Entropy of different phases formed by soft rods

TL;DR

This paper extends the two-phase thermodynamic model to anisotropic soft rods, enabling the calculation of entropy in various liquid crystal phases and determining phase boundaries based on entropy contributions.

Contribution

The work introduces a novel application of the 2PT method to shape anisotropic soft rods, providing a detailed decomposition of entropy into translational and rotational components across different LC phases.

Findings

Entropy values match ideal rigid rotor in dilute limit.

Total entropy magnitude is similar across different LC phases at same packing fraction.

Computed phase boundaries using fluidicity factors align with known phase behavior.

Abstract

Computation of entropy in liquids and liquid crystal phases is a big challenge in statistical physics. In this work, we extend the two-phase thermodynamic model (2PT) to shape anisotropic soft repulsive spherocylinders (SRSs) and report the absolute values of entropy for different liquid crystal (LC) phases for a range of aspect ratios L/D = 2-5. We calculate the density of states (DoS) for different LC phases and decompose it into contributions arising from translational and rotational degrees of freedom. The translational and rotational modes are further partitioned into diffusive, gas-like, and non-diffusive, solid-like components using a fluidicity factor. In the dilute limit, the entropy values obtained from the 2PT method match exactly those of an ideal rigid rotor. We find that, for a given packing fraction, the magnitude of the total entropy is roughly equal regardless of the different LC phases associated with different aspect ratios. We also compute the excess entropy (for L/D = 5) and compare those with the values obtained using the standard integration approach of molecular dynamics (MD) or Monte Carlo (MC) equation of state (EOS) of SRS. The values obtained using both approaches match very well. The rotational and translational fluidicity factors are further used to determine the phase boundaries of different liquid crystal phases for the respective aspect ratios.