A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module

Singular Values, Nematic Disclinations, and Emergent Biaxiality

Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame, that can be extracted from the tensorial description of the nematic order, vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. New defects and degrees of freedom are unveiled and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase.Comment: 5 pages, 1 figure, submitted to PR

Reconfigurable knots and links in chiral nematic colloids

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David and the Borromean rings are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are classified by the quantized self-linking number, a direct measure of the geometric, or Berry's, phase. Forming arbitrary microscopic knots and links in chiral nematic colloids is a demonstration of how relevant the topology can be for the material engineering of soft matter.Comment: 6 pages, 3 figure

Phase Transitions in Microconfined Nematic Liquid Crystals

A brief review of stable phases and phase transitions in microconfined nematic liquid crystals is given. The effects of confinement are studied for the cavities of spherical and cylindrical shape with different surface-liquid crystal interactions. The phase transitions are either of order-disorder type where the magnitude of orientational ordering changes or of the structural type between different configurations of the nematic director field

Topology of three-dimensional active nematic turbulence confined to droplets

Active nematics contain topological defects which under sufficient activity move, create and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three-dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbulence under the spherical confinement, using numerical modelling. In such spherical droplets, we show the three-dimensional structure of the topological defects, which due to closed confinement emerge in the form of closed loops or surface-to-surface spanning line segments. In the turbulent regime, the defects are shown to be strongly spatially and time varying, with ongoing transformations between positive winding, negative winding and twisted profiles, and with defect loops of zero and non-zero topological charge. The timeline of the active turbulence is characterised by four types of bulk topology-linked events --- breakup, annihilation, coalescence and cross-over of the defects --- which we discuss could be used for the analysis of the active turbulence in different three-dimensional geometries. The turbulent regime is separated by a first order structural transition from a low activity regime of a steady-state vortex structure and an offset single point defect. We also demonstrate coupling of surface and bulk topological defect dynamics by changing from strong perpendicular to inplane surface alignment. More generally, this work is aimed to provide insight into three-dimensional active turbulence, distinctly from the perspective of the topology of the emergent three-dimensional topological defects.Comment: 7 figure

Playing the blues, the greens and the reds with cellulose-based structural colours

POCI- 01-0145-FEDER-007688 (Reference UIDB/50025/2020-2023) PTDC/CTM-BIO/6178/2014 M-ERA-NET2/0007/2016 PTDC/CTM-REF/30529/2017 EUTOPIA CA17139 Slovenian Research Agency Grant Z1-5441 P1-0099Structural vivid colours can arise from the interference of light reflected from structures exhibiting periodicity on scales in the range of visible wavelengths. This effect is observed with light reflected from cell-walls of some plants and exoskeletons of certain insects. Sometimes the colour sequence observed for these structures consists of nearly circular concentric rings that vary in colour from Red, Orange, Yellow, Green, Cyan to Blue, from the periphery to the centre, similarly to the colour scheme sequence observed for the rainbow (ROYGB). The sequence of colours has been found for solid films obtained from droplets of aqueous cellulose nanocrystals (CNCs) suspensions and attributed to a "coffee ring"effect. In this work, coloured lyotropic solutions and solid films obtained from a cellulose derivative in the presence of trifluoroacetic acid (TFA), which acts as a "reactive solvent", are revisited. The systems were investigated with spectroscopy, using circularly and linearly polarised light, coupled with a polarised optical microscope (POM) and scanning electron microscopy (SEM). The lyotropic cholesteric liquid crystalline solutions were confined in capillaries to simplify 1D molecular diffusion along the capillary where an unexpected sequence of the structural colours was observed. The development and reappearance of the sequence of vivid colours seem consistent with the reaction-diffusion of the "reactive solvent"in the presence of the cellulosic chains. The strong TFA acts as an auto-catalyst for the chemical reaction between TFA and the hydroxyl groups, existing along the cellulosic chain, and diffuses to the top and bottom along the capillaries, carrying dissolved cellulosic chains. Uncovering the precise mechanism of colour sequence and evolution over time in cellulosic lyotropic solutions has important implications for future optical/sensors applications and for the understanding of the development of cellulose-based structures in nature. This journal isauthorsversionpublishe

Topological and geometric decomposition of nematic textures

Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex structures, which are difficult to classify. Topological charge of point defects in nematics has ambiguously defined sign and its additivity cannot be ensured when defects are observed separately. We demonstrate how the topological charge of complex defect structures can be determined by identifying and counting parts of the texture that satisfy simple geometric rules. We introduce a parameter called the defect rank and show that it corresponds to what is intuitively perceived as a point charge based on the properties of the director field. Finally, we discuss the role of free energy constraints in validity of the classification with the defect rank.Comment: 16 pages, 5 figure