Maier-Saupe model for a mixture of uniaxial and biaxial molecules

Abstract

We introduce shape fluctuations in a liquid-crystalline system by considering an elementary Maier--Saupe lattice model for a mixture of uniaxial and biaxial molecules. Shape variables are treated in the annealed (thermalized) limit. We analyze the thermodynamic properties of this system in terms of temperature $T$, concentration $c$ of intrinsically biaxial molecules, and a parameter $\Delta$ associated with the degree of biaxiality of the molecules. At the mean-field level, we use standard techniques of statistical mechanics to draw global phase diagrams, which are shown to display a rich structure, including uniaxial and biaxial nematic phases, a reentrant ordered region, and many distinct multicritical points. Also, we use the formalism to write an expansion of the free energy in order to make contact with the Landau--de Gennes theory of nematic phase transitions.

References in corpus (1)

• Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

Cited by in corpus (4)

• Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom
• Phase behavior of a lattice-gas model for biaxial nematics
• An Improvement for Quantum Tunneling Radiation of Fermions in a Stationary Kerr-Newman Black Hole Spacetime
• Exact equations of state for nematics