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Dolganov PV, Shuravin NS, Dolganov VK, Kats EI, Stannarius R, Harth K, Trittel T, Park CS, Maclennan JE. Transient hexagonal structures in sheared emulsions of isotropic inclusions on smectic bubbles in microgravity conditions. Sci Rep 2021; 11:19144. [PMID: 34580344 PMCID: PMC8476617 DOI: 10.1038/s41598-021-98166-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2021] [Accepted: 08/19/2021] [Indexed: 11/08/2022] Open
Abstract
We describe the collective behavior of isotropic droplets dispersed over a spherical smectic bubble, observed under microgravity conditions on the International Space Station (ISS). We find that droplets can form two-dimensional hexagonal structures changing with time. Our analysis indicates the possibility of spatial and temporal periodicity of such structures of droplets. Quantitative analysis of the hexagonal structure including the first three coordination circles was performed. A peculiar periodic-in-time ordering of the droplets, related to one-dimensional motion of droplets with non-uniform velocity, was found.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences (ISSP RAS), 142432, Chernogolovka, Moscow Region, Russia
| | - N S Shuravin
- Institute of Solid State Physics, Russian Academy of Sciences (ISSP RAS), 142432, Chernogolovka, Moscow Region, Russia
| | - V K Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences (ISSP RAS), 142432, Chernogolovka, Moscow Region, Russia.
| | - E I Kats
- L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow Region, Russia
| | - R Stannarius
- Institute of Physics, Otto von Guericke University, 39106, Magdeburg, Germany
| | - K Harth
- Institute of Physics, Otto von Guericke University, 39106, Magdeburg, Germany
| | - T Trittel
- Institute of Physics, Otto von Guericke University, 39106, Magdeburg, Germany
| | - C S Park
- Department of Physics, University of Colorado Boulder, Boulder, CO, 80309, USA
| | - J E Maclennan
- Department of Physics, University of Colorado Boulder, Boulder, CO, 80309, USA
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Müller D, Kampmann TA, Kierfeld J. Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals. Sci Rep 2020; 10:12718. [PMID: 32728132 PMCID: PMC7391704 DOI: 10.1038/s41598-020-69544-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2020] [Accepted: 07/10/2020] [Indexed: 11/30/2022] Open
Abstract
Colloidal particles suspended in liquid crystals can exhibit various effective anisotropic interactions that can be tuned and utilized in self-assembly processes. We simulate a two-dimensional system of hard disks suspended in a solution of dense hard needles as a model system for colloids suspended in a nematic lyotropic liquid crystal. The novel event-chain Monte Carlo technique enables us to directly measure colloidal interactions in a microscopic simulation with explicit liquid crystal particles in the dense nematic phase. We find a directional short-range attraction for disks along the director, which triggers chaining parallel to the director and seemingly contradicts the standard liquid crystal field theory result of a quadrupolar attraction with a preferred [Formula: see text] angle. Our results can be explained by a short-range density-dependent depletion interaction, which has been neglected so far. Directionality and strength of the depletion interaction are caused by the weak planar anchoring of hard rods. The depletion attraction robustly dominates over the quadrupolar elastic attraction if disks come close. Self-assembly of many disks proceeds via intermediate chaining, which demonstrates that in lyotropic liquid crystal colloids depletion interactions play an important role in structure formation processes.
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Affiliation(s)
- David Müller
- Physics Department, TU Dortmund University, 44227, Dortmund, Germany
| | | | - Jan Kierfeld
- Physics Department, TU Dortmund University, 44227, Dortmund, Germany.
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M MR, Zuhail KP, Roy A, Dhara S. N-SmA-SmC phase transitions probed by a pair of elastically bound colloids. Phys Rev E 2018; 97:032702. [PMID: 29776110 DOI: 10.1103/physreve.97.032702] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2018] [Indexed: 06/08/2023]
Abstract
The competing effect of surface anchoring of dispersed microparticles and elasticity of nematic and cholesteric liquid crystals has been shown to stabilize a variety of topological defects. Here we study a pair of colloidal microparticles with homeotropic and planar surface anchoring across N-SmA-SmC phase transitions. We show that below the SmA-SmC phase transition the temperature dependence of interparticle separation (D) of colloids with homeotropic anchoring shows a power-law behavior; D∼(1-T/T_{AC})^{α}, with an exponent α≈0.5. For colloids with planar surface anchoring the angle between the joining line of the centers of the two colloids and the far field director shows characteristic variation elucidating the phase transitions.
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Affiliation(s)
- Muhammed Rasi M
- School of Physics, University of Hyderabad, Hyderabad 500046, India
| | - K P Zuhail
- School of Physics, University of Hyderabad, Hyderabad 500046, India
| | - Arun Roy
- Soft Matter Group, Raman Research Institute, Bangalore 500080, India
| | - Surajit Dhara
- School of Physics, University of Hyderabad, Hyderabad 500046, India
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Radzihovsky SP, Cranfill C, Nguyen Z, Park CS, Maclennan JE, Glaser MA, Clark NA. Two-dimensional island emulsions in ultrathin, freely-suspended smectic liquid crystal films. SOFT MATTER 2017; 13:6314-6321. [PMID: 28849846 DOI: 10.1039/c7sm01584d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report a novel type of two-dimensional colloidal emulsion, in which arrays of disc-shaped liquid crystal domains are created in ultrathin, freely-suspended, fluid smectic C liquid crystal films. After a film has been drawn across an aperture, an island emulsion is produced by repeatedly compressing and expanding the film while maintaining vigorous shear and extensional air flow across its area. Once formed, these emulsions restructure over a period of a few minutes to a stable state that then changes only slowly, over the course of several days. This stability enables study of the sedimentation of the emulsion under in-plane gravitation produced by tilting the film, during which the original island emulsion segregates into regions with different kinds of emulsions distinguished by the size, density, and degree of order of the islands. We observe a rich array of phenomena that includes the formation of chains of islands organized into two-dimensional smectics in the dilute phase, and island deformation and coalescence in the condensed phase.
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Affiliation(s)
- Sarah P Radzihovsky
- Soft Materials Research Center and Department of Physics, University of Colorado Boulder, Boulder, CO 80309, USA.
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Burylov SV, Zakhlevnykh AN. Orientational energy of anisometric particles in liquid-crystalline suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012511. [PMID: 23944478 DOI: 10.1103/physreve.88.012511] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2013] [Indexed: 05/02/2023]
Abstract
We obtain a general expression for the orientational energy of an individual anisometric particle suspended in uniform nematic liquid crystals when the main axis of the particle rotates with respect to the nematic director. We show that there is a qualitative and quantitative analogy between the internal and external problems for cylindrical volumes of nematic liquid crystals, and on this basis we obtain an estimate of the orientational energy of a particle of cylindrical (rodlike, needlelike, or ellipsoidal) shape. For an ensemble of such particles we propose a modified form of their orientational energy in the nematic matrix. This orientational energy has the usual second-order term, and additional fourth-order term in the scalar product of the nematic director and the vector which characterizes an average direction of the main axes of the particles. As an example we obtain the expression for the free energy density of ferronematics, i.e., colloidal suspensions of needlelike magnetic particles in nematic liquid crystals. Unlike previous models, the free energy density includes the proposed modified form of the particle orientational energy, and also a contribution describing the surface saddle-splay deformations of the liquid crystal matrix.
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Affiliation(s)
- S V Burylov
- Institute of Transport Systems and Technologies, Ukrainian National Academy of Science, 5 Pisargevsky St., Dnepropetrovsk 49005, Ukraine.
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Pereira MSS, Lyra ML, de Oliveira IN. Elastic mediated force between nanoparticles adsorbed on smectic films under an external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022502. [PMID: 23496530 DOI: 10.1103/physreve.87.022502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2012] [Indexed: 06/01/2023]
Abstract
Within the harmonic approximation, we analytically determine the elastic-mediated interaction between colloidal nanoparticles adsorbed on the surface of smectic films under the influence of an external field. Both cases of free-standing films and films deposited over a solid substrate are considered. We show that the asymptotic decay (1/R in free-standing and exponential in deposited films) is not altered by the external field. However, the external field plays distinct roles according to the film configuration, the interparticle distance, the film thickness, and the surface tension at the film-gas interface. We provide a detailed discussion under the light of the distinct mechanisms controlling the undulations of the surface layer.
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Affiliation(s)
- Maria S S Pereira
- Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, AL, Brazil
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Silvestre NM, Patrício P, Telo da Gama MM, Pattanaporkratana A, Park CS, Maclennan JE, Clark NA. Modeling dipolar and quadrupolar defect structures generated by chiral islands in freely suspended liquid crystal films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041708. [PMID: 19905326 DOI: 10.1103/physreve.80.041708] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2009] [Indexed: 05/28/2023]
Abstract
We report a detailed theoretical analysis of quadrupolar interactions observed between islands, which are disklike inclusions of extra layers, floating in thin, freely suspended smectic- C liquid crystal films. Strong tangential anchoring at the island boundaries results in a strength +1 chiral defect in each island and a companion -1 defect in the film--these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrupolar structures with the associated dipoles pointing in opposite directions. The interaction between such heterochiral-island-defect pairs is complex, with the defects moving to minimize the director field distortion as the distance between the islands changes. The details of the interisland potential and the trajectories of the -1 defects depend strongly on the elastic anisotropy of the liquid crystal, which can be modified in the experiments by varying the material chirality of the liquid crystal. A Landau model that describes the energetics of freely mobile defects is solved numerically to find equilibrium configurations for a wide range of parameters.
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Affiliation(s)
- N M Silvestre
- Departamento de Física da Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa Codex, Portugal.
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Bohley C, Stannarius R. Inclusions in free standing smectic liquid crystal films. SOFT MATTER 2008; 4:683-702. [PMID: 32907171 DOI: 10.1039/b715124a] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Colloidal inclusions in thin free standing liquid crystal films are ideal model systems for 2D anisotropic dispersions. Different types of self-organization in chain and lattice structures have been observed. The orientational elasticity of the anisotropic matrix and capillary forces are the dominating interaction mechanisms between solid or liquid inclusions, the director field, and dislocations of the films. We give an overview of the progress in this field, focussing on different inclusion types and their interactions in thermotropic smectic films.
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Affiliation(s)
- Christian Bohley
- Otto-von-Guericke Universität Magdeburg, Institute of Experimental Physics, Magdeburg, 39106, Germany.
| | - Ralf Stannarius
- Otto-von-Guericke Universität Magdeburg, Institute of Experimental Physics, Magdeburg, 39106, Germany.
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Fukuda J. Configuration of a chiral smectic-C film with a circular inclusion. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2007; 24:91-8. [PMID: 17762911 DOI: 10.1140/epje/i2007-10216-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2007] [Accepted: 08/03/2007] [Indexed: 05/17/2023]
Abstract
It was shown experimentally (P.V. Dolganov et al., Europhys. Lett. 76, 250 (2006)) and by numerical calculations (C. Bohley, R. Stannarius, Eur. Phys. J. E 23, 25 (2007)) that the c -director profile of a two-dimensional chiral smectic-C (SmC) film around a circular inclusion adopts dipolar rather than quadrupolar configuration observed in achiral SmC films. We give an analytical argument on how spontaneous bend inherent in chiral SmC liquid crystals influences the configuration of a SmC liquid crystal film around a circular inclusion imposing tangential anchoring. We find how the angle alpha between two surface defects seen from the center of the inclusion depends on the radius of the inclusion R and the strength of the spontaneous bend q . We show, however, that the contribution of the spontaneous bend to the free energy suffers from mathematical ambiguity; it depends on the mathematical treatment of the outer boundary even when it is at infinity. This might indicate that the shape as well as the treatment of the outer boundary of the film can significantly influence the equilibrium configuration of the c -director and the position of the surface defects.
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Affiliation(s)
- J Fukuda
- Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8568, Japan.
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Bohley C, Stannarius R. Colloidal inclusions in smectic films with spontaneous bend. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2007; 23:25-30. [PMID: 17510750 DOI: 10.1140/epje/i2007-10172-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2007] [Accepted: 04/24/2007] [Indexed: 05/15/2023]
Abstract
Inclusions in free-standing smectic films are simple model systems for two-dimensional anisotropic dispersions. From theory and experiment, different topologies of elastic distortions of the embedding liquid crystal are known. Quadrupolar and different dipolar defect configurations in the vicinity of the inclusion are possible, and these configurations determine the type of interactions between the inclusions. The quadrupolar configuration is often energetically preferred. We show, however, that dipolar director configurations around inclusions can be energetically favourable over quadrupolar arrangements in chiral smectics, as a consequence of a spontaneous-bend term in the elastic-energy formulation. As the inclusion size influences the selection of the deformation types, the corresponding spontaneous-bend constant can be estimated for the strong anchoring limit if the c -director fields around inclusions of different diameters are taken into account.
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Affiliation(s)
- C Bohley
- Institute of Experimental Physics, Nonlinear Phenomena, Universitätsplatz 2, D-39016 Magdeburg, Germany.
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Dolganov PV, Nguyen HT, Kats EI, Dolganov VK, Cluzeau P. Rearrangement of topological defects and anchoring on the inclusion boundary in ferroelectric smectic membranes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:031706. [PMID: 17500710 DOI: 10.1103/physreve.75.031706] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2006] [Indexed: 05/15/2023]
Abstract
We report experiments on a ferroelectric membrane and droplets with tunable surface properties. In smectic membranes the configuration of the c -director field near inclusions may be rearranged drastically with temperature. The transformation of the c -director field results from the competition between the elastic and polar properties of the membranes. We demonstrate that anchoring conditions on the inclusion boundary are not fixed but depend on the temperature. A dipolar c -director configuration near droplets can evolve to a mixed configuration and to a quadrupolar one. These modifications of the c -director field near the inclusions lead to a change of the interaction between the inclusions, their self-organization, and even to the destruction of structures already formed by the inclusions. Our observations open new possibilities for manipulating inclusions and controlling their self-organization.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russia
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Silvestre NM, Patrício P, Telo da Gama MM. Elliptical soft colloids in smectic-C films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021706. [PMID: 17025451 DOI: 10.1103/physreve.74.021706] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2006] [Indexed: 05/12/2023]
Abstract
We investigate theoretically the elliptical shapes of soft colloids in freely standing smectic- C films, that have been reported recently. The colloids favor parallel alignment of the liquid crystal molecules at their surfaces and, for sufficiently strong anchoring, will generate a pair of defects at the poles of the colloidal particles. The elastic free energy of the liquid crystal matrix will, in turn, affect the shape of the colloids. In this study we will focus on elliptical soft colloids and determine how their equilibrium shapes depend on the elastic constants of the liquid crystal, the anchoring strength, the surface tension, and the size of the colloids. A shape diagram is obtained analytically, by minimizing the Frank elastic free energy, in the limit of small eccentricities. The analytical results are verified, and generalized to arbitrary eccentricities, by numerical minimization of an appropriate Landau free energy. The latter is required for an adequate description of the topological defects when the liquid crystal correlation length is comparable to the size of the colloidal particles.
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Affiliation(s)
- N M Silvestre
- Departamento de Física da Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa Codex, Portugal.
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Bohley C, Stannarius R. Energetics of 2D colloids in free-standing smectic-C films. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 20:299-308. [PMID: 16858514 DOI: 10.1140/epje/i2006-10019-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2006] [Accepted: 06/29/2006] [Indexed: 05/10/2023]
Abstract
The formation of regular colloid patterns in free-standing smectic films at the transition from the smectic-C to the isotropic or nematic phase is well known experimentally. The self-organization of isotropic or nematic droplets is caused by their mutual interaction, mediated by elastic distortions of the local director in the surrounding liquid crystal. These distortions are related to the anchoring conditions of the director at the droplet border. We describe analytically the energetics of the liquid crystal environment of a single droplet in one-constant approximation. A method of complex analysis, Conformal Mapping, is employed. Following a suggestion of Dolganov et al. (Phys. Rev. E. 73, 041706 (2006)), energetics of chain and grid patterns built from the colloids are investigated numerically in order to explain experimentally observed formations and their director fields.
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Affiliation(s)
- C Bohley
- Institute of Experimental Physics, Nonlinear Phenomena, Universitätsplatz 2, D-39016, Magdeburg, Germany.
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