title: 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 that 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.
authors.affiliation: Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany.
authors.forename: Raphael
authors.initials: R
authors.lastname: Wittkowski
authors.forename: Hartmut
authors.initials: H
authors.lastname: Löwen
authors.forename: Helmut R
authors.initials: HR
authors.lastname: Brand