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Daddi-Moussa-Ider A, Tjhung E, Pradas M, Richter T, Menzel AM. Rotational dynamics of a disk in a thin film of weakly nematic fluid subject to linear friction. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:58. [PMID: 39322774 DOI: 10.1140/epje/s10189-024-00452-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2024] [Accepted: 09/09/2024] [Indexed: 09/27/2024]
Abstract
Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While in bulk isotropic fluids it is exhaustively studied, this is less so in anisotropic fluids and in confined situations. Here, we combine the latter two by studying the rotation of a disk-like inclusion in a uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms of a perturbative expansion in parameters that quantify anisotropies in viscosity and in additional linear friction with a supporting substrate or other type of confinement, we derive analytical expressions for the resulting hydrodynamic flow and pressure fields as well as for the resistance and mobility coefficients of the rotating disk. It turns out that, in contrast to translational motion, the solutions remain well-behaved also in the absence of the additional linear friction. Comparison with results from finite-element simulations shows very good agreement with those from our analytical calculations. Besides applications to describe technological systems, for instance, in the area of microfluidics and thin cells of aligned nematic liquid crystals, our solutions are important for quantitative theoretical approaches to fluid membranes and thin films in general featuring a preferred direction.
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Affiliation(s)
| | - Elsen Tjhung
- School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
| | - Marc Pradas
- School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK
| | - Thomas Richter
- Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany
| | - Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany
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2
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Híjar H, Majumdar A. Particle-based and continuum models for confined nematics in two dimensions. SOFT MATTER 2024; 20:3755-3770. [PMID: 38629234 DOI: 10.1039/d3sm01684f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2024]
Abstract
We use the particle-based stochastic multi-particle collision dynamics (N-MPCD) algorithm to simulate confined nematic liquid crystals in regular two-dimensional polygons such as squares, pentagons and hexagons. We consider a range of values of the nematicities, U, and simulation domain sizes, R, that canvass nano-sized polygons to micron-sized polygons. We use closure arguments to define mappings between the N-MPCD parameters and the parameters in the continuum deterministic Landau-de Gennes framework. The averaged N-MPCD configurations agree with those predicted by Landau-de Gennes theory, at least for large polygons. We study relaxation dynamics or the non-equilibrium dynamics of confined nematics in polygons, in the N-MPCD framework, and the kinetic traps bear strong resemblance to the unstable saddle points in the Landau-de Gennes framework. Finally, we study nematic defect dynamics inside the polygons in the N-MPCD framework and the finite-size effects slow down the defects and attract them to polygon vertices. Our work is a comprehensive comparison between particle-based stochastic N-MPCD methods and deterministic/continuum Landau-de Gennes methods, and this comparison is essential for new-age multiscale theories.
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Affiliation(s)
| | - Apala Majumdar
- Department of Mathematics and Statistics, University of Strathclyde, UK
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Macías-Durán J, Duarte-Alaniz V, Híjar H. Active nematic liquid crystals simulated by particle-based mesoscopic methods. SOFT MATTER 2023; 19:8052-8069. [PMID: 37700612 DOI: 10.1039/d3sm00481c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
Two Multi-particle collision dynamics algorithms that simulate nematic liquid crystals are generalised to reproduce active behaviour. One of the algorithms is due to Shendruk and Yeomans and is based on particles that carry an orientation vector ordered by a mean-field energy [T. N. Shendruk and J. M. Yeomans, Soft Matter, 2015, 11, 5101]. In the other algorithm, due to Mandal and Mazza, particles possess an order parameter tensor which evolves according to the Qian-Sheng model of nematohydrodynamics [S. Mandal and M. G. Mazza, Phys. Rev. E, 2019, 99, 063319]. For both methods activity is incorporated through a force proportional to the divergence of the local average order parameter tensor. Both implementations produce disclination curves in the nematic fluid that undergo nucleation and self-annihilation dynamics. Topological defects are found to be consistent with those observed in recent experiments of three-dimensional active nematics. Results permit to compare the length-scales over which the different nematic Multi-particle collision dynamics methods operate. The structure and dynamics of the orientation and flow fields agree with those obtained recently in numerical studies of continuum three-dimensional active nematics. Overall, our results open the opportunity to use mesoscopic particle-based approaches to study active liquid crystals in situations such as nonequilibrium states driven by flow or colloidal particles in active anisotropic solvents.
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Affiliation(s)
- Jesús Macías-Durán
- La Salle University Mexico, Benjamin Franklin 45, 06140, Mexico City, Mexico.
| | | | - Humberto Híjar
- La Salle University Mexico, Benjamin Franklin 45, 06140, Mexico City, Mexico.
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Poy G. Hidden traces of chirality in the fluctuations of a fully unwound cholesteric. SOFT MATTER 2023; 19:1115-1130. [PMID: 36722903 DOI: 10.1039/d2sm01646j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Confinement and hydrodynamic interactions often play an important role in the fluctuation dynamics of soft matter systems, which can typically be studied using light scattering techniques. With experimental and theoretical methodologies, I demonstrate here that chirality is an additional critical parameter that leads to diverging decay times and correlation lengths in chiral liquid crystal cells with a fully unwound cholesteric helix. This study combines light scattering measurements made in a tailored microscope geometry and theoretical calculations of the decay dynamics of chiral orientational fluctuations-including hydrodynamics-to establish the existence of two soft chiral modes of fluctuations driving the destabilization of the unwound cholesteric. Despite the achirality of the equilibrium state of unwound cholesterics, this study indicates that chirality hides itself in the orientational fluctuation modes and plays a major role in their dynamics, which can be exploited to locally measure the strength of chirality in frustrated chiral liquid crystal cells.
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Affiliation(s)
- Guilhem Poy
- L2C, Univ Montpellier, CNRS, Montpellier, France.
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5
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Menzel AM. When low-order expansions fail and all higher-order contributions matter-basic example of the mean squared displacement for Brownian motion. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:77. [PMID: 36121547 PMCID: PMC9485100 DOI: 10.1140/epje/s10189-022-00232-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 09/09/2022] [Indexed: 06/15/2023]
Abstract
Hardly any theoretically formulated realistic problem can be solved exactly. Therefore, as a standard, we resort to approximations. In this context, expansions play a major role. We are used to relying on lowest-order expansions and confining our point of view accordingly. However, one should always bear in mind that such considerations may fail at some point. Here, we address a very common example situation, namely, the motion of a Brownian particle. We know that the associated mean-squared displacement in the long term increases linearly in time. Yet, when we take the Fokker-Planck approach in combination with a low-order expansion, the direct route towards this result fails. That is, in the expansion the term linear in time vanishes. Instead, the treatment requires consideration of all higher-order contributions. Together, they restore the linear increase in time. In this way, we stress that care is always mandatory when resorting to low-order expansions, and we present in a traceable way a route to solving the considered problem.
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Affiliation(s)
- Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany.
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Pleiner H, Brand HR. Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers. PHYSICAL SCIENCES REVIEWS 2020. [DOI: 10.1515/psr-2019-0109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
We investigate theoretically the macroscopic dynamics of various types of ordered magnetic fluid, gel, and elastomeric phases. We take a symmetry point of view and emphasize its importance for a macroscopic description. The interactions and couplings among the relevant variables are based on their individual symmetry behavior, irrespective of the detailed nature of the microscopic interactions involved. Concerning the variables we discriminate between conserved variables related to a local conservation law, symmetry variables describing a (spontaneously) broken continuous symmetry (e.g., due to a preferred direction) and slowly relaxing ones that arise from special conditions of the system are considered. Among the relevant symmetries, we consider the behavior under spatial rotations (e.g., discriminating scalars, vectors or tensors), under spatial inversion (discriminating e.g., polar and axial vectors), and under time reversal symmetry (discriminating e.g., velocities from polarizations, or electric fields from magnetic ones). Those symmetries are crucial not only to find the possible cross-couplings correctly but also to get a description of the macroscopic dynamics that is compatible with thermodynamics. In particular, time reversal symmetry is decisive to get the second law of thermodynamics right. We discuss (conventional quadrupolar) nematic order, polar order, active polar order, as well as ferromagnetic order and tetrahedral (octupolar) order. In a second step, we show some of the consequences of the symmetry properties for the various systems that we have worked on within the SPP1681, including magnetic nematic (and cholesteric) elastomers, ferromagnetic nematics (also with tetrahedral order), ferromagnetic elastomers with tetrahedral order, gels and elastomers with polar or active polar order, and finally magnetorheological fluids and gels in a one- and two-fluid description.
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Affiliation(s)
- Harald Pleiner
- Max Planck Institute for Polymer Research , Mainz , Germany
| | - Helmut R. Brand
- Department of Physics , University of Bayreuth , Bayreuth , Germany
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Brand HR, Pleiner H. Cubic and tetragonal liquid crystal phases composed of non-chiral molecules: Chirality and macroscopic properties. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:142. [PMID: 31728772 DOI: 10.1140/epje/i2019-11906-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2019] [Accepted: 10/14/2019] [Indexed: 06/10/2023]
Abstract
We discuss the symmetry properties as well as the macroscopic behavior of the cubic liquid crystal phases showing large chiral domains of either hand in some non-chiral compounds reported recently in the group of Tschierske. These phases are tricontinuous. While they have O or I432 symmetry in each chiral domain, the overall symmetry is [Formula: see text] as there is no net chirality for compounds composed of non-chiral molecules. It turns out that a rather similar type of phase has also been reported for triblock copolymers. Here we analyze in detail the macroscopic static and dynamic behavior of such phases and we predict, among other results, that they show the analog of static and dissipative Lehmann-type effects in their chiral domains. A description of a cubic liquid crystalline phase of Th symmetry, which has not yet been found experimentally, is also included. Suggestions for experiments are outlined to identify such a phase. In addition, we discuss tetragonal liquid crystalline phases of D4h and D4 (I422) symmetry as they have been reported last year experimentally in connection to the Q phase.
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Affiliation(s)
- Helmut R Brand
- Department of Physics, University of Bayreuth, 95440, Bayreuth, Germany
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany
| | - Harald Pleiner
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany.
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Potisk T, Pleiner H, Brand HR. Influence of tetrahedral order on ferromagnetic gel phases. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:35. [PMID: 30900106 DOI: 10.1140/epje/i2019-11798-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Accepted: 02/15/2019] [Indexed: 06/09/2023]
Abstract
We investigate the macroscopic dynamics of gels with tetrahedral/octupolar symmetry, which possess in addition a spontaneous permanent magnetization. We derive the corresponding static and dynamic macroscopic equations for a phase, where the magnetization is parallel to one of the improper fourfold tetrahedral symmetry axes. Apart from elastic strains, we take into account relative rotations between the magnetization and the elastic network. The influence of tetrahedral order on these degrees of freedom is investigated and some experiments are proposed that are specific for such a material and allow to indirectly detect tetrahedral order. We also consider the case of a transient network and predict that stationary elastic shear stresses arise when a temperature gradient is applied.
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Affiliation(s)
- Tilen Potisk
- Department of Physics, University of Bayreuth, 95440, Bayreuth, Germany
| | - Harald Pleiner
- Max Planck Institute for Polymer Research, 55021, Mainz, Germany.
| | - Helmut R Brand
- Department of Physics, University of Bayreuth, 95440, Bayreuth, Germany
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Brand HR, Pleiner H. On the influence of a network on optically isotropic fluid phases with tetrahedral/octupolar order. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:34. [PMID: 28337650 DOI: 10.1140/epje/i2017-11523-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Accepted: 03/01/2017] [Indexed: 06/06/2023]
Abstract
We investigate the influence of transient or permanent elasticity on liquid phases with octupolar (tetrahedral) order, a question that has never been addressed before. The focus will be on optically isotropic liquid phases with tetrahedral order including the T d phase and the chiral T phase introduced by Fel. It turns out that the presence of both, a network as well as tetrahedral order can lead to the formation of chiral domains of both hands in an optically isotropic fluid due to a completely novel mechanism, thus providing a possible macroscopic explanation for recent experimental observations. We study in detail how elasticity influences the macroscopic dynamics of both, the T d and the T phase. The simultaneous presence of a transient network as well as of octupolar order is shown to lead to completely new cross-coupling phenomena for optically isotropic systems including transient dissipative elastic strains due to temperature gradients.
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Affiliation(s)
- Helmut R Brand
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany
| | - Harald Pleiner
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany.
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10
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Puljiz M, Orlishausen M, Köhler W, Menzel AM. Thermophoretically induced large-scale deformations around microscopic heat centers. J Chem Phys 2017; 144:184903. [PMID: 27179505 DOI: 10.1063/1.4948729] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.
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Affiliation(s)
- Mate Puljiz
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | | | - Werner Köhler
- Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Brand HR, Pleiner H, Svenšek D. Macroscopic behavior of polar nematic gels and elastomers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:105. [PMID: 27822626 DOI: 10.1140/epje/i2016-16105-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2016] [Accepted: 10/05/2016] [Indexed: 06/06/2023]
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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Affiliation(s)
- Helmut R Brand
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany
| | - Harald Pleiner
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany.
| | - Daniel Svenšek
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000, Ljubljana, Slovenia
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Brand HR, Fink A, Pleiner H. Macroscopic behavior of ferrocholesteric liquid crystals and ferrocholesteric gels and elastomers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:65. [PMID: 26123769 DOI: 10.1140/epje/i2015-15065-8] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2015] [Revised: 05/21/2015] [Accepted: 05/27/2015] [Indexed: 06/04/2023]
Abstract
We study the influence of macroscopic chirality on the macroscopic properties of superparamagnetic liquid crystals and gels. Specifically we derive macroscopic dynamic equations for ferrocholesteric low molecular weight (LMW) liquid crystals and for ferrocholesteric gels and elastomers in the local description using the director field as macroscopic variable. The magnetization is treated as a macroscopic dynamic degree of freedom and its coupling to all other macroscopic variables is examined in detail. We incorporate into our dynamic analysis terms that are linear in a magnetic field giving rise to a number of cross-coupling terms not possible otherwise. A number of properties that are unique to the class of systems studied arise. As an example for a static property we find a term in the generalized energy which is linear in the electric field and quadratic in the magnetic field. We find that applying a magnetic field to a ferrocholesteric can lead to reversible electric currents, heat currents and concentration currents, which change their sign with a sign change of macroscopic chirality. As an example of a rather intriguing dissipative dynamic contribution we point out that for ferrocholesterics and for ferrocholesteric gels and elastomers in a magnetic field extensional flow leads to electric and heat currents.
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Affiliation(s)
- Helmut R Brand
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany.
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany.
| | - Alexander Fink
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany
| | - Harald Pleiner
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany
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Brand HR, Pleiner H. Macroscopic behavior of ferronematic gels and elastomers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:122. [PMID: 25471930 DOI: 10.1140/epje/i2014-14122-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2014] [Revised: 11/13/2014] [Accepted: 11/13/2014] [Indexed: 06/04/2023]
Abstract
We present the derivation of the macroscopic equations for uniaxial ferronematic gels and elastomers. We deal with the superparamagnetic case, where no permanent magnetization is present and the anisotropy is provided by the nematic director. We include the magnetization as an independent dynamic degree of freedom. As a consequence special emphasis is laid on possible static and dynamic cross-couplings between magnetization and the non-magnetic degrees of freedom, as director reorientations, flow, elastic strains and relative rotations between director and the elastic network. In particular, we find reversible dynamic cross-couplings among rotations of the magnetization, the director, relative rotations, and deformational flow that allow for new possibilities to manipulate such materials. Application of simple (oscillatory) shear induces, in general, a finite magnetization normal to the shear plane and a relative rotation in the shear plane, whose amplitudes are linear in the shear rate. Induced magnetization, induced relative rotation and the director are mutually orthogonal, with the director aligned obliquely to the flow direction. This orientation is independent of the shear rate and is a material property.
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Affiliation(s)
- Helmut R Brand
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany,
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14
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Brand HR, Pleiner H, Svenšek D. Reversible and dissipative macroscopic contributions to the stress tensor: active or passive? THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:40. [PMID: 25260325 DOI: 10.1140/epje/i2014-14083-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2014] [Accepted: 08/29/2014] [Indexed: 06/03/2023]
Abstract
The issue of dynamic contributions to the macroscopic stress tensor has been of high interest in the field of bio-inspired active systems over the last few years. Of particular interest is a direct coupling ("active term") of the stress tensor with the order parameter, the latter describing orientational order induced by active processes. Here we analyze more generally possible reversible and irreversible dynamic contributions to the stress tensor for various passive and active macroscopic systems. This includes systems with tetrahedral/octupolar order, polar and non-polar (chiral) nematic and smectic liquid crystals, as well as active fluids with a dynamic preferred (polar or non-polar) direction. We show that it cannot a priori be seen, neither from the symmetry properties of the macroscopic variables involved, nor from the structure of the cross-coupling contributions to the stress tensor, whether the system studied is active or passive. Rather, that depends on whether the variables that give rise to those cross-couplings in the stress tensor are driven or not. We demonstrate that several simplified descriptions of active systems in the literature that neglect the necessary counter term to the active term violate linear irreversible thermodynamics and lead to an unphysical contribution to the entropy production.
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Affiliation(s)
- H R Brand
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany,
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Pleiner H, Brand HR. Low symmetry tetrahedral nematic liquid crystal phases: Ambidextrous chirality and ambidextrous helicity. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:11. [PMID: 24566665 DOI: 10.1140/epje/i2014-14011-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2014] [Revised: 02/14/2014] [Accepted: 02/14/2014] [Indexed: 06/03/2023]
Abstract
We discuss the symmetry properties as well as the dynamic behavior of various non-polar nematic liquid crystal phases with tetrahedral order. We concentrate on systems that show biaxial nematic order coexisting with octupolar (tetrahedral) order. Non-polar examples are phases with D2 and S4 symmetries, which can be characterized as biaxial nematics lacking inversion symmetry. It is this combination that allows for new features in the statics and dynamics of these phases. The D2-symmetric phase is chiral, even for achiral molecules, and shows ambidextrous chirality in all three preferred directions. The achiral S4-symmetric phase allows for ambidextrous helicity, similar to the higher-symmetric D2d-symmetric phase. Such phases are candidates for nematic phases made from banana-shaped molecules.
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Affiliation(s)
- Harald Pleiner
- Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany,
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Pleiner H, Svenšek D, Brand HR. Active polar two-fluid macroscopic dynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:135. [PMID: 24287686 DOI: 10.1140/epje/i2013-13135-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2013] [Accepted: 11/12/2013] [Indexed: 06/02/2023]
Abstract
We study the dynamics of systems with a polar dynamic preferred direction. Examples include the pattern-forming growth of bacteria as well as shoals of fish, flocks of birds and migrating insects. Due to the fact that the preferred direction only exists dynamically, but not statically, the macroscopic variable of choice is the macroscopic velocity associated with the motion of the active units, which are typically biological in nature. We derive the macroscopic equations for such a system and discuss novel static, reversible and irreversible cross-couplings connected to a second velocity as a variable. We analyze in detail how the macroscopic behavior of an active system with a polar dynamic preferred direction compares to other systems with two velocities including immiscible liquids and electrically neutral quantum liquids such as superfluid (4)He and (3)He . We critically discuss changes in the normal mode spectrum when comparing uncharged superfluids, immiscible liquids and active system with a polar dynamic preferred direction. We investigate the influence of a macroscopic hand (collective effects of chirality) on the macroscopic behavior of such active media.
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Affiliation(s)
- H Pleiner
- Max Planck Institute for Polymer Research, 55021, Mainz, Germany,
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Wittkowski R, Löwen H, Brand HR. Extended dynamical density functional theory for colloidal mixtures with temperature gradients. J Chem Phys 2012; 137:224904. [DOI: 10.1063/1.4769101] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Brand H, Martinoty P, Pleiner H. Physical Properties of Magnetic Gels. CROSS-LINKED LIQUID CRYSTALLINE SYSTEMS 2011. [DOI: 10.1201/b10525-21] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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Brand HR, Pleiner H. Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 31:37-50. [PMID: 20101516 DOI: 10.1140/epje/i2010-10547-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2009] [Revised: 10/30/2009] [Accepted: 11/20/2009] [Indexed: 05/28/2023]
Abstract
We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D(2d) symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D (infinityh) nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D(2d) symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.
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Affiliation(s)
- H R Brand
- Max-Planck-Institute for Polymer Research, Mainz, Germany.
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Abukhdeir NM, Rey AD. Nonisothermal model for the direct isotropic/smectic-A liquid-crystalline transition. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2009; 25:11923-11929. [PMID: 19788233 DOI: 10.1021/la9015965] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
An extension to a high-order model for the direct isotropic/smectic-A liquid-crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase ordering. Multiscale multitransport simulations of the nonisothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth under shallow quench/undercooling conditions. Nonisothermal simulations, where metastable nematic preordering precedes smectic-A growth, were also conducted, and novel nonmonotonic phase-transformation kinetics were observed.
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Brand HR, Cladis PE, Pleiner H. Reversible macroscopic dynamics of polar nematic liquid crystals: reversible currents and their experimental consequences. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:032701. [PMID: 19392000 DOI: 10.1103/physreve.79.032701] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2008] [Indexed: 05/27/2023]
Abstract
Polar liquid crystalline phases are relevant for fluid liquid crystal phases observed in banana liquid crystals as well as for a class of polymeric liquid crystalline materials investigated recently. In this Brief Report we present the reversible dynamics for polar nematic liquid crystals with C_{infinityv} symmetry, where the macroscopic polarization representing polar order acts as an independent macroscopic variable. We find reversible coupling terms, for example, between flow and temperature and concentration gradients specific for the existence of a polar preferred direction. We suggest concrete experiments to check the importance of the reversible dynamic cross-coupling terms presented here.
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Affiliation(s)
- Helmut R Brand
- Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany.
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Soddemann T, Auernhammer GK, Guo H, Dünweg B, Kremer K. Shear-induced undulation of smectic-A: Molecular Dynamics simulations vs. analytical theory. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2004; 13:141-151. [PMID: 15052424 DOI: 10.1140/epje/e2004-00045-0] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Experiments on a variety of systems have shown that layered liquids are unstable under shear even if the liquid layers are planes of constant velocity. We investigate the stability of smectic- A like liquids under shear using Molecular Dynamics simulations and a macroscopic hydrodynamic theory (including the layer normal and the director as independent variables). Both methods show an instability of the layers, which sets in above a critical shear rate. We find a remarkable qualitative and reasonable quantitative agreement between both methods for the spatial homogeneous state and the onset of the instability.
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Affiliation(s)
- Th Soddemann
- Max-Planck-Institut für Polymerforschung, 55021 Mainz, Germany.
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Ryskin AB, Pleiner H, Müller HW. Hydrodynamic instabilities in ferronematics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2003; 11:389-397. [PMID: 15011040 DOI: 10.1140/epje/i2003-10047-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
In the hydrodynamic description of ferronematics there are various dynamic magnetic-field effects, linear in the field strength, that are negligible in usual nematics, but can play a role in ferronematics. Here, we investigate theoretically the influence of these new terms on the thermal convection (Rayleigh-Bénard) and the viscous fingering (Saffman-Taylor) instability in ferronematics in the presence of a strong magnetic field. We find that the instabilities are qualitatively changed due to the occurrence of a finite vorticity component--a feature that is known from simple liquids in the case of a superimposed mechanical rotation. We suggest to use the additional effects (cross-flow within convection rolls, oblique rolls, rotating fingers) for measuring the phenomenological coefficients involved.
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Affiliation(s)
- A B Ryskin
- Max Planck Institute for Polymer Research, PO Box 3148, 55021 Mainz, Germany
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