Generalized Onsager theory of liquid crystals

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Computational Chemistry

Background:

• The Onsager theory provides a theoretical framework for understanding the phase behavior of anisotropic molecules.
• Traditional Onsager theory exhibits inaccuracies in predicting critical transition densities for small aspect ratio hard rods.
• Accurate prediction of transition densities is crucial for understanding and designing liquid crystalline materials.

Purpose of the Study:

• To generalize the two-dimensional Onsager theory by incorporating short-range order and higher-order virial coefficients.
• To improve the accuracy of theoretical predictions for the critical transition density of hard rod systems.
• To investigate the role of molecular shape and intermolecular interactions in liquid crystal phase transitions.

Main Methods:

• Molecular dynamics (MD) simulations were performed on "molecules" composed of linked hard disks.
• Simulations covered a range of aspect ratios (ℓ) from 5 to 13.
• The generalized Onsager theory, including up to the fourth-order virial coefficients and short-range order, was developed and compared with simulation data.

Main Results:

• The generalized Onsager theory demonstrated significantly improved predictions of transition densities compared to the traditional theory.
• Simulation results for transition densities showed good agreement with the predictions of the generalized theory.
• Evidence of an intermediate hexagonal phase was observed in MD simulations for molecules with aspect ratios ℓ≤8, preceding solidification.

Conclusions:

• Incorporating short-range order and higher-order virial coefficients substantially enhances the accuracy of Onsager theory for small aspect ratio hard rods.
• Short-range order is particularly important for molecules with aspect ratios ℓ≤10, relevant to common thermotropic liquid crystals.
• The study reveals the existence of a distinct hexagonal phase in hard rod systems at intermediate densities, offering new insights into their phase diagrams.