We undertake a comprehensive Monte Carlo (MC) study of the ordering kinetics in nematic liquid crystals (NLCs) in 3-dimensions $(d=3)$ by performing deep quenches from the isotropic $(T>T_c)$ to the nematic $(T<T_c)$ phase. The inter-molecular potential between the nematogens, represented by continuous $O(3)$ spins with inversion symmetry, is accurately mimicked by the {\it generalised Lebwohl Lasher} (GLL) model. It incorporates second and fourth order Legendre interactions, and their relative interaction strength is $λ$. For $λ<-0.3$, we observe {\it canted} morphologies with a $λ$-dependent angle-of-tilt between the neighbouring rod-like molecules. For $λ\geq-0.3$, the molecules align to yield {\it uniform} states. The coarsening morphologies obey {\it generalized dynamical scaling} in the two regimes, but the scaling function is not robust with respect to $λ$. The structure factor tail in the canted regime follows the {\it Porod law}: $S(k,t)\sim k^{-4}$, implying that the coarsening dynamics is due to the annihilation of interfacial defects. This is unexpected, as the GLL model is characterised by a continuous order parameter. The uniform regime on the other hand, exhibits the expected {\it generalized Porod decay}: $S(k,t)\sim k^{-5}$, characteristic of scattering from {\it string defects}. Finally, the domain growth obeys the {\it Lifshitz-Allen-Cahn law}: $L(t)\sim t^{1/2}$ for all values of $λ$. Our results for the novel {\it canted} regime are relevant for a large class of systems with orientational ordering, e.g. active matter, membranes, LC elastomers, etc. We hope that our work triggers-off stimulating investigations in them.
Suppression of Active Super-Diffusion: Impact of String Defects and Canted Multi-Domains
School of Interdisciplinary Research, Indian Institute of Technology（印度理工学院跨学科研学院）；Computer Services Centre, Indian Institute of Technology（印度理工学院计算机服务中心）；School of Physical Sciences, Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学物理科学学院）；Department of Physics, Indian Institute of Technology（印度理工学院物理系）
We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime. Constructed from general principles, the theory is universal, with parameters independent of any particular microscopic realization. We show that it exhibits a bend instability similar to that seen in active suspensions, that leads to the proliferation of defects. We find three distinct nonequilibrium steady states: a defect-ordered nematic in which $+\frac{1}{2}$ disclinations develop polar ordering, an undulating nematic state with no defects, and a turb…
We report a hybrid mesophase consisting of magnetic nanorods confined between the non-ionic surfactant bilayers of a lamellar phase. The magnetic field-induced ordering of the nanorods was measured experimentally and modeled by a two-dimensional Onsager theory including the third virial coefficient. The nanorods are strongly confined in layers, with no orientational coupling from one layer to the next. At high volume concentration they exhibit spontaneous in-plane orientational ordering and form a stack of independent two-dimensional nematic systems. This isotropic-nematic transition is first-…
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…
The optical birefringence of rod-like nematogens (7CB, 8CB), imbibed in parallel silica channels with 10 nm diameter and 300 micrometer length, is measured and compared to the thermotropic bulk behavior. The orientational order of the confined liquid crystals, quantified by the uniaxial nematic ordering parameter, evolves continuously between paranematic and nematic states, in contrast to the discontinuous isotropic-to-nematic bulk phase transitions. A Landau-de Gennes model reveals that the strength of the orientational ordering fields, imposed by the silica walls, is beyond a critical thresh…
We report a computer simulation study of an electroneutral mixture of oppositely charged oblate ellipsoids of revolution with aspect ratio A = 1/3. In contrast to hard or soft repulsive ellipsoids, which are purely nematic, this system exhibits a smectic-A phase in which charges of equal sign are counterintuitively packed in layers perpendicular to the nematic director.
Modeling and simulation studies using a high-order Landau-de Gennes type model for the direct isotropic/smectic-A liquid crystal transition are presented showing the existence of meta-stable nematic pre-ordering under certain conditions, in agreement with experimental observations (Tokita, M. et al. Macromolecules 2006, 39, 2021-2023)
We study the effect of dielectric anisotropy of polymers on their equilibrium ordering within mean-field theory but with a formalism that takes into account the full n-body nature of van der Waals forces. Dielectric anisotropy within polymers is to be expected as the electronic properties of the polymer will typically be different along the polymer than across its cross section. It is therefore physically intuitive that larger charge fluctuations can be induced along the chain than perpendicular to it. We show that this dielectric anisotropy leads to n-body interactions which can induce an iso…
Orientational and positional ordering properties of liquid crystal monolayers are examined by means of Fundamental-Measure Density Functional Theory. Particles forming the monolayer are modeled as hard parallelepipeds of square section of size $σ$ and length $L$. The particle centers of mass are restricted to a flat surface and three possible and mutually perpendicular orientations (in-plane and along the layer normal) of their uniaxial axes are allowed. We find that the structure of the monolayer depends strongly on particle shape and density. In the case of rod-like shapes, particles align a…
With quenched disorder, we introduce two-dimensional active nematics suspended in an incompressible fluid. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density, orientation and flow fields. The quenched disorder is introduced such that it interacts with the local orientation at every point with some strength. Disorder strength is tuned from zero to large values. We numerically study the defect dynamics and system's kinetics and find that the finite disorder slows the ordering. The presence of fluid induces large fluctuation in the orientation field, fur…
We study the kinetics of the nematic-isotropic transition in a two-dimensional liquid crystal by using a lattice Boltzmann scheme that couples the tensor order parameter and the flow consistently. Unlike in previous studies, we find the time dependences of the correlation function, energy density, and the number of topological defects obey dynamic scaling laws with growth exponents that, within the numerical uncertainties, agree with the value 1/2 expected from simple dimensional analysis. We find that these values are not altered by the hydrodynamic flow. In addition, by examining shallow que…
The relation between elasticity and yielding is investigated in a model polymer solid by Molecular-Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers - both with bond disorder - as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio Ty/G between the shear yield strength Ty and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the sh…
The biopolymers actin and microtubules are often in an ongoing assembling/disassembling state far from thermal equilibrium. Above a critical density this leads to spatially periodic patterns, as shown by a scaling argument and in terms of a phenomenological continuum model, that meets also Onsager's statistical theory of the nematic--to--isotropic transition in the absence of reaction kinetics. This pattern forming process depends much on nonlinear effects and a common linear stability analysis of the isotropic distribution of the filaments is often misleading. The wave number of the pattern d…
Suspensions of magnetic nanoplatelets in isotropic solvents are very interesting examples of ferrofluids. It has been shown that above a certain concentration ΦNI such suspensions form a ferromagnetic nematic phase, which makes this system a unique example of a dipolar fluid. The formation of a nematic phase is driven by anisotropic electrostatic and long-range dipolar magnetic interactions. Here, we present studies of the evolution of short range positional and orientational magnetic order in the suspensions with volume fractions below and above ΦNI, using small angle neutron scattering (SANS…
The ordering matrix, which was originally introduced by de Gennes, is a well-known mathematical device for describing orientational order of biaxial nematic liquid crystal. In this paper we propose a new interpretation of the ordering matrix. We slightly modify the definition of the ordering matrix and call it the geometric order parameter. The geometric order parameter is a linear transformation which transforms a tensorial quantity of an individual molecule to a tensorial quantity observed at a macroscopic scale. The degree of order is defined as the singular value of the geometric order par…
We have structurally characterized the liquid crystal phase that appears as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-year-old void in the taxonomy of smectics and which we term the "smectic $Z_A$", is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer. The period of this polarization wave ($\sim$180 A) is mesosc…
The optical polarimetry technique is used to explore molecular ordering of nematic liquid crystals 5FPFFPP3 embedded in parallel cylindrical channels of alumina membranes with pore walls covered by a SE-1211 polymer film enhancing normal anchoring. A chemical film deposition from organic solution apparently results in inhomogeneous coverage with local islands on the channels walls. Accordingly, a coexistence of differently ordered LC regions (nanodomains), characterized by positive and negative anisotropy, results in a weak effective (average) optical birefringence. Repeated polymer deposition…
The isotropic-to-nematic transition in an athermal solution of long rigid rods subject to a gravitational (or centrifugal) field is theoretically considered in the Onsager approximation. The new feature emerging in the presence of gravity is a concentration gradient which coupled with the nematic ordering. For rodlike molecules this effect becomes noticeable at centrifugal acceleration g ~ 10^3--10^4 m/s^2, while for biological rodlike objects, such as tobacco mosaic virus, TMV, the effect is important even for normal gravitational acceleration conditions. Rods are concentrated near the bottom…
Phase-ordering dynamics in nematic liquid crystals has been the subject of much active investigation in recent years in theory, experiments and simulations. With a rapid quench from the isotropic to nematic phase a large number of topological defects are formed and dominate the subsequent equilibration process. We present here the results of a molecular dynamics simulation of the Gay-Berne model of liquid crystals after such a quench in a system with 65536 molecules. Twist disclination lines as well as type-1 lines and monopoles were observed. Evidence of dynamical scaling was found in the beh…
We explore the optical birefringence of the nematic binary mixtures 6CB$_{1-x}$7CB$_x$ ($0~\le~x~\le~1$) imbibed into parallel-aligned nanochannels of mesoporous alumina and silica membranes for channel radii of $3.4~\le~R~\le 21.0$ nm. The results are compared with the bulk behavior and analyzed with a Landau-de-Gennes model. Depending on the channel radius the nematic ordering in the cylindrical nanochannels evolves either discontinuously (subcritical regime, nematic ordering field $σ<1/2$) or continuously (overcritical regime, $σ>1/2$), but in both cases with a characteristic paranematic pr…
The biaxial phase in nematic liquid crystals has been elusive for several decades after its prediction in the 1970s. A recent experimental breakthrough was achieved by Liu et al. [PNAS 113, 10479 (2016)] in a liquid crystalline medium with magnetic nanoparticles (MNPs). They exploited the different length scales of dipolar and magneto-nematic interactions to obtain an equilibrium state where the magnetic moments are at an angle to the nematic director. This tilt introduces a second distinguished direction for orientational ordering or biaxiality in the two-component system. Using coarse-graine…
Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon proliferation. Here we construct a general hydrodynamic theory for a two-dimensional active nematic interrupted by a large number of such defects. Our equations describe the flows and spatio-temporal defect chaos characterizing active turbulence, even close to the defect unbinding transition. At high activity, nonequilibrium torques combined with many-body screening cau…
We examine the fluid phase behaviour of the binary mixture of hard superellipses using the scaled particle theory The superellipse is a general two dimensional convex object which can be tuned between circular and rectangular shapes continuously at a given aspect ratio. We find that the shape of the particle affects strongly the stability of isotropic nematic and tetratic phases even if the aspect ratios of both species are fixed. While the isotropic isotropic demixing transition can be ruled out using the scaled particle theory the first order isotropic nematic and the nematic nematic demixin…
A computational study of morphological instabilities of a two-dimensional nematic front under directional growth was performed using a Landau-de Gennes type quadrupolar tensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). A previously derived energy balance, taking anisotropy into account, was utilized to account for latent heat and an imposed morphological gradient in the time-dependent model. Simulations were performed using an initially homeotropic isotropic/nematic interface. Thermal instabilities in both the linear and non-linear reg…
The quadrupolar splittings of perdeuteriated n-decane dissolved in nematic phases formed by mesogenic dimers of the CBnCB series, for n=7,9,10,11 are measured throughout the entire temperature range of these phases. The results of the measurements, are reported together with related measurements using the common nematic phase of 5CB as a solvent for n-decane. The data obtained from the $^{13}$C spectra of the cyanobiphenyl mesogenic units of the monomeric and dimeric solvent molecules yield the order parameter of those units. The information obtained from this set of experiments is used to elu…
We examine the ordering behavior of hard plate-like particle in a very narrow slit-like pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with perpendicular one can be detected at high densities. I…
We examine the ordering properties of rectangular hard rods with length L and diameter D at a single planar wall and between two parallel hard walls using the second-virial density functional theory. The theory is implemented in the three-state Zwanzig approximation, where only three mutually perpendicular directions are allowed for the orientations of hard rods. The effect of varying shape anisotropy is examined at L/D=10, 15 and 20. In contact with a single hard wall, the density profiles show planar ordering, damped oscillatory behavior, and wall induced surface ordering transition below th…
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）
Using grand-canonical Monte Carlo simulations, we investigate the phase diagram of hard rods of length $L$ with additional contact (sticky) attractions on square and cubic lattices. The phase diagram shows a competition between gas-liquid and ordering transitions (which are of demixing type on the square lattice for $L \ge 7$ and of nematic type on the cubic lattice for $L \ge 5$). On the square lattice, increasing attractions initially lead to a stabilization of the isotropic phase. On the cubic lattice, the nematic transition remains of weak first order upon increasing the attractions. In th…
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…
Using Monte Carlo (MC) computer simulations we explore the self-assembly and ordering behavior of a hybrid, soft magnetic system consisting of small magnetic nano-spheres in a liquid-crystalline (LC) matrix. Inspired by recent experiments with colloidal rod-matrices we focus on conditions where the sphere and rod diameters are comparable. Already in the absence of a magnetic field, the nematic ordering of the LC can stabilize formation of magnetic chains along the nematic or smectic director, yielding a state with local (yet no macroscopic) magnetic order. The chains, in turn, increase the ove…
Even though chiral nematic phases were the first liquid crystals experimentally observed more than a century ago, the origin of the thermodynamic stability of cholesteric states is still unclear. In this Letter we address the problem by means of a novel density functional theory for the equilibrium pitch of chiral particles. When applied to right-handed hard helices, our theory predicts an entropy-driven cholesteric phase, which can be either right- or left-handed, depending not only on the particle shape but also on the thermodynamic state. We explain the origin of the chiral ordering as an i…
We propose a simple surface potential favoring the planar degenerate anchoring of nematic liquid crystals, i.e., the tendency of the molecules to align parallel to one another along any direction parallel to the surface. We show that, at lowest order in the tensorial Landau-de Gennes order-parameter, fourth-order terms must be included. We analyze the anchoring and wetting properties of this surface potential. In the nematic phase, we find the desired degenerate planar anchoring, with positive scalar order-parameter and some surface biaxiality. In the isotropic phase, we find, in agreement wit…
Basing our arguments on the theory of active liquid crystals, we demonstrate both analytically and numerically, that the activity can induce an effective free energy which enhances ordering in extensile systems of active rods and in contractile suspensions of active discs. We argue that this occurs because any ordering fluctuation is enhanced by the flow field it produces. A phase-diagram in the temperature-activity plane compares ordering due to a thermodynamic free energy to that resulting from the activity. We also demonstrate that activity can drive variations in concentration, but for a d…
Starting from a minimal physical model of self propelled hard rods on a substrate in two dimensions, we derive a modified Smoluchowski equation for the system. Self -propulsion enhances longitudinal diffusion and modifies the mean field excluded volume interaction. From the Smoluchowski equation we obtain hydrodynamic equations for rod concentration, polarization and nematic order parameter. New results at large scales are a lowering of the density of the isotropic-nematic transition and a strong enhancement of boundary effects in confined self-propelled systems.
Self-assembly of nanoparticles can enable composites with pre-designed properties but remains challenged by reproducing structural diversity of atomic and molecular crystals. We combine anisotropic elastic and weakly screened electrostatic interactions to guide both orientational and triclinic positional self-ordering of inorganic nanocrystals in a nematic fluid host. The lattice periodicity of these low-symmetry colloidal crystals is more than an order of magnitude larger than the nanoparticle size. Orientations of nanocrystals, as well as crystallographic axes of ensuing triclinic colloidal …
Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes formation of recently reported splay nematic liquid-crystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation (SHG) imaging, which additionally allowed for determination of the splay m…
Living active collectives have evolved with remarkable self-patterning ability to meet the physical and biological constraints for growth and survival. However, how complex multicellular patterns emerge from a single founder cell remains elusive. Here, by recourse to an agent-based model, we track the three-dimensional (3D) morphodynamics and cell orientational order of growing bacterial biofilms encased by agarose gels. Confined growth causes spatiotemporally heterogeneous stress buildup in the biofilm. High hydrostatic and low shear stresses at the core of the biofilm promote viscous-to-elas…
We study experimentally the impact of spherical nanoparticles on the orientational order parameters of a host nematic liquid crystal. We use spherical core-shell quantum dots that are surface functionalized to promote homeotropic anchoring on their interface with the liquid crystal host. We show experimentally that the orientational order may be strongly affected by the presence of spherical nanoparticles even at low concentrations. The orientational order of the composite system is probed by means of polarised micro-Raman spectroscopy and by optical birefringence measurements as function of t…
The phase behavior of a melt of monodisperse rod-coil diblocks is studied. We derive a Landau free energy functional for both a compositional and a nematic order parameter. The excluded volume interaction between the rod blocks is modeled by an attractive Maier-Saupe interaction. The incompatibility between rod- and coil blocks is modeled by the usual Flory-Huggins interaction. For a large volume fraction of the rods, a transition from isotropic to nematic to smectic C is observed upon decreasing the temperature, whereas for small rod volume fraction, spherical, hexagonal, and lamellar structu…
We present a Monte Carlo simulation of a polymer nematic for varying volume fractions, concentrating on the structure function of the sample. We achieve nematic ordering with stiff polymers made of spherical monomers that would otherwise not form a nematic state. Our results are in good qualitative agreement with theoretical and experimental predictions, most notably the bowtie pattern in the static structure function.
Phase separation of sequence-disordered liquid crystalline polymers, a promising class of technological and biological relevance, is studied by field theory, and thermodynamic mechanisms responsible for orientational ordering observed in experiments, are discussed. The theory developed predicts that chemical disorder marginally affects the nematic/isotropic biphasic coexistence width, but strongly impacts ordering; above a critical chemical disorder threshold orientational ordering is precluded.
