Microscopic and macroscopic theories for the dynamics of polar liquid crystals

Abstract

We derive and analyze the dynamic equations for polar liquid crystals in two spatial dimensions in the framework of classical dynamical density functional theory (DDFT). Translational density variations, polarization, and quadrupolar order are used as order-parameter fields. The results are critically compared with those obtained using the macroscopic approach of time-dependent Ginzburg-Landau (GL) equations for the analogous order-parameter fields. We demonstrate that for both the microscopic DDFT and the macroscopic GL approach the resulting dissipative dynamics can be derived from a dissipation function. We obtain microscopic expressions for all diagonal contributions and for many of the cross-coupling terms emerging from a GL approach. Thus we establish a bridge between molecular correlations and macroscopic modeling for the dissipative dynamics of polar liquid crystals.

10 pages

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• 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
• Jerky active matter: a phase field crystal model with translational and orientational memory
• Relations between angular and Cartesian orientational expansions
• 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
• Dynamical density functional theory for the diffusion of injected Brownian particles
• Nucleation and shape dynamics of model nematic tactoids around adhesive colloids
• Liquid crystalline growth within a phase-field crystal model
• Dynamical field theories for biaxial liquid crystals