Spontaneous Splay Phases in Polar Nematic Liquid Crystals

Pleiner, Harald; Brand, H. R.

doi:10.1209/0295-5075/9/3/010

Cited by 46 publications

(49 citation statements)

References 14 publications

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“…[117][118][119] There it is assumed that the droplet contains some sort of 'active gel' material that can be described by a polarisation vector p (or alternatively by a tensorial nematic order parameter Q). The evolution of the polarisation field p follows an equation for polar liquid crystals, 120,121 generalised by active reactions 108,109 and coupled to the hydrodynamic flow field v (cf. Marth et al 117 and Tjhung et al 118 ).…”

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confidence: 99%

Computational approaches to substrate-based cell motility

Ziebert

Aranson

2016

npj Comput Mater

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Substrate-based crawling motility of eukaryotic cells is essential for many biological functions, both in developing and mature organisms. Motility dysfunctions are involved in several life-threatening pathologies such as cancer and metastasis. Motile cells are also a natural realisation of active, self-propelled 'particles', a popular research topic in nonequilibrium physics. Finally, from the materials perspective, assemblies of motile cells and evolving tissues constitute a class of adaptive self-healing materials that respond to the topography, elasticity and surface chemistry of the environment and react to external stimuli. Although a comprehensive understanding of substrate-based cell motility remains elusive, progress has been achieved recently in its modelling on the whole-cell level. Here we survey the most recent advances in computational approaches to cell movement and demonstrate how these models improve our understanding of complex self-organised systems such as living cells.

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confidence: 99%

Computational approaches to substrate-based cell motility

Ziebert

Aranson

2016

npj Comput Mater

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“…polar nematic LC exhibit opposite surface charges in the planes perpendicular to p, which give rise to destabilizing electrostatic forces. Second, the homogeneous state is not the energetic ground state, since the existence of P allows for spontaneous structures with a constant splay texture [10]. However, the latter cannot be space filling and is necessarily connected to defects.…”

Section: Polar Ordermentioning

confidence: 99%

Tetrahedral Order in Liquid Crystals

Pleiner

Brand

2016

Braz J Phys

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We review the impact of tetrahedral order on the macroscopic dynamics of bent-core liquid crystals. We discuss tetrahedral order comparing with other types of orientational order, like nematic, polar nematic, polar smectic, and active polar order. In particular, we present hydrodynamic equations for phases, where only tetrahedral order exists or tetrahedral order is combined with nematic order. Among the latter, we discriminate between three cases, where the nematic director (a) orients along a fourfold, (b) along a threefold symmetry axis of the tetrahedral structure, or (c) is homogeneously uncorrelated with the tetrahedron. For the optically isotropic T d phase, which only has tetrahedral order, we focus on the coupling of flow with, e.g., temperature gradients and on the specific orientation behavior in external electric fields. For the transition to the nematic phase, electric fields lead to a temperature shift that is linear in the field strength. Electric fields induce nematic order, again linear in the field strength. If strong enough, electric fields can change the tetrahedral structure and symmetry leading to a polar phase. We briefly deal with the T phase that arises when tetrahedral order occurs in a system of chiral molecules. To case (a), defined above, belong (i) the non-polar, achiral, optically uniaxial D2d phase with ambidextrous helicity (due to a linear gradient Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany free energy contribution) and with orientational frustration in external fields, (ii) the non-polar tetragonal S4 phase, (iii) the non-polar, orthorhombic D2 phase that is structurally chiral featuring ambidextrous chirality, (iv) the polar orthorhombic C2v phase, and (v) the polar, structurally chiral, monoclinic C2 phase. Case (b) results in a trigonal C3v phase that behaves like a biaxial polar nematic phase. An example for case (c) is a splay bend phase, where the ground state is inhomogeneous due to a linear gradient free energy contribution. Finally, we discuss some experiments that show typical effects related to the existence of tetrahedral order. A summary and perspective is given.

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“…In addition, with splay (internal and external) surfaces acquire charges that interact via Coulomb interaction, further reducing the stability of splay phases. For a thorough discussion of the possibility and stability of polar phases with splay textures in two and three dimensions we refer to [3]. As a result, splay phases can only exist close to T c or for large systems.…”

Section: Appendix a Ginzburg-landau Description Of The Phase Transitmentioning

confidence: 99%

“…7 a brief summary and conclusions. In appendix A we give a Ginzburg-Landau-type analysis of the isotropicferroelectric phase transition in polar nematic gels and elastomers thus generalizing earlier work done for low molecular weight liquid crystals [3]. This also defines the ground state whose hydrodynamics we are describing.…”

Section: Introductionmentioning

confidence: 95%

“…About three decades ago there were some early experimental efforts along these lines for nematic [1] and pyramidic [2] low molecular weight liquid crystals. These early experimental investigations triggered a theoretical study of GinzburgLandau type for polar nematics, where it was shown that spontaneous splay phases should play an important role in such systems [3]. More recently liquid crystalline phases formed by bent-core molecules were predicted [4] and shown experimentally [5,6] to have polar directions for smectic liquid crystalline phases.…”

Section: Introductionmentioning

confidence: 99%

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Macroscopic behavior of polar nematic gels and elastomers

2016

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Abstract. We present the derivation of the macroscopic equations for uniaxial polar nematic gels and elastomers. We include the strain field as well as relative rotations as independent dynamic macroscopic degrees of freedom. As a consequence, special emphasis is laid on possible static and dynamic cross-couplings between these macroscopic degrees of freedom associated with the network, and the other macroscopic degrees of freedom including reorientations of the macroscopic polarization. In particular, we find static and dissipative dynamic cross-couplings between strain fields and relative rotations on one hand and the macroscopic polarization on the other that allow for new possibilities to manipulate polar nematics. To give one example each for the effects of a static and a dissipative cross-coupling: we find that a static electric field applied perpendicularly to the polar preferred direction leads to relative rotations while dynamically relative rotations can lead to transverse electric currents. In addition to a permanent network, we also consider the effect of a transient network, which is particularly important for the case of gels, melts and concentrated polymer solutions. A section on the influence of macroscopic chirality is included as well.

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Spontaneous Splay Phases in Polar Nematic Liquid Crystals

Cited by 46 publications

References 14 publications

Computational approaches to substrate-based cell motility

Computational approaches to substrate-based cell motility

Tetrahedral Order in Liquid Crystals

Macroscopic behavior of polar nematic gels and elastomers

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