Domain growth in cholesteric blue phases: Hybrid lattice Boltzmann simulations

Abstract

a b s t r a c tHere we review a hybrid lattice Boltzmann algorithm to solve the equations of motion of cholesteric liquid crystals. The method consists in coupling a lattice Boltzmann solver for the Navier-Stokes equation to a finite difference method to solve the dynamical equations governing the evolution of the liquid crystalline order parameter. We apply this method to study the growth of cholesteric blue phase domains, within a cholesteric phase. We focus on the growth of blue phase II and on a thin slab geometry in which the domain wall is flat. Our results show that, depending on the chirality, the growing blue phase is either BPII with no or few defects, or another structure with hexagonal ordering. We hope that our simulations will spur further experimental investigations on quenches in micron-size blue phase samples. The computational size that our hybrid lattice Boltzmann scheme can handle suggests that large scale simulations of new generation of blue phase liquid crystal devices are within reach.

Channel flow of a tensorial shear-thinning Maxwell model: Lattice Boltzmann simulations

“…One may also exploit that the gradient of the non-Newtonian stresses appears equivalently to an external force density in the Navier-Stokes equations. The dynamics of the non-Newtonian forces is then traced either by a modified LB scheme at the cost of introducing an enlarged set of lattice-node densities [37][38][39] , or through suitable finite-difference solvers in hybrid-LB schemes [40][41][42] . In this paper, we present a modified LB scheme that allows to naturally incorporate non-Newtonian stresses, including flow-induced pressure and normal-stress differences relevant close to the glass transition.…”

Structure of Blue Phase III of Cholesteric Liquid Crystals

“…However, DTCs cannot be smoothly patched together to fill the whole of space; disclination lines are required at the interstices between the cylinders. If an external field is used to align the DTCs, the disclinations can form a simple linear array [4], but more generally they meet at junctions forming a multiply connected network. The resulting structure is highly colored (''blue'') since the spacing between defects lies in the optical range.…”

Ordering dynamics of blue phases entails kinetic stabilization of amorphous networks

“…It is possible (18) that small nuclei of BPs persist on heating far into the isotropic phase, allowing hysteresis-free growth on reducing the temperature again. Whatever the source of the required nuclei, simulation studies of their subsequent growth can illuminate fundamental issues in phase transition dynamics, as exemplified by previous work on hard-sphere colloids (19,20).Our hybrid lattice Boltzmann technique is summarized in Materials and Methods and in the SI Appendix, and detailed elsewhere (10,11,21). Briefly, it marries a finite difference code for the advective relaxation of the order parameter tensor QðrÞ (with r spatial position) (22), governed by a suitable free-energy functional F½Q (23), to an efficient parallel lattice Boltzmann (LB) code for a forced Navier-Stokes equation for momentum transport, like that used previously to simulate multiscale colloidal materials (24).…”

“…This advance has allowed us to address elsewhere the motion of planar interfaces between competing phases (11). By the same methods, we address below the domain growth of the ordered BPs from an isolated nucleus of the stable phase.…”

“…Our hybrid lattice Boltzmann technique is summarized in Materials and Methods and in the SI Appendix, and detailed elsewhere (10,11,21). Briefly, it marries a finite difference code for the advective relaxation of the order parameter tensor QðrÞ (with r spatial position) (22), governed by a suitable free-energy functional F½Q (23), to an efficient parallel lattice Boltzmann (LB) code for a forced Navier-Stokes equation for momentum transport, like that used previously to simulate multiscale colloidal materials (24).…”