Field-driven dynamics of nematic microcapillaries

Polymer-dispersed liquid crystal (PDLC) composites have long been a focus of study for their unique electro-optical properties which have resulted in various applications such as switchable (transparent/translucent) windows. These composites are manufactured using desirable "bottom-up" techniques, such as phase separation of a liquid crystal/polymer mixture, which enable production of PDLC films at very large scales. LC domains within PDLCs are typically spheroidal, as opposed to rectangular for an LCD panel, and thus exhibit substantially different behaviour in the presence of an external field. The fundamental difference between spheroidal and rectangular nematic domains is that the former results in the presence of nanoscale orientational defects in LC order while the latter does not. Progress in the development and optimization of PDLC electro-optical properties has progressed at a relatively slow pace due to this increased complexity. In this work, continuum simulations are performed in order to capture the complex formation and electric field-driven switching dynamics of approximations of PDLC domains. Using a simplified elliptic cylinder (microcapillary) geometry as an approximation of spheroidal PDLC domains, the effects of geometry (aspect ratio), surface anchoring, and external field strength are studied through the use of the Landau--de Gennes model of the nematic LC phase.Comment: 22 pages, 9 figures, Physical Review

Pair creation, motion, and annihilation of topological defects in 2D nematics

We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the linearized static equations inside a uniformly aligned state. Topological charge conservation requires a fixed difference between the number of half charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair, or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced

Defect unbinding in active nematics

We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane that separates the quasi-long-range ordered (nematic) and disordered (isotropic) phases. Below a critical activity, defects remain bound as rotational noise decorrelates the directed dynamics of +1/2 defects, stabilizing the quasi-long-range ordered nematic state. This activity threshold vanishes at low temperature, leading to a re-entrant transition. At large enough activity, active forces always exceed thermal ones and the perturbative result fails, suggesting that in this regime activity will always disorder the system. Crucially, rotational diffusion being a two-dimensional phenomenon, defect unbinding cannot be described by a simplified one-dimensional model.Comment: 15 pages (including SI), 4 figures. Significant technical improvements without changing the result

Cross-talk between topological defects in different fields revealed by nematic microfluidics

Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors, and biological materials. Although topological defects and their mutual interactions have been extensively studied, little is known about the interplay between defects in different fields -- especially when they co-evolve -- within the same physical system. Here, using nematic microfluidics, we study the cross-talk of topological defects in two different material fields -- the velocity field and the molecular orientational field. Specifically, we generate hydrodynamic stagnation points of different topological charges at the center of star-shaped microfluidic junctions, which then interact with emergent topological defects in the orientational field of the nematic director. We combine experiments, and analytical and numerical calculations to demonstrate that a hydrodynamic singularity of given topological charge can nucleate a nematic defect of equal topological charge, and corroborate this by creating $-1$, $-2$ and $-3$ topological defects in $4-$, $6-$, and $8-$arm junctions. Our work is an attempt toward understanding materials that are governed by distinctly multi-field topology, where disparate topology-carrying fields are coupled, and concertedly determine the material properties and response.Comment: 18 pages, 9 figure