Hard rigid rods on a Bethe-like lattice

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Materials science

Background:

• Excluded volume interactions are crucial in modeling dense systems of anisotropic particles.
• The Bethe approximation is a common mean-field technique for lattice models.
• Understanding phase transitions in systems of rigid rods is key to designing new materials.

Purpose of the Study:

• To investigate the validity of the Bethe approximation for systems of rigid rods with excluded volume interactions.
• To develop a lattice model that allows for dense packing of rods and exact solutions.
• To characterize the phase transitions of these rod systems on different lattice structures.

Main Methods:

• Analysis of self-consistent field equations for rigid rods.
• Construction of a novel "random locally treelike layered lattice".
• Investigation of isotropic-nematic phase transitions using the new lattice model.

Main Results:

• The Bethe approximation is shown to be inexact for this system on the Bethe lattice.
• The newly constructed lattice allows for dense rod packing and exact Bethe equation solutions.
• Continuous isotropic-nematic transitions occur for k-mers (k ≥ 4) on a four-coordinated lattice.
• Discontinuous transitions are observed for even coordination numbers q ≥ 6, but only for k ≥ k(min)(q).

Conclusions:

• The Bethe approximation's limitations are highlighted for dense anisotropic systems.
• The random locally treelike layered lattice provides an accurate model for dense rod packing.
• The nature of phase transitions in rod systems depends on lattice coordination and particle length.