High-Order Nonlinear Electrophoresis in a Nematic Liquid Crystal.

Electrophoresis is the motion of particles relative to a surrounding fluid driven by a uniform electric field. In conventional electrophoresis, the electrophoretic velocity grows linearly with the applied field. Nonlinear effects with a quadratic speed vs field dependence are gaining research interest since an alternating current field could drive them. Here, we report on the giant nonlinearity of electrophoresis in a nematic liquid crystal in which the speed grows with the fourth and sixth powers of the electric field. The mechanism is attributed to the shear thinning of the nematic environment induced by the moving colloid. The observed giant nonlinear effect dramatically enhances the efficiency of electrophoretic transport.

Hierarchical Organization of Single Crystal Polymorphs of Azobenzene Chromophore in Anisotropic Media Subjected to Local Thermal Gradients upon Cold Spraying.

The present article entails the emergence of diverse crystal polymorphs following thermal quenching into various coexistence regions of binary azobenzene chromophore (ACh)/diacrylate (DA) solution and of azobenzene/nematic liquid crystal (E7) mixture. Development of various crystal topologies encompassing rhomboidal and hexagonal shapes can be witnessed in a manner dependent on thermal quenched depths into the crystal + liquid coexistence region of ACh/DA system. Upon spraying with compressed carbon dioxide (CO2 ) fluid, the local temperature gradient is generated resulting in spherulitic morphology showing discrete lamellae undergoing twisting locally in some regions and branched dendrites or seaweeds in another. When ACh/E7 blend is sprayed using compressed CO2 fluid, hierarchical organization of various discrete faceted single crystals including needle, rectangular, rhombus, and truncated hexagonal crystals radiating from the spherulite core can be discerned in a brighter region (off cross-polarization) polarized optical microscopy (POM) and nematic disclination in a darker cross-polarized region. Of particular interest is that the observed faceted single-crystal polymorphs in ACh/E7 may be contrasted to the lamellar twisting and branching observed in the ACh/DA system and plausible mechanisms of polymer spherulitic growth are discussed.

Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with an isotropic phase.

Nuclei of ordered materials emerging from the isotropic state usually show a shape topologically equivalent to a sphere; the well-known examples are crystals and nematic liquid crystal droplets. In this work, we explore experimentally and theoretically the toroidal in shape nuclei of columnar lyotropic chromonic liquid crystals coexisting with the isotropic phase. The geometry of these toroids depends strongly on concentrations of the disodium cromoglycate (DSCG) and the crowding agent, polyethylene glycol (PEG). High concentrations of DSCG and PEG result in thick toroids with small central holes, while low concentrations yield thin toroids with wide holes. The multitude of the observed shapes is explained by the balance of bending elasticity and anisotropic interfacial tension.

Ion-dependent DNA configuration in bacteriophage capsids.

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Stability analysis of flow of active extensile fibers in confined domains.

In this article, we study shear flow of active extensile filaments confined in a narrow channel. They behave as nematic liquid crystals that we assumed are governed by the Ericksen-Leslie equations of balance of linear and angular momentum. The addition of an activity source term in the Leslie stress captures the role of the biofuel prompting the dynamics. The dimensionless form of the governing system includes the Ericksen, activity, and Reynolds numbers together with the aspect ratio of the channel as the main driving parameters affecting the stability of the system. The active system that guides our analysis is composed of microtubules concentrated in bundles, hundreds of microns long, placed in a narrow channel domain, of aspect ratios in the range between 10-2 and 10-3 dimensionless units, which are able to align due to the combination of adenosine triphosphate-supplied energy and confinement effects. Specifically, this work aims at studying the role of confinement on the behavior of active matter. It is experimentally observed that, at an appropriately low activity and channel width, the active flow is laminar, with the linear velocity profile and the angle of alignment analogous to those in passive shear, developing defects and becoming chaotic, at a large activity and a channel aspect ratio. The present work addresses the laminar regime, where defect formation does not play a role. We perform a normal mode stability analysis of the base shear flow. A comprehensive description of the stability properties is obtained in terms of the driving parameters of the system. Our main finding, in addition to the geometry and magnitude of the flow profiles, and also consistent with the experimental observations, is that the transition to instability of the uniformly aligned shear flow occurs at a threshold value of the activity parameter, with the transition also being affected by the channel aspect ratio. The role of the parameters on the vorticity and angular profiles of the perturbing flow is also analyzed and found to agree with the experimentally observed transition to turbulent regimes. A spectral method based on Chebyshev polynomials is used to solve the generalized eigenvalue problems arising in the stability analysis.

Topological transformations of a nematic drop.

Morphogenesis of living systems involves topological shape transformations which are highly unusual in the inanimate world. Here, we demonstrate that a droplet of a nematic liquid crystal changes its equilibrium shape from a simply connected tactoid, which is topologically equivalent to a sphere, to a torus, which is not simply connected. The topological shape transformation is caused by the interplay of nematic elastic constants, which facilitates splay and bend of molecular orientations in tactoids but hinders splay in the toroids. The elastic anisotropy mechanism might be helpful in understanding topology transformations in morphogenesis and paves the way to control and transform shapes of droplets of liquid crystals and related soft materials.

Shear flow of active matter in thin channels.

We study the shear flow of active filaments confined in a thin channel for extensile and contractile fibers. We apply the Ericksen-Leslie equations of liquid crystal flow with an activity source term. The dimensionless form of this system includes the Ericksen, activity, and Reynolds numbers, together with the aspect ratio of the channel, as the main driving parameters. We perform a normal mode stability analysis of the base shear flow. For both types of fibers, we arrive at a comprehensive description of the stability properties and their dependence on the parameters of the system. The transition to unstable frequencies in extensile fibers occurs at a positive threshold value of the activity parameter, whereas for contractile ones a complex behavior is found at low absolute value of the activity number. The latter might be an indication of the biologically relevant plasticity and phase transition issues. In contrast with extensile fibers, flows of contractile ones are also found to be highly sensitive to the Reynolds number. The work on extensile fibers is guided by experiments on active filaments in confined channels and aims at quantifying their findings in the prechaotic regime.

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

Discrete-to-continuum modeling of weakly interacting incommensurate chains.

In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross section of a three-dimensional system consisting of a graphene sheet suspended over a substrate. The continuum model recovers both qualitatively and quantitatively the behavior observed in the corresponding discrete model. The numerical solutions for both models demonstrate the presence of large commensurate regions separated by localized incommensurate domain walls.

Electro-osmosis in nematic liquid crystals.

We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. We verify the model by comparing its predictions to the results of the experiments on the substrate-controlled liquid-crystal-enabled electrokinetics. In the experiments, a nematic liquid crystal confined to a thin planar cell with surface-patterned anchoring conditions exhibits electro-osmotic flows along the "guiding rails" imposed by the spatially varying director. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix and the full set of nematic viscosities.

Swimming photochromic azobenzene single crystals in triacrylate solution.

Self-motion of a growing single crystal of azobenzene chromophore in triacrylate solution (TA) is investigated in relation to the solid-liquid phase diagram bound by the solidus and liquidus lines. Upon thermal quenching from the isotropic melt to the crystal + liquid gap, various single crystals develop in a manner dependent on concentration and supercooling depth. During the crystal growth, TA solvent is rejected from the growing faceted fronts, enriching with TA in close proximity to the crystal-solution interface. The concentration gradient that formed as the result of TA expulsion induces convective flows in the solution and generates spatial variability of surface tension usually responsible for Marangoni effect. Either or both of these phenomena may have contributed to the observed self-motion including swimming, sinking, and floating of the azobenzene rhomboidal crystal in TA solution. A stationary rhomboidal crystal is also shown to swim upon irradiation with the UV light because of a mechanical torque generated by the trans-cis isomerization. Judging from the sinking or floating behavior of the azobenzene crystal, it may be inferred that the nucleation occurs at the solution-air interface.

Snell's law of refraction observed in thermal frontal polymerization.

We demonstrate that Snell's law of refraction can be applied to thermal fronts propagating through a boundary between regions that support distinct frontal velocities. We use the free-radical frontal polymerization of a triacrylate with clay filler that allows for two domains containing two different concentrations of a peroxide initiator to be molded together. Because the polymerization reaction rates depend on the initiator concentration, the propagation speed is different in each domain. We study fronts propagating in two parallel strips in which the incident angle is 90 degrees. Our data fit Snell's law v(r)/v(i)=sin theta(r)/sin theta(i), where v(r) is the refracted velocity, v(i) is the incident velocity, theta(r) is the angle of refraction, and theta(i) is the incident angle. Further, we study circular fronts propagating radially from an initiation point in a high-velocity region into a low-velocity region (and vice versa). We demonstrate the close resemblance between the numerically simulated and experimentally observed thermal reaction fronts. By measuring the normal velocity and the angle of refraction of both simulated and experimental fronts, we establish that Snell's law holds for thermal frontal polymerization in our experimental system. Finally we discuss the regimes in which Snell's law may not be valid.