arXiv subjects

Jonathan V. Selinger

Publications and source records attributed to Jonathan V. Selinger.

At least 19 recordsLinked to original sources

arXiv2026

Theory of hybrid defects, with coupled orientational order parameters, on flat and curved surfaces

Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic order. In these systems, defect structures can be quite complex. Here, we investigate phases with two types of two-dimensional orientational order, $m$-atic and $n$-atic, where $m$ and $n$ are two distinct integers. We simulate these phases in a flat disk with strong radial anchoring, and on a spherical surface, because both of these geometries require the presence of defects. If the coupling between the two types of order is weak, then the defects are connected by a network of diffuse walls, and the system forms a stable domain structure. As the coupling increases, the domain walls become sharper and shorter. For very strong coupling, the higher-order defects merge into the lower-order defects, forming stretched defect cores.

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arXiv2025

Spontaneous Cholesteric Phase in Ferroelectric Nematic Liquid Crystals: Preference for Integer Number of Pitches

In a ferroelectric nematic liquid crystal, the electrostatic interaction can induce a spontaneous cholesteric helix, even if the material is not chiral. If the liquid-crystal cell is infinitely thick, then the predicted pitch depends continuously on material parameters. Here, we consider how the prediction must be modified in a cell of finite thickness. If the Debye screening length is large enough, we find that the free energy has multiple minima. In these minima, the cholesteric pitch is locked to the cell thickness, so that the cell contains an integer number of pitches. However, if the screening length is smaller, then the cholesteric pitch can vary continuously.

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arXiv2024

Flexoelectricity versus Electrostatics in Polar Nematic Liquid Crystals

Polar nematic liquid crystals have two special features, compared with conventional nematic liquid crystals. First, because of flexoelectricity, the combination of polar order and splay reduces the free energy. Second, because of electrostatics, any splay generates a bound charge density, which increases the free energy. To assess the competition between these two effects, we develop a theory that combines flexoelectricity and electrostatics. The theory predicts a phase diagram that includes ferroelectric, antiferroelectric, and conventional nematic phases.

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arXiv2023

Applications of the Peach-Koehler Force in Liquid Crystals

In solids, external stress induces the Peach-Koehler force, which drives dislocations to move. Similarly, in liquid crystals, an external angular stress creates an analogous force, which drives disclinations to move. In this work, we develop a method to calculate the relevant angular stress either analytically or numerically, and hence to determine the force on a disclination. We demonstrate this method by applying the Peach-Koehler force theory to four problems: (a) Single disclination in a liquid crystal cell between two uniform in-plane alignments perpendicular to each other. (b) Array of disclinations in a liquid crystal cell with patterned substrates. (c) Pair of disclinations in a long capillary tube with homeotropic anchoring. (d) Radial hedgehog or disclination loop inside a sphere with homeotropic anchoring, and its response to an applied magnetic field. In all of these problems, the Peach-Koehler force theory predicts the equilibrium defect structure, and the predictions are consistent with the results of minimizing the total free energy.

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arXiv2022

Frank-Read Mechanism in Nematic Liquid Crystals

In a crystalline solid under mechanical stress, a Frank-Read source is a pinned dislocation segment that repeatedly bows and detaches, generating concentric dislocation loops. We demonstrate that in nematic liquid crystals, an analogous Frank-Read mechanism can generate concentric disclination loops. Using experiment, simulation, and theory, we study a disclination segment pinned between surface defects on one substrate in a nematic cell. Under applied twist of the nematic director, the pinned segment bows and emits a new disclination loop which expands, leaving the original segment intact; loop emission repeats for each additional 180$^\circ$ of applied twist. We present experimental micrographs showing loop expansion and snap-off, numerical simulations of loop emission under both quasistatic and dynamic loading, and theoretical analysis considering both free energy minimization and the balance of competing forces. We find that the critical stress for disclination loop emission scales as the inverse of segment length, and changes as a function of strain rate and temperature, in close analogy to the Frank-Read source mechanism in crystals. Lastly, we discuss how Frank-Read sources could be used to modify microstructural evolution in both passive and active nematics.

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arXiv2022

Explicit Demonstration of Geometric Frustration in Chiral Liquid Crystals

Many solid materials and liquid crystals exhibit geometric frustration, meaning that they have an ideal local structure that cannot fill up space. For that reason, the global phase must be a compromise between the ideal local structure and geometric constraints. As an explicit example of geometric frustration, we consider a chiral liquid crystal confined in a long cylinder with free boundaries. When the radius of the tube is sufficiently small, the director field forms a double-twist configuration, which is the ideal local structure. However, when the radius becomes larger (compared with the natural twist of the liquid crystal), the double-twist structure cannot fill space, and hence the director field must transform into some other chiral structure that can fill space. This space-filling structure may be either (1) a cholesteric phase with single twist, or (2) a set of double-twist regions separated by a disclination, which can be regarded as the beginning of a blue phase. We investigate these structures using theory and simulations, and show how the relative free energies depend on the system size, the natural twist, and the disclination energy. As another example, we also study a cholesteric liquid crystal confined between two infinite parallel plates with free boundaries.

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arXiv2022

Violation of Ericksen inequalities in lyotropic chromonic liquid crystals

By analyzing elastic theory for nematic liquid crystals, we distinguish three regimes of elastic constants. In one regime, the Ericksen inequalities are satisfied, and the ground state of the director field is uniform. In a second regime, certain necessary inequalities are violated, and the free energy is thermodynamically unstable. Between those possibilities, there is an intermediate regime, where the Ericksen inequalities are violated but the system is still stable. Remarkably, lyotropic chromonic liquid crystals are in the intermediate regime. We investigate the nonuniform structure of the director field in that regime, show that it depends sensitively on system geometry, and discuss the implications for lyotropic chromonic liquid crystals.

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arXiv2021

Modulated phases of nematic liquid crystals induced by tetrahedral order

Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes: twist, bend, splay, and a fourth mode $\Delta$ related to saddle-splay. The first three of these modes are known to induce modulated phases. Here, we consider modulated phases induced by the fourth mode. We develop a theory for tetrahedral order in liquid crystals, and show that it couples to the $\Delta$ mode of director deformation. Because of geometric frustration, the $\Delta$ mode cannot fill space by itself, but rather must be accompanied by twist or splay. Hence, it may induce a spontaneous cholesteric phase, with either handedness, or a splay nematic phase.

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arXiv2021

Coarse-grained theory for motion of solitons and skyrmions in liquid crystals

Recent experiments have found that applied electric fields can induce motion of skyrmions in chiral nematic liquid crystals. To understand the magnitude and direction of the induced motion, we develop a coarse-grained approach to describe dynamics of skyrmions, similar to our group's previous work on the dynamics of disclinations. In this approach, we represent a localized excitation in terms of a few macroscopic degrees of freedom, including the position of the excitation and the orientation of the background director. We then derive the Rayleigh dissipation function, and hence the equations of motion, in terms of these macroscopic variables. We demonstrate this theoretical approach for 1D motion of a sine-Gordon soliton, and then extend it to 2D motion of a skyrmion. Our results show that skyrmions move in a direction perpendicular to the induced tilt of the background director. When the applied field is removed, skyrmions move in the opposite direction but not with equal magnitude, and hence the overall motion may be rectified.

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arXiv2021

Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals

This article analyzes modulated phases in liquid crystals, from the long-established cholesteric and blue phases to the recently discovered twist-bend, splay-bend, and splay nematic phases, as well as the twist-grain-boundary (TGB) and helical nanofilament variations on smectic phases. The analysis uses the concept of four fundamental modes of director deformation: twist, bend, splay, and a fourth mode related to saddle-splay. Each mode is coupled to a specific type of molecular order: chirality, polarization perpendicular and parallel to the director, and octupolar order. When the liquid crystal develops one type of spontaneous order, the ideal local structure becomes nonuniform, with the corresponding director deformation. In general, the ideal local structure is frustrated; it cannot fill space. As a result, the liquid crystal must form a complex global phase, which may have a combination of deformation modes, and may have a periodic array of defects. Thus, the concept of an ideal local structure under geometric frustration provides a unified framework to understand the wide variety of modulated phases.

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arXiv2020

Alignment induced re-configurable walls for patterning and assembly of liquid crystal skyrmions

Skyrmions have attracted rapidly growing interest due to their topological properties and unique aspects for potential novel applications such as data storage and soft robotics. They can also serve as key elements for materials by design, self-assembly, and functional soft materials. While not real particles, these skyrmions behave like particles-they interact with each other and can be actuated by means of electric field, surface anchoring, and light. On the other hand, they are field configurations which have properties not possessed by real particles. Here, we show that, by means of alignment induced attractive and repulsive walls, skyrmions in chiral nematic liquid crystals can be precisely controlled and programmed to serve as suitable building blocks for the realization of the above goals. Our work may stimulate new experimental efforts and concomitant applications in this direction.

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arXiv2020

Geometry and mechanics of disclination lines in 3D nematic liquid crystals

In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble $+1/2$ or $-1/2$ defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the director deformation modes around the disclination, as well as the nematic order tensor inside the disclination core. Based on this analysis, we construct a vector to represent the orientation of the disclination, as well as tensors to represent higher-order structure. We apply this method to simulations of a 3D disclination arch, and determine how the structure changes along the contour length. We then use this geometric analysis to investigate three types of forces acting on a disclination: Peach-Koehler forces due to external stress, interaction forces between disclination lines, and active forces. These results apply to the motion of disclination lines in both conventional and active liquid crystals.

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arXiv2020

Alignment of a topological defect by an activity gradient

As a method for controlling active materials, researchers have suggested designing patterns of activity on a substrate, which should guide the motion of topological defects. To investigate this concept, we model the behavior of a single defect of topological charge $+1/2$, moving in an activity gradient. This modeling uses three methods: (1) approximate analytic solution of hydrodynamic equations, (2) macroscopic, symmetry-based theory of the defect as an effective oriented particle, and (3) numerical simulation. All three methods show that an activity gradient aligns the defect orientation, and hence should be useful to control defect motion.

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arXiv2020

Liquid crystal director fields in three-dimensional non-Euclidean geometries

This paper investigates nematic liquid crystals in three-dimensional curved space, and determines which director deformation modes are compatible with each possible type of non-Euclidean geometry. Previous work by Sethna et al. showed that double twist is frustrated in flat space $R^3$, but can fit perfectly in the hypersphere $S^3$. Here, we extend that work to all four deformation modes (splay, twist, bend, and biaxial splay) and all eight Thurston geometries. Each pure mode of director deformation can fill space perfectly, for at least one type of geometry. This analysis shows the ideal structure of each deformation mode in curved space, which is frustrated by the requirements of flat space.

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arXiv2020

Annihilation trajectory of defects in smectic-C films

In a 2D liquid crystal, each topological defect has a topological charge and a characteristic orientation, and hence can be regarded as an oriented particle. Theories predict that the trajectories of annihilating defects depend on their relative orientation. Recently, these predictions have been tested in experiments on smectic-C films. Those experiments find curved trajectories that are similar to the predictions, but the detailed relationship between the defect orientations and the far-field director is different. To understand this difference, we extend the previous theories by adding the effects of elastic anisotropy, and find that it significantly changes the curved trajectories.

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arXiv2020

Theory of the splay nematic phase: Single vs. double splay

Recent experiments have reported a novel splay nematic phase, which has alternating domains of positive and negative splay. To model this phase, previous studies have considered a 1D splay modulation of the director field, accompanied by a 1D modulation of polar order. When the flexoelectric coupling between splay and polar order becomes sufficiently strong, the uniform nematic state becomes unstable to the formation of a modulated phase. Here, we re-examine this theory in terms of a new approach to liquid crystal elasticity, which shows that pure splay deformation is double splay rather than planar single splay. Following that reasoning, we propose a structure with a 2D splay modulation of the director field, accompanied by a 2D modulation of polar order, and show that the 2D structure generally has a lower free energy than the 1D structure.

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arXiv2019

Minimization principle for shear alignment of liquid crystals

If a static perturbation is applied to a liquid crystal, the director configuration changes to minimize the free energy. If a shear flow is applied to a liquid crystal, one might ask: Does the director configuration change to minimize any effective potential? To address that question, we derive the Leslie-Ericksen equations for dissipative dynamics, and determine whether they can be expressed as relaxation toward a minimum. The answer may be yes or no, depending on the number of degrees of freedom. Using theory and simulations, we consider two specific examples, reverse tilt domains under simple shear flow and dowser configurations under plane Poiseuille flow, and demonstrate that each example shows relaxation toward the minimum of an effective potential.

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arXiv2019

Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals

This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which breaks the director gradient tensor into four distinct types of mathematical objects, representing splay, twist, bend, and a fourth deformation mode. With this construction, the Oseen-Frank free energy can be written as the sum of squares of the four modes, and saddle-splay can be regarded as bulk rather than surface elasticity. This interpretation leads to an alternative way to think about several previous results in liquid-crystal physics, including: (1) free energy balance between cholesteric and blue phases, (2) director deformations in hybrid-aligned-nematic cells, (3) spontaneous twist of achiral liquid crystals confined in a torus or cylinder, and (4) curvature of smectic layers.

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