Compared to isotropic liquids, orientational order of nematic liquid crystals makes their rheological properties more involved, and thus requires fine control of the flow parameters to govern the orientational patterns. In microfluidic channels with perpendicular surface alignment, nematics discontinuously transition from perpendicular structure at low flow rates to flow-aligned structure at high flow rates. Here we show how precise tuning of the driving pressure can be used to stabilize and manipulate a previously unresearched topologically protected chiral intermediate state which arises before the homeotropic to flow-aligned transition. We characterize the mechanisms underlying the transition and construct a phenomenological model to describe the critical behaviour and the phase diagram of the observed chiral flow state, and evaluate the effect of a forced symmetry breaking by introduction of a chiral dopant. Finally, we induce transitions on demand through channel geometry, application of laser tweezers, and careful control of the flow rate.
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 …
We study the static equilibria of a simplified Leslie--Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient $\mathcal{G}$ and inverse anchoring strength, $\mathcal{B}$. We numerically find multiple static equilibria for admissible pairs $(\mathcal{G}, \mathcal{B})$ and classify them according to their winding numbers and stability. The case $\mathcal{G}=0$ is analytically tractable and we numerically study how the solution landscape is transformed as $\mathcal{G}$ increases. We study the one-dimensional dynamical …
"Active nematics" are orientationally ordered but apolar fluids composed of interacting constituents individually powered by an internal source of energy. When activity exceeds a system-size dependent threshold, spatially uniform active apolar fluids undergo a hydrodynamic instability leading to spontaneous macroscopic fluid flow. Here, we show that a special class of spatially non-uniform configurations of such active apolar fluids display laminar (i.e., time-independent) flow even for arbitrarily small activity. We also show that two-dimensional active nematics confined on a surface of non-v…
We study colloidal particles in a nematic-liquid-crystal-filled microfluidic channel and show how elastic interactions between the particle and the channel wall lead to different particle dynamics compared with conventional microfluidics. For a static particle, in the absence of a flow field, the director orientation on the particle surface undergoes a rapid transition from uniform to homeotropic anchoring as a function of the anchoring strength and the particle size. In the presence of a flow field, in addition to fluid viscous stresses on the particle, nematic-induced elastic stresses are ex…
Universitat de Barcelona（巴塞罗那大学）；Institute of Nanoscience and Nanotechnology, IN2UB, Universitat de Barcelona（巴塞罗那大学纳米科学与技术研究所）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院理论与计算物理中心）；Departamento de Física, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院物理系）；Institute for Bioengineering of Catalonia, The Barcelona Institute for Science and Technology（加泰罗尼亚生物工程学院，巴塞罗那科学技术研究院）
We investigate condensation of a long confined chiral nematic polymer inside a spherical enclosure, mimicking condensation of DNA inside a viral capsid. The Landau-de Gennes nematic free energy {\sl Ansatz} appropriate for nematic polymers allows us to study the condensation process in detail with different boundary conditions at the enclosing wall that simulate repulsive and attractive polymer-surface interactions. Increasing the chirality, we observe a transformation of the toroidal condensate into a closed surface with an increasing genus, akin to the ordered domain formation observed in cr…
Two-dimensional nematics possess peculiar properties that have been studied recently using computer simulation and various theoretical models. Here we review our own contribution to the field using density-functional theory, and present some preliminary simulation results on confined two-dimensional nematics. First we discuss the possible stable bulk phases and phase diagrams and the relation between phases and particle geometry. We then explore the adsorption properties on a single substrate and the confinement effects that arise when the fluid is confined between parallel walls. Next, confin…
The effect of rough walls on the phase behaviour of a confined liquid crystal (LC) fluid is studied using constant pressure Monte Carlo simulations. The LC is modelled as a fluid of soft ellipsoidal molecules and the rough walls are represented as a hard wall with a number of molecules randomly embedded in them. It is found that the isotropic-nematic (IN) transition is shifted to higher pressures for rougher walls.
A spontaneous buckling transition in thin layers of monodomain nematic liquid crystalline gel was observed by polarized light microscopy. The coupling between the orientational ordering of liquid crystalline solvent and the translational ordering of crosslinked polymer backbones inside the nematic gel contributes to such buckling transition. As the nematic mesogens become more ordered when the gel is cooled down from a higher gelation temperature, the polymeric backbones tend to elongate along the direction parallel to the nematic director, which is perpendicular to the rigid glass surfaces in…
We present computer simulations of long thin hard spherocylinders in a narrow planar slit. We observe a transition from the isotropic to a nematic phase with quasi-long-range orientational order upon increasing the density. This phase transition is intrinsically two dimensional and of the Kosterlitz-Thouless type. The effective two-dimensional density at which this transition occurs increases with plate separation. We qualitatively compare some of our results with experiments where microtubules are confined in a thin slit, which gave the original inspiration for this work.
We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer {\sl via} the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy {\sl ansatz} is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and …
We use numerical modelling to study the flow patterns of an active nematic confined in a cylindrical capillary, considering both planar and homeotropic boundary conditions. We find that active flow emerges not only along the capillary axis but also within the plane of the capillary, where radial vortices are formed. If topological defects are imposed by the boundary conditions, they act as local pumps driving the flow. At higher activity we demonstrate escape of the active defects and flow into the third dimension, indicating the importance of dimensionality in active materials. We argue that …
We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory the analytical expressions of the free energy, the pressure and the chemical potentials of HS and HSC have been derived. The improvement of obtained results is considered by introducing the Carnahan-Starling-like and Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic transition are calculated from the bifurcation analysis of the integral equati…
Motivated by recent experiments on the rod-like virus bacteriophage fd, confined to circular and annular domains, we present a theoretical study of structural transitions in these geometries. Using the continuum theory of nematic liquid crystals, we examine the competition between bulk elasticity and surface anchoring, mediated by the formation of topological defects. We show analytically that bulk defects are unstable with respect to defects sitting at the boundary. Moreover, in case of an annulus, whose topology does not require the presence of topological defects, under weak anchoring condi…
Within the macroscopic Landau-de Gennes approach, we examine the Gaussian normal mode fluctuations of semi-infinite nematic liquid crystals in a regime of critical wetting. It is argued that surface free-energy potentials that strongly suppress the long-range nematic order favor the appearance of bound biaxial nematic-director fluctuation modes, located in the domain occupied by the thermodynamic phase wetting the wall. Instead, substrates enhancing the orientational order promote the existence of uniaxial nematic-director local excitations. Close to the phase coexistence temperature both type…
We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter $S\simeq1$. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in …
We studied in-plane bistable alignments of nematic liquid crystals confined by two frustrated surfaces by means of Monte Carlo simulations of the Lebwohl-Lasher spin model. The surfaces are prepared with orientational checkerboard patterns, on which the director field is locally anchored to be planar yet orthogonal between the neighboring blocks. We found the director field in the bulk tends to be aligned along the diagonal axes of the checkerboard pattern, as reported experimentally [J.-H. Kim et al., Appl. Phys. Lett. 78, 3055 (2001)]. The energy barrier between the two stable orientations i…
Topological delocalisation of confined 3D active nematics
Johns Hopkins University（约翰斯·霍普金斯大学）；Università degli Studi di Bari Aldo Moro（巴里阿尔多·莫罗大学）；INFN（意大利国家核物理研究所）；University of Edinburgh（爱丁堡大学）；Universitat de Barcelona（巴塞罗那大学）
Using Monte Carlo simulation, we study a fluid of two-dimensional hard rods inside a small circular cavity bounded by a hard wall, from the dilute regime to the high-density, layering regime. Both planar and homeotropic anchoring of the nematic director can be induced at the walls through a free-energy penalty. The circular geometry creates frustration in the nematic phase and a polar-symmetry configuration with a distorted director field plus two $+1/2$ disclinations is created. At higher densities, a quasi-uniform structure is observed with a (minimal) director distortion which is relaxed vi…
We report the results of Monte Carlo simulations of the Lebwohl--Lasher model of nematic liquid crystals confined to cylindrical cavities with homeotropic anchoring. We show that the ratio of the bulk to surface couplings is not in general equal to the corresponding parameter K/W used in elastic theory (where K is the Frank elastic constant in the one constant approximation and W is the surface anchoring strength). By measuring the temperature dependence of K/W (which is equivalent to the surface extrapolation length) we are able to reconcile the results of our simulations as well as others wi…
Various director configurations of a nematic liquid crystal, confined in a toroidal volume and subject to an external magnetic field, were evaluated numerically by performing finite element calculations in three dimensions. The equilibrium director field is found from a minimization of the elasto-magnetic energy of the nematic. The director at the inner surface of the torus is fixed, either along homeotropic or tangential direction. We consider both a homogeneous and an azimuthal magnetic field, with its direction being in conflict with the respective surface anchoring. The relative stability …
Using novel micro-printing techniques, we develop a versatile experimental setup that allows us to study how lateral confinement tames the active flows and defect properties of the microtubule/kinesin active nematic system. We demonstrate that the active length scale that determines the self-organization of this system in unconstrained geometries loses its relevance under strong lateral confinement. Dramatic transitions are observed from chaotic to vortex lattices and defect-free unidirectional flows. Defects, which determine the active flow behavior, are created and annihilated on the channel…
Active nematic fluids confined in narrow channels generate spontaneous flows when the activity is sufficiently intense. Recently, it was shown that if the molecular anchoring at the channel walls is conflicting flows are initiated even in the zero activity limit. An analytical laminar velocity profile for this specific configuration was derived within a simplified nematohydrodynamic model in which the nematic order parameter is a fixed-magnitude unit vector n. In this study we explore systematically active flows in this confined geometry with a more general theoretical model that uses a second…
We investigate imbibition of a monodisperse emulsion into a low-aspect ratio microfluidic channel with the height h comparable to the droplet diameter d. For confinement ratio d/h = 1.2, the tightly confined disk-like droplets in the channel move more slowly compared to the average suspension velocity. Behind the meniscus that drives the imbibition, there is a droplet-free region, separated from the suspension region by a sharp concentration front. The suspension exhibits strong droplet density and velocity fluctuations, but on average, the suspension domain remains uniform. For weaker confine…
This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the interaction of defects with the underlying curvature. This chapter concludes with two cases of three-dimensional nematic phases confined to spaces with curved boundaries, namely a torus and a spherical shell.
Nontrivial shape of colloidal particles create complex elastic distortions and topological defects in liquid crystals and play a key role in governing their electrophoretic propulsion through the medium. Here, we report experimental results on defects and electrophoretic transport of anisometric (snowman-shaped) dielectric particles subjected to an alternating electric field perpendicular to the director in a nematic liquid crystal. We demonstrate that the shape asymmetry gives rise to defect-polymorphism by nucleating point or ring defects at multiple locations on the particle and controls th…
Elasticity-Driven Periodic Polarization Patterns in Confined Chiral Ferroelectric Nematic Fluid
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；CENN Nanocenter（CENN纳米中心）；Department of Physics, Faculty of Science and Technology, University of the Basque Country UPV/EHU（巴斯克国立大学理学院物理系）；School of Chemistry, University of Leeds（利兹大学化学学院）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学院）
Topological defects resulted from boundary constraints in confined liquid crystals have attracted extensive research interests. In this paper, we use numerical simulation to study the phase transition dynamics in the context of stochastic resonance in a bistable liquid crystal device containing defects. This device is made of nematic liquid crystals confined in a shallow square well, and is described by the planar Lebwohl-Lasher model. The stochastic phase transition processes of the system in the presence of a weak oscillating potential is simulated using an over-damped Langevin dynamics. Our…
Understanding the flow of liquid crystals in microfluidic environments plays an important role in many fields, including device design and microbiology. We perform hybrid lattice-Boltzmann simulations of a nematic liquid crystal flowing under an applied pressure gradient in two-dimensional channels with various anchoring boundary conditions at the substrate walls. We investigate the relation between flow rate and pressure gradient and the corresponding profile of the nematic director, and find significant departures from the linear Poiseuille relation. We also identify a morphological transiti…
We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates towards the confinement core over multiple rotation cycles, while…
We investigate the pseudo-Casimir force in a slab of material composed of nematically ordered long polymers. We write the total mesoscopic energy together with the constraint connecting the local density and director fluctuations and evaluate the corresponding fluctuation free energy by standard methods. It leads to a pseudo-Casimir force of a different type than in the case of standard, short molecule nematic. We investigate its separation dependence and its magnitude and explicitly derive the relevant limiting cases.
Vertically vibrated rod-shaped granular materials confined to quasi-2D containers self organize into distinct patterns. We find, consistent with theory and simulation, a density dependent isotropic-nematic transition. Along the walls, rods interact sterically to form a wetting layer. For high rod densities, complex patterns emerge as a result of competition between bulk and boundary alignment. A continuum elastic energy accounting for nematic distortion and local wall anchoring reproduces the structures seen experimentally.
Ordering in Confined Two-Dimensional Nematic Systems: Mesoscopic Simulations Based on Different Mean-Field Potentials
Research Center, La Salle University Mexico（墨西哥拉萨勒大学研究中心）；Faculty of Sciences, National Autonomous University of Mexico（墨西哥国立自治大学理学院）；Department of Mathematics, University of Manchester（曼彻斯特大学数学系）
Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains (Poulin et al., Science 275, 1770 (1997)). The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements …
The theory of elastic interaction of micron size axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self energy of one colloidal particle and interaction energy between two particles in arbitrary confined NLC with strong anchoring condition on the bounding surface. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness $L$ are considered and found to be exponentially screened on far distances with decay length $λ_{dd}=\frac{L}π$. It is predicted that boundi…
Topological defects in active liquid crystals can be confined by introducing gradients of activity. Here, we examine the dynamical behavior of two defects confined by a sharp gradient of activity that separates an active circular region and a surrounding passive nematic material. Continuum simulations are used to explain how the interplay among energy injection into the system, hydrodynamic interactions, and frictional forces governs the dynamics of topologically required self-propelling $+1/2$ defects. Our findings are rationalized in terms of a phase diagram for the dynamical response of def…
Solitons in nematic liquid crystals offer intriguing opportunities for transport and sensing in microfluidic systems. Little is known about the elementary conditions that are needed to create solitons in nematic materials. In this work, theory, simulations and experiments are used to study the generation and propagation of solitary waves (or "solitons") in nematic liquid crystals upon the application of an alternating current (AC) electric field. We find that these solitary waves exhibit "butterfly"-like or "bullet"-like structures that travel in the direction perpendicular to the applied elec…
Nematic and columnar phases of lyotropic chromonic liquid crystals (LCLCs) have been long studied for their fundamental and applied prospects in material science and medical diagnostics. LCLC phases represent different self-assembled states of disc-shaped molecules, held together by noncovalent interactions that lead to highly sensitive concentration and temperature dependent properties. Yet, microscale insights into confined LCLCs, specifically in the context of confinement geometry and surface properties, are lacking. Here, we report the emergence of time dependent textures in static disodiu…
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 s…
Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase diagram as a function of curvature, alignment strength and activity and reproduce phases seen in recent experiments on active microtubules moving on the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a band of polar matter wrapping …
Double Splay Nematic Order in Confined Polar Fluids
Southern University of Science and Technology（南方科技大学）；The Hongkong University of Science and Technology（香港科技大学）；South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology（华南理工大学 emergent soft matter 学院 / 华南软物质科学与技术先进研究院）；Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology（华南理工大学 广东省功能与智能杂化材料器件重点实验室）
We provide a minimal model for an active nematic film in contact with both a solid substrate and a passive isotropic fluid, and explore its dynamics in one and two dimensions using a combination of hybrid Lattice Boltzmann simulations and analytical calculations. By imposing nematic anchoring at the substrate while active flows induce a preferred alignment at the interface ("active anchoring"), we demonstrate that directed fluid flow spontaneously emerges in cases where the two anchoring types are opposing. In one dimension, our model reduces to an analogue of a loaded elastic column. Here, th…
We combine theory, numerical calculations, and experiments to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an effective quasi-two-dimensional description of the Stokes flow around the particle via the Brinkman equation, which can be solved in a time that is two orders of magnitude faster than the three-dimensional problem. The computational speedup enables us to calculate the full trajectories of particles in the channel. To test our scheme, we study the motion of du…
We study the effect of random porous matrices on the ordering in nematic liquid crystals. The randomness destroys orientational lang-range order and drives the liquid crystal into a glass state. We predict two glass phases one of which possesses quasi-long-range order. In this state the correlation length is infinite and the correlation function of the order parameter obeys a power dependence on the distance. The small-angle light-scattering amplitude diverges but slower than in the bulk nematic. In the uniaxially strained porous matrices two new phases emerge. One type of strain induces an an…
When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are large enough, the system shows multistability. Our lattice Boltzmann simulations demonstrate dynamic couplings between the multistable defect pattern and the flow in a regular porous matrix. At sufficiently low flow speed, the topological defects are pinned at the quiescent positions. As the flow speed is increased, the defects show cyclic motions and nonlinea…
We study geometrically-controlled twist transitions of a nematic confined between a sinusoidal grating and a flat substrate. In these cells the transition to the twisted state is driven by surface effects. We have identified the mechanisms responsible for the transition analytically and used exact numerical calculations to study the range of surface parameters where the twist instability occurs. Close to these values the cell operates under minimal external fields or temperature variations.
Solute dispersion in pre-turbulent confined active nematics
Universidade de Lisboa（里斯本大学）；Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院）；Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院理论与计算物理中心）；Departamento de Física, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院物理系）
