arXiv subjects

Jonathan V. Selinger

Publications and source records attributed to Jonathan V. Selinger.

At least 37 records · Page 2Linked to original sources

arXiv2018

Theory of defect motion in 2D passive and active nematic liquid crystals

The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the dynamics of orientational order is coupled with backflow of the fluid, and because a liquid crystal has several distinct viscosity coefficients. Here, we suggest a coarse-grained, variational approach, which describes the motion of defects as effective `particles.' For passive liquid crystals, the theory shows how the drag depends on defect orientation, and shows the coupling between translational and rotational motion. For active liquid crystals, the theory provides an alternative way to describe motion induced by the activity coefficient.

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arXiv2017

Active Brownian particles near straight or curved walls: Pressure and boundary layers

Unlike equilibrium systems, active matter is not governed by the conventional laws of thermodynamics. Through a series of analytic calculations and Langevin dynamics simulations, we explore how systems cross over from equilibrium to active behavior as the activity is increased. In particular, we calculate the profiles of density and orientational order near straight or circular walls, and show the characteristic width of the boundary layers. We find a simple relationship between the enhancements of density and pressure near a wall. Based on these results, we determine how the pressure depends on wall curvature, and hence make approximate analytic predictions for the motion of curved tracers, as well as the rectification of active particles around small openings in confined geometries.

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arXiv2017

Comparing skyrmions and merons in chiral liquid crystals and magnets

When chiral liquid crystals or magnets are subjected to applied fields or other anisotropic environments, the competition between favored twist and anisotropy leads to the formation of complex defect structures. In some cases, the defects are skyrmions, which have 180° double twist going outward from the center, and hence can pack together without singularities in the orientational order. In other cases, the defects are merons, which have 90° double twist going outward from the center; packing such merons requires singularities in the orientational order. In the liquid crystal context, a lattice of merons is regarded as a blue phase. Here, we perform theoretical and computational studies of skyrmions and merons in chiral liquid crystals and magnets. Through these studies, we calculate the phase diagrams for liquid crystals and magnets in terms of dimensionless ratios of energetic parameters. We also predict the range of metastability for liquid crystal skyrmions, and show that these skyrmions can move and interact as effective particles. The results show how the properties of skyrmions and merons depend on the vector or tensor nature of the order parameter.

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arXiv2017

Orientation of topological defects in 2D nematic liquid crystals

Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter, 2016, 12, 6490] pointed out that topological defects are not point-like objects but actually have orientational properties, which strongly affect the energetics and motion of the defects. That paper developed a mathematical formalism which describes the orientational properties as vectors. Here, we agree with the basic concept of defect orientation, but we suggest an alternative mathematical formalism. We represent the defect orientation by a tensor, with a rank that depends on the topological charge: rank 1 for a charge of +1/2, rank 3 for a charge of -1/2. Using this tensor formalism, we calculate the orientation-dependent interaction between defects, and we present numerical simulations of defect motion.

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arXiv2017

Theory of helicoids and skyrmions in confined cholesteric liquid crystals

Cholesteric liquid crystals experience geometric frustration when they are confined between surfaces with anchoring conditions that are incompatible with the cholesteric twist. Because of this frustration, they develop complex topological defect structures, which may be helicoids or skyrmions. We develop a theory for these structures, which extends previous theoretical research by deriving exact solutions for helicoids with the assumption of constant azimuth, calculating numerical solutions for helicoids and skyrmions with varying azimuth, and interpreting the results in terms of competition between terms in the free energy.

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arXiv2016

Theory of Liquid Crystal Elastomers: From Polymer Physics to Differential Geometry

In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.

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arXiv2015

Dynamic Theory of Polydomain Liquid-Crystal Elastomers

When liquid-crystal elastomers are prepared without any alignment, disordered polydomain structures emerge as the materials are cooled into the nematic phase. These polydomain structures have been attributed to quenched disorder in the cross-linked polymer network. As an alternative explanation, we develop a theory for the dynamics of the isotropic-nematic transition in liquid-crystal elastomers, and show that the dynamics can induce a polydomain structure with a characteristic length scale, through a mechanism analogous to the Cahn-Hilliard equation for phase separation.

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arXiv2014

Brownian Motion of Arbitrarily Shaped Particles in Two-Dimensions

Here we implement microfabricated boomerang particles with unequal arm lengths as a model for non-symmetry particles and study their Brownian motion in a quasi-two dimensional geometry by using high precision single particle motion tracking. We show that due to the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a non-linear crossover from short time faster to long time slower diffusion, and the mean displacements for fixed initial orientation are non-zero and saturate out at long time. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e. the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in 3D where the CoH only exists for high symmetry particles, the CoH always exists for Brownian motion in 2D. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the 6 anisotropic diffusion coefficients only 5 are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally we classify the behavior of 2D Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group.

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arXiv2014

Modeling Smectic Layers in Confined Geometries: Order Parameter and Defects

We identify problems with the standard complex order parameter formalism for smectic-A (SmA) liquid crystals, and discuss possible alternative descriptions of smectic order. In particular, we suggest an approach based on the real smectic density variation rather than a complex order parameter. This approach gives reasonable numerical results for the smectic layer configuration and director field in sample geometries, and can be used to model smectic liquid crystals under nanoscale confinement for technological applications.

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arXiv2014

Theory of Polar Blue Phases

In liquid crystals, if flexoelectric couplings between polar order and director gradients are strong enough, the uniform nematic phase can become unstable to formation of a modulated polar phase. Previous theories have predicted two types of modulation, twist-bend and splay-bend; the twist-bend phase has been found in recent experiments. Here, we investigate other types of modulation, using lattice simulations and Landau theory. In addition to twist-bend and splay-bend, we also find polar blue phases, with 2D or 3D modulations of both director and polar order. We compare polar blue phases with chiral blue phases, and discuss opportunities for observing them experimentally.

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arXiv2013

Brownian Motion of Boomerang Colloidal Particles

We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short time faster to long time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to a superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

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arXiv2013

Polymer-disordered liquid crystals: Susceptibility to electric field

When nematic liquid crystals are embedded in random polymer networks, the disordered environment disrupts the long-range order, producing a glassy state. If an electric field is applied, it induces large and fairly temperature-independent orientational order. To understand the experiments, we simulate a liquid crystal in a disordered polymer network, visualize the domain structure, and calculate the response to a field. Furthermore, using an Imry-Ma-like approach we predict the domain size and estimate the field-induced order. The simulations and analytic results agree with each other, and suggest how the materials can be optimized for electro-optic applications.

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arXiv2013

Statistical mechanics of bend flexoelectricity and the twist-bend phase in bent-core liquid crystals

We develop a Landau theory for bend flexoelectricity in liquid crystals of bent-core molecules. In the nematic phase of the model, the bend flexoelectric coefficient increases as we reduce the temperature toward the nematic to polar phase transition. At this critical point, there is a second order transition from high-temperature uniform nematic phase to low-temperature nonuniform polar phase composed of twist-bend or splay-bend deformations. To test the predictions of Landau theory, we perform Monte Carlo simulations to find the director and polarization configurations as functions of temperature, applied electric field, and interaction parameters.

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arXiv2013

Lipid Segregation on Cylindrically and Spherically Curved Membranes

We investigate how an externally imposed curvature influences lipid segregation on two-phase-coexistent membranes. We show that the bending-modulus contrast of the two phases and the curvature act together to yield a reduced effective line tension. On largely curved membranes, a state of multiple domains (or rafts) forms due to a mechanism analogous to that causing magnetic-vortex formation in type-II superconductors. We determine the criterion for such multi-domain state to occur; we then calculate respectively the size of the domains formed on cylindrically and spherically curved membranes.

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arXiv2013

Shape and Chirality Transitions in Off-Axis Twist Nematic Elastomer Ribbons

Using both experiments and finite element simulations, we explore the shape evolution of off-axis nematic elastomer ribbons as a function of temperature. The elastomers are prepared by cross-linking the mesogens with planar anchoring of the director at top and bottom surfaces with a 90 degree left-handed twist. Shape evolution depends sensitively on the off-axis director orientation at the sample mid-plane. When the director at midplane is parallel to either the ribbon's long or short axes, ribbons form either helicoids or spirals depending on the aspect ratio and temperature. If the director at midplane is more than 5 degrees off-axis, then they form only spiral ribbons. Samples in all these geometries show a remarkable transition from right- to left-handed chiral shapes on change of temperature. Simulation studies provide insight into the mechanisms driving shape evolution and enable engineering design of these materials for future applications.

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arXiv2011

Coarse-Grained Modeling of a Deformable Nematic Vesicle

We develop a coarse-grained particle-based model to simulate membranes with nematic liquid-crystal order. The coarse-grained particles form vesicles which, at low temperature, have orientational order in the local tangent plane. As the strength of coupling between the nematic director and the vesicle curvature increases, the vesicles show a morphology transition from spherical to prolate and finally to a tube. We also observe the shape and defect arrangement around the tips of the prolate vesicle.

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arXiv2011

Deformation of an asymmetric thin film

Experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [Y. Klein, E. Efrati, and E. Sharon, Science 315, 1116 (2007)], we represent the effect of chemical vapors by a change in the target metric tensor. In this problem, unlike that earlier work, the target metric is asymmetric between the two sides of the film. Changing this metric induces a curvature of the film, which may be curvature into a partial cylinder or a partial sphere. We calculate the elastic energy for each of these shapes, and show that the sphere is favored for films smaller than a critical size, which depends on the film thickness, while the cylinder is favored for larger films.

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arXiv2011

Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals

Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals--increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [L. M. Lopatina and J. V. Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.

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