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Goh S, Menzel AM, Wittmann R, Löwen H. Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels. J Chem Phys 2023; 158:054909. [PMID: 36754783 DOI: 10.1063/5.0133207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Magnetic gels are composite materials consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction and consider the approximate incompressibility of the embedding media and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.
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Affiliation(s)
- Segun Goh
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
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Brand HR, Pleiner H. A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:17. [PMID: 35218411 PMCID: PMC8882122 DOI: 10.1140/epje/s10189-022-00172-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 02/14/2022] [Indexed: 06/14/2023]
Abstract
We present the macroscopic dynamics of polar nematic liquid crystals in a two-fluid context. We investigate the case of a nonchiral as well as of a chiral solvent. In addition, we analyze how the incorporation of a strain field for polar nematic gels and elastomers in a solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the polar subsystem and the solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from the other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in polar nematics to heat currents and in polar cholesterics to temporal changes of the polarization. In polar cholesterics, shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in polar nematic gels uniaxial stresses or strains generate temporal variations of the velocity difference.
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Affiliation(s)
- Helmut R. Brand
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
| | - Harald Pleiner
- Max Planck Institute for Polymer Research, 55021 Mainz, Germany
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3
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Pleiner H, Brand HR. Ferromagnetic nematics: A macroscopic two-fluid description. J Chem Phys 2022; 156:044504. [DOI: 10.1063/5.0080118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Harald Pleiner
- Max Planck Institute for Polymer Research, 55021 Mainz, Germany
| | - Helmut R. Brand
- Max Planck Institute for Polymer Research, 55021 Mainz, Germany
- Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany
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4
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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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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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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: 8] [Impact Index Per Article: 0.9] [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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8
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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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9
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Menzel AM. Bridging from particle to macroscopic scales in uniaxial magnetic gels. J Chem Phys 2014; 141:194907. [DOI: 10.1063/1.4901275] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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10
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Diaz Calleja R, Díaz-Boïls P, Llovera-Segovia P, Quijano A. On the nonlinear behaviour of nematic single crystal elastomers under biaxial mechanic and electrical force fields. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:22. [PMID: 25080174 DOI: 10.1140/epje/i2014-14066-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2014] [Accepted: 06/25/2014] [Indexed: 06/03/2023]
Abstract
A slab of nematic-side-chain-liquid-single-crystal elastomer (NSCLSCE), with the director initially oriented in the z -direction, is subjected to a pair of equal mechanical loads and electrical force fields in the x , y directions. The electric fields tend to make easier the rotation of the director after the application of the mechanical force field. A nonlinear expression for the free energy density is used to obtain the interval of stretching for which the system becomes unstable. However, the elastic energy of the network is assumed to be linear. The stress-strain curves predicted by the model show an unstable zone between two linearly increasing segments. The possibility of bifurcation phenomena has been examined.
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Affiliation(s)
- Ricardo Diaz Calleja
- ITE, Universitat Politècnica de València, Camino de Vera s/n, E-46022, Valencia, Spain,
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11
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Brand HR, Pleiner H, Svenšek D. Lehmann effects and rotatoelectricity in liquid crystalline systems made of achiral molecules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:024501. [PMID: 24032968 DOI: 10.1103/physreve.88.024501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Indexed: 06/02/2023]
Abstract
We discuss Lehmann effects and rotato-electricity for liquid crystalline phases made of achiral molecules. We point out that for static and dynamic Lehmann effects to exist, it is not necessary to have chiral molecules provided the overall structure has macroscopic chirality. This question is of direct relevance for liquid crystalline phases formed by bent-core molecules provided they have a sufficiently low symmetry. This includes systems which break parity symmetry and have overall C(2) or C(1) symmetry. We point out that for liquid crystalline gels and elastomers one should be able to observe rotato-electricity for systems with macroscopic chirality. Rotatoelectricity is associated with the relative rotations between two subsystems, namely, between the network and the director, in an external electric field. Candidates include gels and even monolayers prepared from bent-core molecules with sufficiently low symmetry.
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Affiliation(s)
- Helmut R Brand
- Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany and Max-Planck-Institute for Polymer Research, P.O. Box 3148, 55021 Mainz, Germany
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12
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Annunziata MA, Menzel AM, Löwen H. Hardening transition in a one-dimensional model for ferrogels. J Chem Phys 2013; 138:204906. [DOI: 10.1063/1.4807003] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Wu X, Cao H, Guo R, Li K, Wang F, Yang H. Effect of cholesteric liquid crystalline elastomer with binaphthalene crosslinkings on thermal and optical properties of a liquid crystal that show smectic A-cholesteric phase transition. POLYM ADVAN TECHNOL 2012. [DOI: 10.1002/pat.3075] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Xiaojuan Wu
- Department of Materials Physics and Chemistry, School of Materials Science and Engineering; University of Science and Technology Beijing; Beijing 100083 P. R. China
| | - Hui Cao
- Department of Materials Physics and Chemistry, School of Materials Science and Engineering; University of Science and Technology Beijing; Beijing 100083 P. R. China
| | - Renwei Guo
- Department of Materials Physics and Chemistry, School of Materials Science and Engineering; University of Science and Technology Beijing; Beijing 100083 P. R. China
| | - Kexuan Li
- Department of Materials Physics and Chemistry, School of Materials Science and Engineering; University of Science and Technology Beijing; Beijing 100083 P. R. China
| | - Feifei Wang
- Department of Materials Physics and Chemistry, School of Materials Science and Engineering; University of Science and Technology Beijing; Beijing 100083 P. R. China
| | - Huai Yang
- Department of Materials Physics and Chemistry, School of Materials Science and Engineering; University of Science and Technology Beijing; Beijing 100083 P. R. China
- Department of Materials Science and Engineering, College of Engineering; Peking University; Beijing 100871 P. R. China
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14
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Wu X, Cao H, Guo R, Li K, Wang F, Gao Y, Yao W, Zhang L, Chen X, Yang H. Influence of Interim Alkyl Chain Length on Phase Transitions and Wide-Band Reflective Behaviors of Side-Chain Liquid Crystalline Elastomers with Binaphthalene Crosslinkings. Macromolecules 2012. [DOI: 10.1021/ma300618t] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Xiaojuan Wu
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Hui Cao
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Renwei Guo
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Kexuan Li
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Feifei Wang
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Yanzi Gao
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Wenhuan Yao
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
| | - Lanying Zhang
- Department of Materials Science
and Engineering, College of Engineering, Peking University, Beijing
100871, P. R. China
| | - Xiaofang Chen
- Department
of Polymer Science
and Engineering and The Key Laboratory of Polymer Chemistry and Physics
of Ministry of Education, College of Chemistry, Peking University,
Beijing 100871, P. R. China
| | - Huai Yang
- Department of Materials
Physics
and Chemistry, School of Materials Science and Engineering, University
of Science and Technology Beijing, Beijing 100083, P. R. China
- Department of Materials Science
and Engineering, College of Engineering, Peking University, Beijing
100871, P. R. China
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15
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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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17
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Menzel AM, Pleiner H, Brand HR. Response of prestretched nematic elastomers to external fields. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2009; 30:371-377. [PMID: 19960220 DOI: 10.1140/epje/i2009-10535-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2009] [Revised: 10/20/2009] [Accepted: 10/23/2009] [Indexed: 05/28/2023]
Abstract
We investigate the response of prestretched nematic side-chain liquid single-crystal elastomers to superimposed external shear, electric, and magnetic fields of small amplitude. The prestretching direction is oriented perpendicular to the initial nematic director orientation, which enforces director reorientation. Furthermore, the shear plane contains the direction of prestretch. In this case, we obtain a strongly decreased effective shear modulus in the vicinity of the onset and the completion of the enforced director rotation. For the same regions, we find that it becomes comparatively easy to reorient the director by external electric and magnetic fields. These results were derived using conventional elasticity theory and its coupling to relative director-network rotations.
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Affiliation(s)
- A M Menzel
- Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany.
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18
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Menzel AM, Brand HR. Instabilities in nematic elastomers in external electric and magnetic fields. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 26:235-249. [PMID: 18461276 DOI: 10.1140/epje/i2007-10320-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2007] [Accepted: 03/27/2008] [Indexed: 05/26/2023]
Abstract
In this paper we study the macroscopic behavior of nematic side-chain liquid single crystal elastomers exposed to an external electric or magnetic field. For this purpose we use the framework of a continuum model. The geometries investigated comprise the bend and the twist geometry known from the classical Frederiks transition in low molecular weight liquid crystals. For the bend geometry we find a laterally homogeneous and a two-dimensional undulatory instability, which may compete at onset. In the case of the twist geometry three instabilities can occur at onset, two of which are two dimensional and clearly show undulations. As a major result we propose how the values of the twist coefficient K(2) and the values of the material parameters D(1) and D(2) connected to relative rotations between the director field and the polymer network can be determined from experimental observations. In addition, we explain why a twist experiment is probably the most suitable set-up in order to measure the material parameter D(1).
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Affiliation(s)
- A M Menzel
- Theoretische Physik III, Universität Bayreuth, Bayreuth, Germany.
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19
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Müller M, Schöpf W, Rehberg I, Timme A, Lattermann G. Fréedericksz transition in a thermoreversible nematic gel. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061701. [PMID: 18233855 DOI: 10.1103/physreve.76.061701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2007] [Indexed: 05/25/2023]
Abstract
A thermoreversible (physical) gel of a nematic liquid crystal in its planar configuration is investigated. The transition temperatures of the gel are thermally and rheologically determined. The temperature for the nematic-isotropic transition is higher than that for the gel-sol transition, allowing the network to grow in the oriented nematic phase. The electrical Fréedericksz transition of the gel is investigated by using both an optical and an electrical detection method. The transition can be adjusted within a large voltage range by selecting the temperature of the sample. This behavior is determined by the thermal properties of the thermoreversible gel network.
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Affiliation(s)
- Matthias Müller
- Experimentalphysik V, Universität Bayreuth, Bayreuth, Germany.
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