A thermal gradient-induced circular motion of particles placed on ferroelectric nematic liquid crystal sessile drops is demonstrated and explained. Unlike hurricanes and tornadoes that are the prime examples for thermal motors and where turbulent flows are apparent, here the texture without tracer particles appears completely steady indicating laminar flow. We provide a simple model showing that the tangential arrangement of the ferroelectric polarization combined with the vertical thermal gradient and the pyroelectricity of the fluid drives the rotation of the tracer particles that become electrically charged in the fluid. These observations provide a fascinating example of the unique nature of fluid ferroelectric liquid crystals.
Using a microscopic model of interacting polar biofilaments and motor proteins, we characterize the phase diagram of both homogeneous and inhomogeneous states in terms of experimental parameters. The polarity of motor clusters is key in determining the organization of the filaments in homogeneous isotropic, polarized and nematic states, while motor-induced bundling yields spatially inhomogeneous structures.
We characterize two-dimensional (2D) microtubule-based active nematics driven by light-responsive kinesin motor clusters. We assess two constructs of optogenetic kinesin: opto-K401, a processive motor, and opto-K365, a non-processive motor. Measurements reveal an order of magnitude improvement in the contrast of nematic flow speeds between maximally- and minimally-illuminated states for opto-K365 motors. Focusing on opto-K365 nematics, we characterize both the steady-state flow and defect density as a function of applied light and examine the transient behavior between steady-states. The stead…
In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the c…
Biological motors are marvels of nature that inspire creation of their synthetic counterparts with comparable nanoscale dimensions, high efficiency and diverse functions. Molecular motors have been synthesized, but obtaining nanomotors through self-assembly remains challenging. Here we describe a self-assembled colloidal motor with a repetitive light-driven rotation of transparent micro-particles immersed in a liquid crystal and powered by a continuous exposure to unstructured ~1 nW light. A monolayer of azobenzene molecules defines how the liquid crystal's optical axis mechanically couples to…
In nature interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviours. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors and depleting agent. It shows a rich behaviour evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of …
Active forces occurring within cells can drive crucial biological processes that involve spontaneous organization and shape change, such as cell division. Motivated by recent in vitro experiments of nematic droplets of cytoskeletal filaments and motors that self-organize and divide, we present a minimal hydrodynamic model that combines the nonequilibrium kinetics of motor-filament interactions with equilibrium nematic phase separation. The motors organize within droplets and structure filaments into polarized aster defects. At large motor activity, they can even deform or divide the droplet, o…
Cytoskeletal active nematics exhibit striking non-equilibrium dynamics that are powered by energy-consuming molecular motors. To gain insight into the structure and mechanics of these materials, we design programmable clusters in which kinesin motors are linked by a double-stranded DNA linker. The efficiency by which DNA-based clusters power active nematics depends on both the stepping dynamics of the kinesin motors and the chemical structure of the polymeric linker. Fluorescence anisotropy measurements reveal that the motor clusters, like filamentous microtubules, exhibit local nematic order.…
Recent experiments have shown how nematically-ordered tactoid shaped actin droplets can be reorganized and divided by the action of myosin molecular motors. In this paper, we consider how similar morphological changes can potentially be achieved under equilibrium conditions. Using simulations, both atomistic and continuum, and a phenomenological model, we explore how the nucleation dynamics, shape changes, and the final steady state of a nematic tactoid droplet can be modified by interactions with model adhesive colloids that mimic a myosin motor cluster. Our results provide a prescription for…
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the …
Nematic solids respond strongly to changes in ambient heat or light, significantly differently parallel and perpendicular to the director. This phenomenon is well characterized for uniform director fields, but not for defect textures. We analyze the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for some disclination defects with an eye towards reversibly inducing three-dimensional shapes from flat sheets of material, at the nano-scale all the way to macroscopic objects, including non-developable surfaces. The latter offers a new paradigm to…
We consider the effects of polydispersity on isotropic-nematic phase equilibria in thermotropic liquid crystals, using a Maier-Saupe theory with factorized interactions. A sufficient spread (approx. 50%) in the interaction strengths of the particles leads to phase separation into two or more nematic phases, which can in addition coexist with an isotropic phase. The isotropic-nematic coexistence region widens dramatically as polydispersity is increased, leading to re-entrant isotropic-nematic phase separation in some regions of the phase diagram. We show that similar phenomena will occur also f…
A theoretical study of the variation of thermodynamic and transport properties of calamitic liquid crystals across the isotropic-nematic phase transition is carried out by calculating the {\it wavenumber (k) and time (t)} dependent intermediate scattering function of the liquid, via computer simulations of model nematogens. The objective is to understand the experimentally observed anomalies and sharp variation in many thermodynamic and transport properties, namely specific heat $C$, sound attenuation coefficient $Γ$, thermal diffusivity $D_T$ and sound velocity $c_s$ are as the I-N transition…
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…
It is known that the doping of liquid crystal with dyes usually changes the physical properties of the host, like the transition temperatures and the optical absorption among others. In this work we report a study of the nonlinear optical refraction of a dye doped sample of the E7 thermotropic liquid crystal by the Z-scan technique. It was found that the nonlinear refraction of the sample is higher than the undoped one, diverging at the clearing point. Close to the N-I transition, the nonlinear birefringence is characterized by a critical exponent that seams to confirm the tricritical hypothes…
We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxia…
During the early developmental process of organisms, the formation of the left-right laterality requires a subtle mechanism, as it is associated with other principal body axes. Any inherent chiral feature in an egg cell can in principal trigger this spontaneous breaking of chiral symmetry. Individual microtubules, major cytoskeletal filaments, are known as chiral objects. However, to date there lacks convincing evidence of a hierarchical connection of the molecular nature of microtubules to large-scale chirality, particularly at the length scale of an entire cell. Here we assemble an in-vitro …
We show theoretically that thermomechanical effects in dye-doped nematic liquid crystals when illuminated by laser beams, can become important and lead to molecular reorientation at intensities substantially lower than that needed for optical Fréedericksz transition. We propose a 1D model that assumes homogenous intensity distribution in the plane of the layer and is capable to describe such a thermally induced threshold lowering. We consider a particular geometry, with a linearly polarized light incident perpendicularly on a layer of homeotropically aligned dye-doped nematics.
In an attempt to quantitatively characterize the recently observed slow dynamics in the isotropic and nematic phase of liquid crystals, we investigate the single-particle orientational dynamics of rodlike molecules across the isotropic-nematic transition in computer simulations of a family of model systems of thermotropic liquid crystals. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. In order to obtain a quantitative measure of glassy dyn…
In this work, a theoretical study of phase equilibrium in mixtures of a calamitic nematic liquid crystal and hard spherical nanoparticles is presented. A mean-field thermodynamic model is used, where the interactions are considered to be proportional to the number of contacts, which in turn are proportional to the areas and area fractions of each component. It is shown that, as the radius of the particle is increased, the effect of the particles on the isotropic-nematic transition is less pronounced, and that for large radius the miscibility increases as the particle radius increases.
Optical birefringence measurements on a rod-like liquid crystal (8OCB), imbibed in silica channels (7 nm diameter), are presented and compared to the thermotropic bulk behavior. The orientational and positional order of the confined liquid evolves continuously at the paranematic-to-nematic and sizeably broadened at the nematic-to-smectic order transition, resp., in contrast to the discontinuous and well-defined second-order character of the bulk transitions. A Landau-de-Gennes analysis reveals identical strengths of the nematic and smectic ordering fields (imposed by the walls) and indicates t…
We present the first systematic measurements of the dynamic response of a glassy soft-solid formed on dispersing colloids in a thermotropic nematic liquid crystal. Through applying a simple theoretical model, we reveal that the nematic elasticity dominates at low frequencies (longest timescales) and prevents flow. The Ericksen number $E_R$, determines a critical frequency $ω_c$, above which the viscous component $G'' \propto ω^{1/2}$. We find that the value of tan$δ$ is independent of the colloidal volume fraction ($ϕ$), and is determined by the ratio of lengthscales associated with the defect…
Suspended droplets of cholesteric (chiral nematic) liquid crystals spontaneously rotate in the presence of a heat flux due to a temperature gradient, a phenomenon known as Lehmann effect. So far, it is not clear whether this effect is due to the chirality of the phase and the molecules or only to the chirality of the director field. Here, we report the continuous rotation in a temperature gradient of nematic droplets of a lyotropic chromonic liquid crystal featuring a twisted bipolar configuration. The achiral nature of the molecular components leads to a random handedness of the spontaneous t…
This paper reviews the research work on the liquid crystalline (LC) polymer vesicles (polymersomes), where the thermotropic nematic and smectic phases are displayed in the lyotropic bilayer polymer membrane. LC polymersomes possess the properties of both liquid crystals and polymers, the two essential soft matters. LC polymersomes offer, on the one hand, novel examples of the interplay between orientational order and the curved geometry of a two dimensional membrane. Spherical, ellipsoidal and tetrahedral vesicles are discussed. On the other hand, LC polymersomes enable novel design of stimuli…
This is a series of four lectures presented at the 2015 Enrico Fermi summer school in Varenna. The aim of the lectures is to give an introduction to the hydrodynamics of active matter concentrating on low Reynolds number examples such as cells and molecular motors. Lecture 1 introduces the hydrodynamics of single active particles, covering the Stokes equation and the Scallop Theorem, and stressing the link between autonomous activity and the dipolar symmetry of the far flow field. In lecture 2 I discuss applications of this mathematics to the behaviour of microswimmers at surfaces and in exter…
In the framework of a field theoretical approach we study Maier-Saupe nematogenic fluid in contact with a hard wall. The pair interaction potential of the considered model consists of an isotropic and an anisotropic Yukawa terms. In the mean field approximation the contact theorem is proved. For the case of the nematic director being oriented perpendicular to the wall, analytical expressions for the density and order parameter profiles are obtained. It is shown that in a certain thermodynamic region the nematic fluid near the interface can be more diluted and less orientationally ordered than …
Unconventional superconductivity is characterized by the spontaneous symmetry breaking of the macroscopic superconducting wavefunction in addition to the gauge symmetry breaking, such as rotational-symmetry breaking with respect to the underlying crystal-lattice symmetry. Particularly, superconductivity with spontaneous rotational-symmetry breaking in the wavefunction amplitude and thus in bulk properties, not yet reported previously, is intriguing and can be termed "nematic" superconductivity in analogy to nematic liquid-crystal phases. Here, based on specific-heat measurements of the single-…
We study transformations of self-organized defect arrays at the nematic-smectic A liquid crystal phase transition, and show that these defect configurations are correlated, or "remembered", across the phase transition. A thin film of thermotropic liquid crystal is subjected to hybrid anchoring by an air interface and a water substrate, and viewed under polarized optical microscopy. Upon heating from smectic-A to nematic, a packing of focal conic domains melts into a dense array of boojums---nematic surface defects---which then coarsens by pair-annihilation. With the aid of Landau-de Gennes num…
Thermotropic biaxial nematic phases seem to be rare, but biaxial smectic A phases less so. Here we use molecular field theory to study a simple two-parameter model, with one parameter promoting a biaxial phase and the second promoting smecticity. The theory combines the biaxial Maier-Saupe and McMillan models. We use alternatively the Sonnet-Virga-Durand (SVD) and geometric mean approximations (GMA) to characterize molecular biaxiality by a single parameter. For non-zero smecticity and biaxiality, the model always predicts a ground state biaxial smectic A phase. For a low degree of smectic ord…
The scaled particle theory is developed for the description of thermodynamical properties of a mixture of hard spheres and hard spherocylinders. Analytical expressions for free energy, pressure and chemical potentials are derived. From the minimization of free energy, a nonlinear integral equation for the orientational singlet distribution function is formulated. An isotropic-nematic phase transition in this mixture is investigated from the bifurcation analysis of this equation. It is shown that with an increase of concentration of hard spheres, the total packing fraction of a mixture on phase…
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…
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…
Optical birefringence and light absorption measurements reveal four regimes for the thermotropic behavior of a nematogen liquid (7CB) upon sequential filling of parallel-aligned capillaries of 12 nm diameter in a monolithic, mesoporous silica membrane. No molecular reorientation is observed for the first adsorbed monolayer. In the film-condensed state (up to 1 nm thickness) a weak, continuous paranematic-to-nematic (P-N) transition is found, which is shifted by 10 K below the discontinuous bulk transition at T_IN=305K. The capillary-condensed state exhibits a more pronounced, albeit still cont…
To most existing non-equilibrium theories, the modeling of non-isothermal processes was a hard task. Intrinsic difficulties involved the non-equilibrium temperature, the coexistence of conserved energy and dissipative entropy, etc. In this paper, by taking the non-isothermal flow of nematic liquid crystals as a typical example, we illustrated that thermodynamically consistent models in either vectorial or tensorial forms could be constructed within the framework of Conservation-Dissipation Formalism (CDF). And the classical isothermal Ericksen-Leslie model and Qian-Sheng model were shown to be…
Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression f…
The paper describes preliminary investigations of a new effect in conducting anisotropic liquids, which leads to thermoelectric conversion of energy. Nematic liquid crystals with semiconducting dopes are used. A thermoelectric figure of merit ZT = 0.2 is obtained in experiments. The effect can be explained by assuming that the thermocurrent in semiconducting nematics, in contrast to the Seebeck effect, is a nonlinear function of the temperature gradient and of the temperature itself. Though the discovered effect has to be further investigated, the data obtained suggest that it can be effective…
We extend the Langevin dynamics so that particles can be exchanged with a particle reservoir. We show that grand canonical ensembles are realized at equilibrium and derive the relations of thermodynamics for processes between equilibrium states. As an application of the proposed evolution rule, we devise a simple model of Brownian motors driven by particle exchange. KEYWORDS: Langevin Dynamics, Thermodynamics, Open Systems
Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a quasi-two-dimensional (2D) nematic phase, and driven by ATP-fueled kinesin motor proteins. This system exhibits robust chaotic advection and gives rise to a pronounced fractal structure in the nematic contours. We characterize such experimentally derived fractals using the power spectrum and discover that the power spectrum decays as $k^{-β}$ for large wavenumbers …
We derive a fully covariant theory of the hydrodynamics of nematic and polar active surfaces, subjected to internal and external forces and torques. We study the symmetries of polar and nematic surfaces and find that in addition to 5 different types of in-plane isotropic surfaces, polar and nematic surfaces can be classified into 5 polar, 2 pseudopolar, 5 nematic and 2 pseudonematic types of surfaces. We give examples of physical realisations of the different types of surfaces we have identified. We obtain expressions for the equilibrium tensions, moments, and external forces and torques actin…
Recent experiments on mixed liquid crystals have highlighted the hugely significant role of ferromagnetic nanoparticle impurities in defining the nematic-smectic-A phase transition point. Structured around a Flory-Huggins free energy of isotropic mixing and Landau-de Gennes free energy, this article presents a phenomenological mean-field model that quantifies the role of such impurities in analyzing thermodynamic phases, in a mixture of thermotropic smectic liquid crystal and ferromagnetic nanoparticles. First we discuss the impact of ferromagnetic nanoparticles on the isotropic-ferronematic a…
We have studied the effects of quenched random disorder created by dispersed aerosil nanoparticle gels on the nematic to smectic-A (N-SmA) and smectic-A to reentrant nematic (SmA- RN) phase transitions of thermotropic liquid crystal mixtures of 6OCB (hexyloxycyanobiphenyl) and 8OCB (octyloxycyanobiphenyl). These effects are probed using high-resolution synchrotron x-ray diffraction techniques. We find that the reentrant characteristics of the system are largely unchanged by the presence of the aerosil gel network. By comparing measurements of the smectic static structure amplitude for this 8OC…
The possible symmetries of the biaxial nematic phase are examined against the implications of the presently available experimental results. Contrary to the widespread notion that biaxial nematics have orthorhombic symmetry, our study shows that a monoclinic ($C_{2h}$) symmetry is more likely to be the case for the recently observed phase biaxiality in thermotropic bent-core and calamitc tetrapode nematic systems. The methodology for differentiating between the possible symmetries of the biaxial nematic phase by NMR and by IR spectroscopy measurements is presented in detail. The manifestations …
We present a unified formulation of a rotationally invariant nonlinear elasticity for a variety of spontaneously anisotropic phases, and use it to study thermal fluctuations in nematic elastomers and spontaneously anisotropic gels. We find that in a thermodynamic limit homogeneous nematic elastomers are universally incompressible, are characterized by a universal ratio of shear moduli, and exhibit an anomalous elasticity controlled by a nontrivial low temperature fixed point perturbative in D=3-epsilon dimensions. In three dimensions, we make predictions that are asymptotically exact.
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…
We propose a novel approach to the solution of nematic Liquid Crystal models based on the derivation of a system of nonlinear wave equations for order parameters such that the occurrence of uniaxial and biaxial phase transitions can be interpreted as the propagation of a two-dimensional shock wave in the space of thermodynamic parameters. We obtain the exact equations of state for an integrable model of biaxial nematic liquid crystals and show that the classical transition from isotropic to uniaxial phase in absence of external fields is the result of a van der Waals type phase transition, whe…
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 present a model of classical hard-core dimers on the square lattice that contains an Ising nematic phase in its phase diagram. We consider a model with an attractive interaction for parallel dimers on a given plaquette of the square lattice and an attractive interaction for neighboring parallel dimers on the same row ({\it viz} column) of the lattice. By extensive Monte carlo simulations we find that with a finite density of holes the phase diagram has, with rising temperatures, a columnar crystalline phase, an Ising nematic liquid phase and a disordered fluid phase, separated by Ising cont…
