1,721,004 research outputs found
Stability Against the Odds: The Case of Chromonic Liquid Crystals
Full text linkThe ground state of chromonic liquid crystals, as revealed by a number of recent experiments, is quite different from that of ordinary nematic liquid crystals: it is twisted instead of uniform. The common explanation provided for this state within the classical elastic theory of Frank demands that one Ericksen’s inequality is violated. Since in general such a violation makes Frank’s elastic free-energy functional unbounded below, the question arises as to whether the twisted ground state can be locally stable. We answer this question in the affirmative. In reaching this conclusion, a central role is played by the specific boundary conditions imposed in the experiments on the boundary of rigid containers and by a general formula that we derive here for the second variation in Frank’s elastic free energy
Shape bistability in 2D chromonic droplets
No full textAn extensive experimental study of the shapes of two-dimensional bipolar droplets of the chromonic nematic phase of disodium cromoglycate (DSCG) sandwiched between glass plates, by Kim et al was published in (2013 J. Phys.: Condens. Matter 25 404202). The paper includes a mathematical model of this system. We have extended this study by further theoretical modelling. Our results are in good, quantitative agreement with the experimental data. The model has produced what promises to be a more accurate estimate for the isotropic surface tension at the nematic/isotropic solution interface - and predicts a regime of shape bistability (which has not yet been observed) for larger droplets, where tactoids (pointed, zeppelin-shaped droplets) and smooth-edged discoids can coexist in equilibrium. The general method presented in this paper is also applied to the tactoids formed by F-actin filaments in solution, for which an estimate is given for the value of the isotropic surface tension at the nematic/isotropic interface
Geometric method to determine planar anchoring strength for chromonics
No full textChromonic nematics are lyotropic liquid crystals that have already been known for half a century, but have only recently raised interest for their potential applications in life sciences. Determining elastic constants and anchoring strengths for rigid substrates has thus become a priority in the characterization of these materials. Here we present a method to determine chromonics' planar anchoring strength. We call it geometric as it is based on recognition and fitting of the stable equilibrium shapes of droplets surrounded by the isotropic phase in a thin cell with plates enforcing parallel alignments of the nematic director. We apply our method to shapes observed in experiments; they resemble elongated rods with round ends, which are called bâtonnets. Our theory also predicts other droplets' equilibrium shapes, which are either slender and round, called discoids, or slender and pointed, called tactoids. In particular, sufficiently small droplets are expected to display shape bistability, with two equilibrium shapes, one tactoid and one discoid, exchanging roles as stable and metastable shapes upon varying their common area
Singular twist waves in chromonic liquid crystals
No full textChromonic liquid crystals are lyotropic nematic phases whose applications span from food to drug industries. It has recently been suggested that the elastic energy density governing the equilibrium distortions of these materials may be quartic in the measure of twist. Here we show that the non-linear twist-wave equation associated with such an energy has smooth solutions that break down in a finite time, giving rise to the formation of a shock wave, under rather generic assumptions on the initial profile. The critical time at which smooth solutions become singular is estimated analytically with an accuracy that numerical calculations for a number of exemplary cases prove to be satisfactory
Paradoxes for chromonic liquid crystal droplets
No full textChromonic liquid crystals constitute a novel lyotropic phase, whose elastic properties have so far been modeled within the classical Oseen-Frank theory, provided that the twist constant is assumed to be considerably smaller than the saddle-splay constant, in violation of one Ericksen inequality. This paper shows that paradoxical consequences follow from such a violation for droplets of these materials surrounded by an isotropic fluid. For example, tactoids with a degenerate planar anchoring simply disintegrate indefinitely in myriads of smaller ones
Singular Damped Twist Waves in Chromonic Liquid Crystals
Full text linkChromonics are special classes of nematic liquid crystals, for which a quartic elastic theory seems to be more appropriate than the classical quadratic Oseen–Frank theory. The relaxation dynamics of twist director profiles are known to develop a shock wave in finite time in the inviscid case, where dissipation is neglected. This paper studies the dissipative case. We give a sufficient criterion for the formation of shocks in the presence of dissipation, and we estimate the critical time at which these singularities develop. Both criterion and estimate depend on the initial director profile. We put our theory to the test on a class of initial kink profiles, and we show how accurate our estimates are by comparing them to the outcomes of numerical solutions
What a twist cell experiment tells about a quartic twist theory for chromonics
No full textThe elastic theory of chromonic liquid crystals is not completely established. We know, for example, that for anomalously low twist constants (needed for chromonics) the classical Oseen-Frank theory may entail paradoxical consequences when applied to describe the equilibrium shapes of droplets surrounded by an isotropic phase: contrary to experimental evidence, they are predicted to dissolve in a plethora of unstable smaller droplets. We proposed a quartic twist theory that prevents such an instability from happening. Here, we apply this theory to the data of two experiments devised to measure the planar anchoring strength at the plates bounding a twist cell filled with a chromonic liquid crystal; these data had previously been interpreted within the Oseen-Frank theory. We show that the quartic twist theory affords a better agreement with the experimental data, while delivering in one case a larger value for the anchoring strength
Spiralling defect cores in chromonic hedgehogs
No full textAn elastic quartic twist theory has recently been proposed for chromonic liquid crystals, intended to overcome the paradoxical conclusions encountered by the classical Oseen-Frank theory when applied to droplets submerged in an isotropic fluid environment. However, available experimental data for chromonics confined to cylindrical cavities with degenerate planar anchoring on their lateral boundary can be explained equally well by both competing theories. This paper identifies a means to differentiate these theories both qualitatively and quantitatively. They are shown to predict quite different core defects for the twisted hedgehogs that chromonics generate when confined to a fixed spherical cavity with homeotropic anchoring. In the quartic twist theory, the defect core is estimated to be nearly one order of magnitude larger (few microns) than in the other and, correspondingly, the director field lines describe Archimedean spirals instead of logarithmic ones
An Elastic Quartic Twist Theory for Chromonic Liquid Crystals
Full text linkChromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen’s inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist (Paparini and Virga in Phys. Rev. E 106: 044703, 2022). To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate
Spiralling defect cores in chromonic hedgehogs
No full textAn elastic quartic twist theory has recently been proposed for chromonic liquid crystals, intended to overcome the paradoxical conclusions encountered by the classical Oseen-Frank theory when applied to droplets submerged in an isotropic fluid environment. However, available experimental data for chromonics confined to cylindrical cavities with degenerate planar anchoring on their lateral boundary can be explained equally well by both competing theories. This paper identifies a means to differentiate these theories both qualitatively and quantitatively. They are shown to predict quite different core defects for the twisted hedgehogs that chromonics generate when confined to a fixed spherical cavity with homeotropic anchoring. In the quartic twist theory, the defect core is estimated to be nearly one order of magnitude larger (few microns) than in the other and, correspondingly, the director field lines describe Archimedean spirals instead of logarithmic ones
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