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arXiv · 1103.2154

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

Raphael Wittkowski·Hartmut Löwen·Helmut R. Brand
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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.

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Raphael Wittkowski, Hartmut Löwen, Helmut R. Brand. 2011-03-10. Polar liquid crystals in two spatial dimensions: the bridge from microscopic to macroscopic modeling. https://doi.org/10.1103/physreve.83.061706

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