Polar liquid crystals in two spatial dimensions: the bridge from microscopic to macroscopic modeling

Abstract

Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions. Starting from microscopic density functional theory, we derive a phase-field-crystal expression for the free-energy density which involves three local order-parameter fields, namely the translational density, the polarization, and the nematic order parameter. Various coupling terms between the order-parameter fields are obtained which are in line with macroscopic considerations. Since the coupling constants are brought into connection with the molecular correlations, we establish a bridge from microscopic to macroscopic modeling. Our theory provides a starting point for further numerical calculations of the stability of polar liquid-crystalline phases and is also relevant for modeling of microswimmers which are intrinsically polar.

11 pages

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Cited by in corpus (22)

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• Tuned, driven, and active soft matter
• Classical dynamical density functional theory: from fundamentals to applications
• Traveling and resting crystals in active systems
• Nonequilibrium dynamics of mixtures of active and passive colloidal particles
• Active crystals and their stability
• Active crystals on a sphere
• Dynamical Crystallites of Active Chiral Particles
• Extended dynamical density functional theory for colloidal mixtures with temperature gradients
• Collective dynamics of active Brownian particles in three spatial dimensions: a predictive field theory
• Microscopic and macroscopic theories for the dynamics of polar liquid crystals
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Relations between angular and Cartesian orientational expansions
• Scale coupling and interface pinning effects in the phase-field-crystal model
• Orientational order parameters for arbitrary quantum systems
• Microscopic approach to entropy production
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Structure and dynamics of interfaces between two coexisting liquid crystalline phases
• Liquid crystalline growth within a phase-field crystal model
• Dynamical field theories for biaxial liquid crystals
• Phase Field Crystal model for particles with n-fold rotational symmetry in two dimensions