1103/PhysRevE.72.051704

M3 - Article

VL - 72

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5

M1 - 051704

ER -