Hidden scale invariance in the Gay-Berne model

Area of Science:

• * Computational physics and physical chemistry.
• * Statistical mechanics and condensed matter physics.

Background:

• * The Gay-Berne model describes rod-shaped molecules, crucial for understanding liquid crystal phases.
• * Hidden scale invariance and isomorph theory predict regions of similar physical behavior in thermodynamic phase diagrams.

Purpose of the Study:

• * To numerically investigate isomorphs in the isotropic and nematic phases of the calamitic Gay-Berne model.
• * To demonstrate the invariance of dynamics and structure along identified isomorphs.
• * To compare isomorph invariance with behavior along a similar isochore.

Main Methods:

• * Numerical simulations of the Gay-Berne liquid crystal model.
• * Analysis of virial and potential-energy thermal fluctuations.
• * Calculation of mean-square displacement and time-autocorrelation functions (velocity, angular velocity, force, torque, orientational order parameters).
• * Examination of radial distribution functions for molecular and orientational structure.

Main Results:

• * Strong correlations between virial and potential-energy fluctuations indicate hidden scale invariance.
• * Isomorphs were identified and studied in both isotropic and nematic phases.
• * Dynamics and structure showed good invariance along isomorphs, unlike along an isochore.
• * Short-time deviations in orientational correlations were linked to the assumption of constant moment of inertia.

Conclusions:

• * The thermodynamic phase diagram of the calamitic Gay-Berne model is effectively one-dimensional within the studied regions, supporting isomorph theory.
• * Isomorph theory offers potential simplifications for future theoretical and numerical studies of liquid crystals.
• * The findings highlight the utility of isomorph theory in understanding complex molecular systems.