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 regimes were observed and compared to past experimental and theoretical observations. A sharp-interface model for the study of linear morphological instabilities, taking into account additional complexity resulting from liquid crystalline order, was derived. Results from the sharp-interface model were compared to those from full two-dimensional simulation identifying the specific limitations of simplified sharp-interface models for this liquid crystal system. In the nonlinear regime, secondary instabilities were observed to result in the formation of defects, interfacial heterogeneities, and bulk texture dynamics.
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 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 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…
Active matter comprised of self-propelled interacting units holds a major promise for extraction of useful work from its seemingly chaotic out-of-equilibrium dynamics. Streamlining active matter to produce work is especially important at microscale, where the viscous forces prevail over inertia and the useful modes of transport require very specific non-reciprocal type of motion. Here we report that microscopic active droplets representing aqueous dispersions of swimming bacteria Bacillus subtilis show unidirectional propulsion when placed in an inactive nematic medium. Random motion of bacter…
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 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…
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…
We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 μm-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic - smectic B interface presents a facet in one direction -- the direction parallel to the smectic layers -- and is otherwise rough, and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V a…
The potential of mean torque governing the orientational ordering of prochiral solutes in the two nematic phases (N and Nx) formed by certain classes of symmetric achiral bimesogens is formulated and used for the analysis of existing NMR measurements on solutes of various symmetries dissolved in the two phases. Three distinct attributes of the solvent phase, namely polarity of the orientational ordering, chirality of the constituent molecules and spatial modulation of the local director, are identified as underlying three possible mechanisms for the generation of chiral asymmetry in the low te…
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$180 A) is mesosc…
We present a simplified molecular model of mesogenic dimers consisting of two identical uniaxial mesogenic cores separated by a fixed-length spacer and allowed to assume only two, statistically equivalent, conformations which are non-planar and of opposite handedness. In the mean-field approximation, with additive interactions among the mesogenic cores, the model yields up to three positionally disordered phases, one isotropic and two nematic. The low temperature nematic phase ($\mathrm{N_X}$) has a local two-fold symmetry axis which is also a direction of molecular polar ordering and is tight…
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…
An intermediate nematic phase is proposed for the interpretation of recent experimental results on phase biaxiality in bent-core nematics. The phase is macroscopically uniaxial but consists of microscopic biaxial, and possibly polar, domains. On applying an electric field the phase exhibits substantial macroscopic biaxial ordering resulting from the collective alignment of the domains. A phenomenological theory is developed for the molecular order in this phase and for its transitions to purely uniaxial and to spontaneously biaxial nematic phases.
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…
Molecular dynamics simulations of selected members of the cyano-biphenyl series of dimers (CBnCB) have been set up using atomistic detail interactions among intermolecular pairs of united atoms and allowing fully for the flexibility of the spacer chain. Detailed results are presented for the CB7CB dimers, showing an isotropic fluid phase and two nematic phases. The positional and orientational correlation functions extracted from the simulations are used to elucidate the structure of the low-temperature nematic phase. Polar molecular ordering is clearly identified along a direction undergoing …
The phase behavior of the system of parallel rigid triblock copolymers is examined using the second-virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel particles can form not only uniform nematic and smectic A phases, but a smectic-C phase too. The stability and structure of the tilted structure is controlled by only the diameter and the length of the central…
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…
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…
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）
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-…
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…
We explore the nematic ordering of the rod-like liquid crystals 5CB and 6CB, embedded into parallel-aligned nanochannels in mesoporous silicon and silica membranes as a function of mean channel radius (4.7<=R <=8.3 nm), and thus geometrical confinement strength, by optical birefringence measurements in the infrared region. The orientational order inside the nanochannels results in an excess birefringence, which is proportional to the nematic order parameter. It evolves continuously upon cooling with a precursor behavior, typical of a paranematic state at high temperatures. These observations a…
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…
We experimentally investigate the structural behavior of an interacting colloidal monolayer being driven across a decagonal quasiperiodic potential landscape created by an optical interference pattern. When the direction of the driving force is varied, we observe the monolayer to be directionally locked on angles corresponding to the symmetry axes of the underlying potential. At such locking steps we observe a dynamically ordered smectic phase in agreement with recent simulations. We demonstrate, that such dynamical ordering is due to the interaction of particle lanes formed by interstitial an…
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.
We have studied the nucleation and the physical properties of a -1/2 wedge disclination line near the free surface of a confined nematic liquid crystal. The position of the disclination line has been related to the material parameters (elastic constants, anchoring energy and favored anchoring angle of the molecules at the free surface). The use of a planar model for the structure of the director field (whose predictions have been contrasted to those of a fully three-dimensional model) has allowed us to relate the experimentally observed position of the disclination line to the relevant propert…
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.
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 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…
A high-resolution dielectric and calorimetric study of the isotropic (I) to nematic (N) phase transition of carbon nanotube (CNT) dispersed liquid crystal (LC) functional composites as a function of CNT concentration is reported. The evolution of the I-N phase transition, the temperature dependence of local nematic ordering formed by dispersed CNTs in the LC media and the transition enthalpy were coherently monitored. Anisotropic CNTs induce local deformation to the nematic director of LC and form lyotropic pseudo-nematic phase in the LC media. Results clearly indicate the dramatic impact of d…
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…
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 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…
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…
