Physics of colloidal dispersions in nematic liquid crystals

1 What is a liquid crystal 2 1.1 Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Cholesterics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Columnar phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Lyotropic liquid crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Introduction to Liquid Crystals

Flattening the Earth, Two Thousand Years of Map Projections

Introduction to liquid crystals

Surface-attached bacterial biofilms are self-replicating active liquid crystals and the dominant form of bacterial life on earth (1-4). In conventional liquid crystals and solid-state materials, the interaction potentials between the molecules that comprise the system determine the material properties. However, for growth-active biofilms it is unclear whether potential-based descriptions can account for the experimentally observed morphologies, and which potentials would be relevant. Here, we overcame previous limitations of single-cell imaging techniques (5,6) to reconstruct and track all individual cells inside growing three-dimensional (3D) biofilms with up to 10,000 individuals. Based on these data, we identify, constrain, and provide a microscopic basis for an effective cell-cell interaction potential, which captures and predicts the growth dynamics, emergent architecture, and local liquid crystalline order of Vibrio cholerae biofilms. Furthermore, we show how external fluid flows control the microscopic structure and 3D morphology of biofilms. Our analysis implies that local cellular order and global biofilm architecture in these active bacterial communities can arise from mechanical cell-cell interactions, which cells can modulate by regulating the production of particular matrix components. These results establish an experimentally validated foundation for improved continuum theories of active matter and thereby contribute to solving the important problem of controlling biofilm growth.

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Emergence of three-dimensional order and structure in growing biofilms.

The core structure of nematic defects cannot be represented by the usual director field, but requires the description by the full orial calculus.

Alignment tensor versus director: Description of defects in nematic liquid crystals.

Using two order tensors, we propose a mean-field model to describe the uniaxial and biaxial phases of nematogenic molecules presenting a shape dispersion of their biaxial dielectric susceptibility. We recover the classical isotropic-uniaxial-biaxial sequence of phases. The phase diagram exhibits a tricritical point, a feature that cannot be retraced in the other mean-field models established for molecules without shape dispersion.

Dielectric shape dispersion and biaxial transitions in nematic liquid crystals.

From a variational principle, we derive the equations of motion for nematic liquid crystals described by a second-rank order tensor. The only constitutive ingredients are the densities of the free energy and the dissipation, both subject to appropriate invariance requirements. We show that this theory is sufficiently general to encompass others as special cases. Comparing this theory with other theories also suggests criteria to avoid the proliferation of viscosity coefficients

Continuum theory for nematic liquid crystals with tensorial order

This is a book on the dissipative dynamics of ordered fluids, with a particular focus on liquid crystals It covers a whole range of different theories, mainly concerned with nematic liquid crystals in both their chiral and nonchiral variants The authors begin by giving a detailed account of the molecular origins of orientational order in fluids

Dissipative Ordered Fluids: Theories for Liquid Crystals

We study a class of quadratic Hamiltonians which describe both fully attractive and partly repulsive molecular interactions, characteristic of biaxial liquid crystal molecules. To treat the partly repulsive interactions we establish a minimax principle for the associated mean-field free energy. We show that the phase diagram described by Sonnet et al. [Phys. Rev. E 67, 061701 (2003)] is universal. Our predictions are in good agreement with the recent observations on both V-shaped and tetrapodal molecules.

André M. Sonnet

Papers

Alignment tensor versus director: Description of defects in nematic liquid crystals.

Dielectric shape dispersion and biaxial transitions in nematic liquid crystals.

Continuum theory for nematic liquid crystals with tensorial order

Dissipative Ordered Fluids: Theories for Liquid Crystals

Universal mean-field phase diagram for biaxial nematics obtained from a minimax principle.