1
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Vasileiadis T, Schöttle M, Theis M, Retsch M, Fytas G, Graczykowski B. Elasticity Mapping of Colloidal Glasses Reveals the Interplay between Mesoscopic Order and Granular Mechanics. SMALL METHODS 2024:e2400855. [PMID: 39139008 DOI: 10.1002/smtd.202400855] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2024] [Indexed: 08/15/2024]
Abstract
Colloidal glasses (CGs) made of polymer (polymethylmethacrylate) nanoparticles are promising metamaterials for light and sound manipulation, but fabrication imperfections and fragility can limit their functionality and applications. Here, the vibrational mechanical modes of nanoparticles are probed to evaluate the nanomechanical and morphological properties of various CGs architectures. Utilizing the scanning micro-Brillouin light scattering (µ-BLS), the effective elastic constants and nanoparticles' sizes is determined as a function of position in a remote and non-destructive manner. This method is applied to CG mesostructures with different spatial distributions of their particle size and degree of order. These include CGs with single-sized systems, binary mixtures, bilayer structures, continuous gradient structures, and gradient mixtures. The microenvironments govern the local mechanical properties and highlight how the granular mesostructure can be used to develop durable functional polymer colloids. A size effect is revealed on the effective elastic constant, with the smallest particles and ordered assemblies forming robust structures, and classify the various types of mesoscale order in terms of their mechanical stiffness. The work establishes scanning µ-BLS as a tool for mapping elasticity, particle size, and local structure in complex nanostructures.
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Affiliation(s)
- Thomas Vasileiadis
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, Poznan, 61-614, Poland
| | - Marius Schöttle
- Department of Chemistry, Physical Chemistry I, University of Bayreuth, Universitätsstr. 30, 95447, Bayreuth, Germany
| | - Maximilian Theis
- Department of Chemistry, Physical Chemistry I, University of Bayreuth, Universitätsstr. 30, 95447, Bayreuth, Germany
| | - Markus Retsch
- Department of Chemistry, Physical Chemistry I, University of Bayreuth, Universitätsstr. 30, 95447, Bayreuth, Germany
- Bavarian Center for Battery Technology (BayBatt), Weiherstraße 26, 95448, Bayreuth, Germany
- Bavarian Polymer Institute (BPI), Bayreuth Center for Colloids and Interfaces (BZKG), Universitätsstraße 30, 95447, Bayreuth, Germany
| | - George Fytas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany
- Institute of Electronic Structure and Laser, FORTH, N. Plastira 100, Heraklion, 70013, Greece
| | - Bartlomiej Graczykowski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, Poznan, 61-614, Poland
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany
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2
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Diego M, Pirro M, Kim B, Anufriev R, Nomura M. Tailoring Phonon Dispersion of a Genetically Designed Nanophononic Metasurface. ACS NANO 2024; 18:18307-18313. [PMID: 38958360 PMCID: PMC11256740 DOI: 10.1021/acsnano.4c01954] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Revised: 05/31/2024] [Accepted: 06/11/2024] [Indexed: 07/04/2024]
Abstract
Phonon engineering at the nanoscale holds immense promise for a myriad of applications. However, the design of phononic devices continues to rely on regular shapes chosen according to long-established simple rules. Here, we demonstrate an inverse design approach to create a two-dimensional phononic metasurface exhibiting a highly anisotropic phonon dispersion along the main axes of the Brillouin zone. A partial hypersonic bandgap of approximately 3.5 GHz is present along one axis, with gap closure along the orthogonal axis. Such a level of control is achieved through genetically optimized unit cells, with shapes exceeding conventional intuition. We experimentally validated our theoretical predictions using Brillouin light scattering, confirming the effectiveness of the inverse design method. Our approach unlocks the potential for automated engineering of phononic metasurfaces with on-demand functionalities, thus leading toward innovative phononic devices beyond the limitations of traditional design paradigms.
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Affiliation(s)
- Michele Diego
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
| | - Matteo Pirro
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
| | - Byunggi Kim
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
| | - Roman Anufriev
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
| | - Masahiro Nomura
- Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
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3
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Cang Y, Sainidou R, Rembert P, Matyjaszewski K, Bockstaller M, Graczykowski B, Fytas G. Architecture Controls Phonon Propagation in All-Solid Brush Colloid Metamaterials. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2023:e2304157. [PMID: 37972268 DOI: 10.1002/smll.202304157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Revised: 10/27/2023] [Indexed: 11/19/2023]
Abstract
Brillouin light scattering and elastodynamic theory are concurrently used to determine and interpret the hypersonic phonon dispersion relations in brush particle solids as a function of the grafting density with perspectives in optomechanics, heat management, and materials metrology. In the limit of sparse grafting density, the phonon dispersion relations bear similarity to polymer-embedded colloidal assembly structures in which phonon dispersion can be rationalized on the basis of perfect boundary conditions, i.e., isotropic stiffness transitions across the particle interface. In contrast, for dense brush assemblies, more complex dispersion characteristics are observed that imply anisotropic stiffness transition across the particle/polymer interface. This provides direct experimental validation of phonon propagation changes associated with chain conformational transitions in dense particle brush materials. A scaling relation between interface tangential stiffness and crowding of polymer tethers is derived that provides a guideline for chemists to design brush particle materials with tailored phononic dispersion characteristics. The results emphasize the role of interfaces in composite materials systems. Given the fundamental relevance of phonon dispersion to material properties such as thermal transport or mechanical properties, it is also envisioned that the results will spur the development of novel functional hybrid materials.
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Affiliation(s)
- Yu Cang
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Zhangwu Road 100, Shanghai, 200092, China
| | - Rebecca Sainidou
- Laboratoire Ondes et Milieux Complexes UMR CNRS 6294, UNIHAVRE, Normandie University, 75 rue Bellot, Le Havre, F-76600, France
| | - Pascal Rembert
- Laboratoire Ondes et Milieux Complexes UMR CNRS 6294, UNIHAVRE, Normandie University, 75 rue Bellot, Le Havre, F-76600, France
| | - Krzysztof Matyjaszewski
- Chemistry Department, Carnegie Mellon University, 4400 Forbes Avenue, Pittsburgh, PA, 15213, USA
| | - Michael Bockstaller
- Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA
| | - Bartlomiej Graczykowski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, Poznan, 61-614, Poland
| | - George Fytas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany
- Institute of Electronic Structure and Laser, FORTH, N. Plastira 100, Heraklion, 70013, Greece
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4
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Xiong K, Ren J, Marchesoni F, Huang J. Phononic band gap in random spring networks. Phys Rev E 2023; 108:044306. [PMID: 37978624 DOI: 10.1103/physreve.108.044306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 09/07/2023] [Indexed: 11/19/2023]
Abstract
We investigate the relation between topological and vibrational properties of networked materials by analyzing, both numerically and analytically, the properties of a random spring network model. We establish a pseudodispersion relation, which allows us to predict the existence of distinct transitions from extended to localized vibrational modes in this class of materials. Consequently, we propose an alternative method to control phonon and elastic wave propagation in disordered networks. In particular, the phonon band gap of our spring network model can be enhanced by either increasing its average degree or decreasing its assortativity coefficient. Applications to phonon band engineering and vibrational energy harvesting are briefly discussed.
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Affiliation(s)
- Kezhao Xiong
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
- College of Sciences, Xi'an University of Science and Technology, Xi'an 710054, China
| | - Jie Ren
- MOE Key Laboratory of Advanced Micro-Structured Materials and Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Fabio Marchesoni
- MOE Key Laboratory of Advanced Micro-Structured Materials and Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
- Department of Physics, University of Camerino, 62032 Camerino, Italy
| | - Jiping Huang
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
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5
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Varghese J, Mohammadi R, Pochylski M, Babacic V, Gapinski J, Vogel N, Butt HJ, Fytas G, Graczykowski B. Size-dependent nanoscale soldering of polystyrene colloidal crystals by supercritical fluids. J Colloid Interface Sci 2023; 633:314-322. [PMID: 36459936 DOI: 10.1016/j.jcis.2022.11.090] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 11/15/2022] [Accepted: 11/17/2022] [Indexed: 11/25/2022]
Abstract
HYPOTHESIS Polymer particles self-assembled into colloidal crystals have exciting applications in photonics, phononics, templates for nanolithography, and coatings. Cold soldering utilizing polymer plasticization by supercritical fluids enables a novel, low-cost, low-effort, chemical-free means for uniform mechanical strengthening of fragile polymer colloidal crystals at moderate temperatures. Here, we aim to elucidate the role of particle size and gas-specific response for the most efficient soldering, exploring the full potential of this method. EXPERIMENTS We investigate the elastic properties of polystyrene colloidal crystals made of nanoparticles with different diameters (143 to 830 nm) upon treatment with supercritical Ar and He at room temperature. By employing Brillouin light scattering, we quantify the effect of nanoparticle size on the strengthening of interparticle contacts, evaluating the permanent change in the effective elastic modulus upon cold soldering. FINDINGS The relative change in the effective elastic modulus reveals nonmonotonic dependence on the particle size with the most efficient soldering for mid-sized nanoparticles (about 610 nm diameter). We attribute this behavior to the crucial role of intrinsic fabrication impurities, which reduces the nanoparticles' free surface exposed to plasticization by supercritical fluids. Supercritical Ar, a good solvent for polystyrene, enabled effective soldering of nanoparticles, whereas high-pressure He treatment is entirely reversible.
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Affiliation(s)
- Jeena Varghese
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Reza Mohammadi
- Institute of Particle Technology, Friedrich-Alexander Universität Erlangen-Nürnberg, Cauerstrasse 4, Erlangen D-91058, Germany
| | - Mikolaj Pochylski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Visnja Babacic
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Jacek Gapinski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Nicolas Vogel
- Institute of Particle Technology, Friedrich-Alexander Universität Erlangen-Nürnberg, Cauerstrasse 4, Erlangen D-91058, Germany
| | - Hans-Juergen Butt
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - George Fytas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Bartlomiej Graczykowski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland; Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
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6
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Jansen M, Tisdale WA, Wood V. Nanocrystal phononics. NATURE MATERIALS 2023; 22:161-169. [PMID: 36702886 DOI: 10.1038/s41563-022-01438-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 11/14/2022] [Indexed: 06/18/2023]
Abstract
Colloidal nanocrystals are successfully used as nanoscale building blocks for creating hierarchical solids with structures that range from amorphous networks to sophisticated periodic superlattices. Recently, it has been observed that these superlattices exhibit collective vibrations, which stem from the correlated motion of the nanocrystals, with their surface-bound ligands acting as molecular linkers. In this Perspective, we describe the work so far on collective vibrations in nanocrystal solids and their as-of-yet untapped potential for phononic applications. With the ability to engineer vibrations in the hypersonic regime through the choice of nanocrystal and linker composition, as well as by controlling their size, shape and chemical interactions, such superstructures offer new opportunities for phononic crystals, acoustic metamaterials and optomechanical systems.
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Affiliation(s)
- Maximilian Jansen
- Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland
| | - William A Tisdale
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Vanessa Wood
- Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland.
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7
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Menath J, Mohammadi R, Grauer JC, Deters C, Böhm M, Liebchen B, Janssen LMC, Löwen H, Vogel N. Acoustic Crystallization of 2D Colloidal Crystals. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2206593. [PMID: 36281801 DOI: 10.1002/adma.202206593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Revised: 10/13/2022] [Indexed: 06/16/2023]
Abstract
2D colloidal crystallization provides a simple strategy to produce defined nanostructure arrays over macroscopic areas. Regularity and long-range order of such crystals is essential to ensure functionality, but difficult to achieve in self-assembling systems. Here, a simple loudspeaker setup for the acoustic crystallization of 2D colloidal crystals (ACDC) of polystyrene, microgels, and core-shell particles at liquid interfaces is introduced. This setup anneals an interfacial colloidal monolayer and affords an increase in average grain size by almost two orders of magnitude. The order is characterized via the structural color of the colloidal crystal, the acoustic annealing process is optimized via the frequency and the amplitude of the applied sound wave, and its efficiency is rationalized via the surface coverage-dependent interactions within the interfacial colloidal monolayer. Computer simulations show that multiple rearrangement mechanisms at different length scales, from the local motion around voids to grain boundary movements via consecutive particle rotations around common centers, collude to remove defects. The experimentally simple ACDC process, paired with the demonstrated applicability toward complex particle systems, provides access to highly defined nanostructure arrays for a wide range of research communities.
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Affiliation(s)
- Johannes Menath
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
| | - Reza Mohammadi
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
| | - Jens Christian Grauer
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, D-40225, Düsseldorf, Germany
| | - Claudius Deters
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, D-40225, Düsseldorf, Germany
| | - Maike Böhm
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
| | - Benno Liebchen
- Institute of Physics: Theory of Soft Matter, Technical University of Darmstadt, Hochschulstraße 12, 64289, Darmstadt, Germany
| | - Liesbeth M C Janssen
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, D-40225, Düsseldorf, Germany
| | - Nicolas Vogel
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
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8
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Ma J. Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review. SMALL SCIENCE 2022. [DOI: 10.1002/smsc.202200052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Affiliation(s)
- Jihong Ma
- Department of Mechanical Engineering University of Vermont Burlington VT 05405 USA
- Materials Science Program University of Vermont Burlington VT 05405 USA
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9
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Ng RC, El Sachat A, Cespedes F, Poblet M, Madiot G, Jaramillo-Fernandez J, Florez O, Xiao P, Sledzinska M, Sotomayor-Torres CM, Chavez-Angel E. Excitation and detection of acoustic phonons in nanoscale systems. NANOSCALE 2022; 14:13428-13451. [PMID: 36082529 PMCID: PMC9520674 DOI: 10.1039/d2nr04100f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 08/15/2022] [Indexed: 06/15/2023]
Abstract
Phonons play a key role in the physical properties of materials, and have long been a topic of study in physics. While the effects of phonons had historically been considered to be a hindrance, modern research has shown that phonons can be exploited due to their ability to couple to other excitations and consequently affect the thermal, dielectric, and electronic properties of solid state systems, greatly motivating the engineering of phononic structures. Advances in nanofabrication have allowed for structuring and phonon confinement even down to the nanoscale, drastically changing material properties. Despite developments in fabricating such nanoscale devices, the proper manipulation and characterization of phonons continues to be challenging. However, a fundamental understanding of these processes could enable the realization of key applications in diverse fields such as topological phononics, information technologies, sensing, and quantum electrodynamics, especially when integrated with existing electronic and photonic devices. Here, we highlight seven of the available methods for the excitation and detection of acoustic phonons and vibrations in solid materials, as well as advantages, disadvantages, and additional considerations related to their application. We then provide perspectives towards open challenges in nanophononics and how the additional understanding granted by these techniques could serve to enable the next generation of phononic technological applications.
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Affiliation(s)
- Ryan C Ng
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
| | | | - Francisco Cespedes
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
- Departamento de Física, Universidad Autónoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
| | - Martin Poblet
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
| | - Guilhem Madiot
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
| | - Juliana Jaramillo-Fernandez
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
| | - Omar Florez
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
- Departamento de Física, Universidad Autónoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
| | - Peng Xiao
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
- Departamento de Física, Universidad Autónoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
| | - Marianna Sledzinska
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
| | - Clivia M Sotomayor-Torres
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
- ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain
| | - Emigdio Chavez-Angel
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain.
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10
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Cang Y, Sainidou R, Rembert P, Magnabosco G, Still T, Vogel N, Graczykowski B, Fytas G. Origin of the Acoustic Bandgaps in Hypersonic Colloidal Phononics: The Role of the Elastic Impedance. J Phys Chem B 2022; 126:6575-6584. [PMID: 35997523 PMCID: PMC9442645 DOI: 10.1021/acs.jpcb.2c03923] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Revised: 08/11/2022] [Indexed: 11/30/2022]
Abstract
How phonons propagate in nanostructures determines the flow of elastic and thermal energy in dielectric materials. However, a reliable theoretical prediction of the phonon dispersion relation requires experimental verification both near to and far from the Brillouin zone of the nanostructure. We report on the experimental hypersonic phonon dispersion of hard (SiO2) and soft (polymer) fcc colloidal crystals infiltrated in liquid polydimethylsiloxane with different elastic impedance contrast using Brillouin light spectroscopy. We discuss the distinct differences with first-principles full elastodynamic calculations involving a multiple-scattering theory. Interparticle contacts strongly impact the long-wavelength speed of sound and the nature of the particle vibration resonance-induced hybridization hypersonic bandgap. The absence of the order-induced Bragg bandgap in SiO2 and its presence in soft opals cannot be fully accounted for by the theory, limiting its predictive power. Bridging the elasticity of the two colloidal crystals with suitable SiO2 core-shell (polymer) particles reveals an unprecedented crossover behavior in the dispersion relation. In view of many conversational parameters, the control tuning of phonon propagation in soft matter-based hypersonic phononics remains challenging.
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Affiliation(s)
- Yu Cang
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- School
of Aerospace Engineering and Applied Mechanics, Tongji University, Zhangwu
Road 100, Shanghai 200092, China
| | - Rebecca Sainidou
- Laboratoire
Ondes et Milieux Complexes UMR CNRS 6294, UNIHAVRE, Normandie University, 75 rue Bellot, F-76600 Le Havre, France
| | - Pascal Rembert
- Laboratoire
Ondes et Milieux Complexes UMR CNRS 6294, UNIHAVRE, Normandie University, 75 rue Bellot, F-76600 Le Havre, France
| | - Giulia Magnabosco
- Institute
of Particle Technology, Friedrich-Alexander
University Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Tim Still
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Nicolas Vogel
- Institute
of Particle Technology, Friedrich-Alexander
University Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Bartlomiej Graczykowski
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Faculty
of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, Poznan 61-614, Poland
| | - George Fytas
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Institute
of Electronic Structure and Laser, FO.R.T.H, N. Plastira 100, /0013, Heraklion 71110, Greece
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11
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Che S, Zhang J, Mou F, Guo X, Kauffman JE, Sen A, Guan J. Light-Programmable Assemblies of Isotropic Micromotors. Research (Wash D C) 2022; 2022:9816562. [PMID: 35928302 PMCID: PMC9297725 DOI: 10.34133/2022/9816562] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Accepted: 06/15/2022] [Indexed: 12/27/2022] Open
Abstract
“Life-like” nonequilibrium assemblies are of increasing significance, but suffering from limited steerability as they are generally based on micro/nanomotors with inherent asymmetry in chemical composition or geometry, of which the vigorous random Brownian rotations disturb the local interactions. Here, we demonstrate that isotropic photocatalytic micromotors, due to the persistent phoretic flow from the illuminated to shadowed side irrespective of their Brownian rotations, experience light-programmable local interactions (reversibly from attraction to repulsion and/or alignment) depending on the direction of the incident lights. Thus, they can be organized into a variety of tunable nonequilibrium assemblies, such as apolar solids (i.e., immobile colloidal crystal), polar liquids (i.e., phototactic colloidal stream), and polar solids (i.e., phototactic colloidal crystal), which can further be “cut” into a predesigned pattern by utilizing the switching motor-motor interactions at superimposed-light edges. This work facilitates the development of active matters and motile functional microdevices.
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Affiliation(s)
- Shengping Che
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, International School of Materials Science and Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan 430070, China
| | - Jianhua Zhang
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, International School of Materials Science and Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan 430070, China
- Department of Chemistry, The Pennsylvania State University, University Park, PA 16802, USA
| | - Fangzhi Mou
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, International School of Materials Science and Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan 430070, China
| | - Xia Guo
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, International School of Materials Science and Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan 430070, China
| | - Joshua E. Kauffman
- Department of Chemistry, The Pennsylvania State University, University Park, PA 16802, USA
| | - Ayusman Sen
- Department of Chemistry, The Pennsylvania State University, University Park, PA 16802, USA
| | - Jianguo Guan
- State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, International School of Materials Science and Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan 430070, China
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12
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Menath J, Eatson J, Brilmayer R, Andrieu-Brunsen A, Buzza DMA, Vogel N. Defined core-shell particles as the key to complex interfacial self-assembly. Proc Natl Acad Sci U S A 2021; 118:e2113394118. [PMID: 34949640 PMCID: PMC8719876 DOI: 10.1073/pnas.2113394118] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/09/2021] [Indexed: 11/18/2022] Open
Abstract
The two-dimensional self-assembly of colloidal particles serves as a model system for fundamental studies of structure formation and as a powerful tool to fabricate functional materials and surfaces. However, the prevalence of hexagonal symmetries in such self-assembling systems limits its structural versatility. More than two decades ago, Jagla demonstrated that core-shell particles with two interaction length scales can form complex, nonhexagonal minimum energy configurations. Based on such Jagla potentials, a wide variety of phases including cluster lattices, chains, and quasicrystals have been theoretically discovered. Despite the elegance of this approach, its experimental realization has remained largely elusive. Here, we capitalize on the distinct interfacial morphology of soft particles to design two-dimensional assemblies with structural complexity. We find that core-shell particles consisting of a silica core surface functionalized with a noncrosslinked polymer shell efficiently spread at a liquid interface to form a two-dimensional polymer corona surrounding the core. We controllably grow such shells by iniferter-type controlled radical polymerization. Upon interfacial compression, the resulting core-shell particles arrange in well-defined dimer, trimer, and tetramer lattices before transitioning into complex chain and cluster phases. The experimental phase behavior is accurately reproduced by Monte Carlo simulations and minimum energy calculations, suggesting that the interfacial assembly interacts via a pairwise-additive Jagla-type potential. By comparing theory, simulation, and experiment, we narrow the Jagla g-parameter of the system to between 0.9 and 2. The possibility to control the interaction potential via the interfacial morphology provides a framework to realize structural features with unprecedented complexity from a simple, one-component system.
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Affiliation(s)
- Johannes Menath
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Jack Eatson
- G. W. Gray Centre for Advanced Materials, Department of Physics and Mathematics, University of Hull, Hull HU6 7RX, United Kingdom
| | - Robert Brilmayer
- Macromolecular Chemistry, Smart Membranes, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - Annette Andrieu-Brunsen
- Macromolecular Chemistry, Smart Membranes, Technical University of Darmstadt, 64287 Darmstadt, Germany
| | - D Martin A Buzza
- G. W. Gray Centre for Advanced Materials, Department of Physics and Mathematics, University of Hull, Hull HU6 7RX, United Kingdom
| | - Nicolas Vogel
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, 91058 Erlangen, Germany;
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13
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Wang J, Kang E, Sultan U, Merle B, Inayat A, Graczykowski B, Fytas G, Vogel N. Influence of Surfactant-Mediated Interparticle Contacts on the Mechanical Stability of Supraparticles. THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2021; 125:23445-23456. [PMID: 34737841 PMCID: PMC8558861 DOI: 10.1021/acs.jpcc.1c06839] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Revised: 09/15/2021] [Indexed: 05/14/2023]
Abstract
Colloidal supraparticles are micron-scale spherical assemblies of uniform primary particles, which exhibit emergent properties of a colloidal crystal, yet exist as a dispersible powder. A prerequisite to utilize these emergent functionalities is that the supraparticles maintain their mechanical integrity upon the mechanical impacts that are likely to occur during processing. Understanding how the internal structure relates to the resultant mechanical properties of a supraparticle is therefore of general interest. Here, we take the example of supraparticles templated from water/fluorinated oil emulsions in droplet-based microfluidics and explore the effect of surfactants on their mechanical properties. Stable emulsions can be generated by nonionic block copolymers consisting of a hydrophilic and fluorophilic block and anionic fluorosurfactants widely available under the brand name Krytox. The supraparticles formed in the presence of both types of surfactants appear structurally similar, but differ greatly in their mechanical properties. While the nonionic surfactant induces superior mechanical stability and ductile fracture behavior, the anionic Krytox surfactant leads to weak supraparticles with brittle fracture. We complement this macroscopic picture with Brillouin light spectroscopy that is very sensitive to the interparticle contacts for subnanometer-thick adsorbed layers atop of the nanoparticle. While the anionic Krytox does not significantly affect the interparticle bonds, the amphiphilic nonionic surfactant drastically strengthens these bonds to the point that individual particle vibrations are not resolved in the experimental spectrum. Our results demonstrate that seemingly subtle changes in the physicochemical properties of supraparticles can drastically impact the resultant mechanical properties.
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Affiliation(s)
- Junwei Wang
- Institute
of Particle Technology, Friedrich-Alexander
University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
| | - Eunsoo Kang
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Umair Sultan
- Institute
of Particle Technology, Friedrich-Alexander
University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
- Institute
of Chemical Reaction Engineering, Friedrich-Alexander
University Erlangen-Nürnberg, Egerlandstrasse 3, 91058 Erlangen, Germany
| | - Benoit Merle
- Materials
Science and Engineering I and Interdisciplinary Center for Nanostructured
Films (IZNF), Friedrich-Alexander University
Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Alexandra Inayat
- Institute
of Chemical Reaction Engineering, Friedrich-Alexander
University Erlangen-Nürnberg, Egerlandstrasse 3, 91058 Erlangen, Germany
| | - Bartlomiej Graczykowski
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Faculty
of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, Poznan 61-614, Poland
| | - George Fytas
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- E-mail:
| | - Nicolas Vogel
- Institute
of Particle Technology, Friedrich-Alexander
University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
- E-mail:
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14
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Kim YJ, Kim JH, Jo IS, Pine DJ, Sacanna S, Yi GR. Patchy Colloidal Clusters with Broken Symmetry. J Am Chem Soc 2021; 143:13175-13183. [PMID: 34392686 DOI: 10.1021/jacs.1c05123] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Colloidal clusters are prepared by assembling positively charged cross-linked polystyrene (PS) particles onto negatively charged liquid cores of swollen polymer particles. PS particles at the interface of the liquid core are closely packed around the core due to interfacial wetting. Then, by evaporating solvent in the liquid cores, polymers in the cores are solidified and the clusters are cemented. As the swelling ratio of PS cores increases, cores at the center of colloidal clusters are exposed, forming patchy colloidal clusters. Finally, by density gradient centrifugation, high-purity symmetric colloidal clusters are obtained. When silica-PS core-shell particles are swollen and serve as the liquid cores, hybrid colloidal clusters are obtained in which each silica nanoparticle is relocated to the liquid core interface during the swelling-deswelling process breaking symmetry in colloidal clusters as the silica nanoparticle in the core is comparable in size with the PS particle in the shell. The configuration of colloidal clusters is determined once the number of particles around the liquid core is given, which depends on the size ratio of the liquid core and shell particle. Since hybrid clusters are heavier than PS particles, they can be purified using centrifugation.
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Affiliation(s)
- You-Jin Kim
- School of Chemical Engineering, Sungkyunkwan University, Suwon, Gyeonggi 16419, Republic of Korea
| | - Jae-Hyun Kim
- School of Chemical Engineering, Sungkyunkwan University, Suwon, Gyeonggi 16419, Republic of Korea
| | - In-Seong Jo
- School of Chemical Engineering, Sungkyunkwan University, Suwon, Gyeonggi 16419, Republic of Korea
| | - David J Pine
- Department of Chemical & Biomolecular Engineering, New York University, Brooklyn, New York 11201, United States
| | | | - Gi-Ra Yi
- School of Chemical Engineering, Sungkyunkwan University, Suwon, Gyeonggi 16419, Republic of Korea.,Department of Chemical Engineering, POSTECH, Pohang, Gyeongbuk 37673, Republic of Korea
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15
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Cang Y, Liu B, Das S, Xu X, Xie J, Deng X, Fytas G. Surface contacts strongly influence the elasticity and thermal conductivity of silica nanoparticle fibers. Phys Chem Chem Phys 2021; 23:3707-3715. [PMID: 33398320 DOI: 10.1039/d0cp05377e] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Granular materials are often encountered in science and engineering disciplines, in which controlling the particle contacts is one of the critical issues for the design, engineering, and utilization of their desired properties. The achievable rapid fabrication of nanoparticles with tunable physical and chemical properties facilitates tailoring the macroscopic properties of particle assemblies through contacts at the nanoscale. Models have been developed to predict the mechanical properties of macroscopic granular materials; however, their predicted power in the case of nanoparticle assemblies is still uncertain. Here, we investigate the influence of nanocontacts on the elasticity and thermal conductivity of a granular fiber comprised of close-packed silica nanoparticles. A complete elastic moduli characterization was realized by non-contact and non-destructive Brillouin light spectroscopy, which also allowed resolving the stiffness of the constituent particles in situ. In the framework of effective medium models, the strong enhancement of the elastic moduli is attributed to the formation of adhesive nanocontacts with physical and/or chemical bondings. The nanoparticle contacts are also responsible for the increase in the fiber thermal conductivity that emphasizes the role of interface thermal resistance, which tends to be ignored in most porosity models. This insight into the fundamental understanding of structure-property relationships advances knowledge on the manipulation of granular systems at the nanoscale.
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Affiliation(s)
- Yu Cang
- School of Aerospace Engineering and Applied Mechanics, Tongji University, 100 Zhangwu Road, 200092, Shanghai, China and Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany.
| | - Bohai Liu
- Center for Phononics and Thermal Energy Science, School of Physical Science and Engineering, Tongji University, Shanghai, 200092, China
| | - Sudatta Das
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany.
| | - Xiangfan Xu
- Center for Phononics and Thermal Energy Science, School of Physical Science and Engineering, Tongji University, Shanghai, 200092, China
| | - Jingli Xie
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Xu Deng
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - George Fytas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany.
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16
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Tang L, Yao X, Wu G, Tang D. Band Gaps Characteristics Analysis of Periodic Oscillator Coupled Damping Beam. MATERIALS 2020; 13:ma13245748. [PMID: 33339294 PMCID: PMC7767037 DOI: 10.3390/ma13245748] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Revised: 12/07/2020] [Accepted: 12/13/2020] [Indexed: 11/16/2022]
Abstract
The vibration of the periodic oscillator coupled damping beam model is reduced through the band gaps designing method, which can be applied in equivalent engineering structures. In this paper, the flexural wave dispersion relations of the infinite long periodic oscillator coupled damping beam were calculated using the reverberation-ray matrix method combined with the Bloch theorem. The flexural wave vibration frequency response function of the finite long periodic oscillator coupled damping beam was carried out using the finite element method. The flexural wave vibration band gaps occur in the infinite long periodic oscillator coupled damping beam model in both the analytical and numerical results. In these band gaps, flexural waves' propagation is prohibited, and flexural vibration is significantly suppressed. Furthermore, the effects of structure and material parameters on the flexural wave vibration band gaps characteristics are studied. Thus, the structural vibration reduction design can be realized by adjusting the related parameters of the periodic coupled damping beam structures and the equivalent 2D periodic stiffened plate structures.
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Affiliation(s)
- Li Tang
- College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China; (L.T.); (X.Y.)
| | - Xiongliang Yao
- College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China; (L.T.); (X.Y.)
| | - Guoxun Wu
- College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China; (L.T.); (X.Y.)
- Correspondence: ; Tel.: +86-18504511485
| | - Dong Tang
- College of Harbour Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China;
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17
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Vasileiadis T, Zhang H, Wang H, Bonn M, Fytas G, Graczykowski B. Frequency-domain study of nonthermal gigahertz phonons reveals Fano coupling to charge carriers. SCIENCE ADVANCES 2020; 6:eabd4540. [PMID: 33355135 PMCID: PMC11206219 DOI: 10.1126/sciadv.abd4540] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2020] [Accepted: 11/04/2020] [Indexed: 05/24/2023]
Abstract
Telecommunication devices exploit hypersonic gigahertz acoustic phonons to mediate signal processing with microwave radiation, and charge carriers to operate various microelectronic components. Potential interactions of hypersound with charge carriers can be revealed through frequency- and momentum-resolved studies of acoustic phonons in photoexcited semiconductors. Here, we present an all-optical method for excitation and frequency-, momentum-, and space-resolved detection of gigahertz acoustic waves in a spatially confined model semiconductor. Lamb waves are excited in a bare silicon membrane using femtosecond optical pulses and detected with frequency-domain micro-Brillouin light spectroscopy. The population of photoexcited gigahertz phonons displays a hundredfold enhancement as compared with thermal equilibrium. The phonon spectra reveal Stokes-anti-Stokes asymmetry due to propagation, and strongly asymmetric Fano resonances due to coupling between the electron-hole plasma and the photoexcited phonons. This work lays the foundation for studying hypersonic signals in nonequilibrium conditions and, more generally, phonon-dependent phenomena in photoexcited nanostructures.
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Affiliation(s)
- Thomas Vasileiadis
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Heng Zhang
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Hai Wang
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Mischa Bonn
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - George Fytas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
| | - Bartlomiej Graczykowski
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
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18
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Babacic V, Varghese J, Coy E, Kang E, Pochylski M, Gapinski J, Fytas G, Graczykowski B. Mechanical reinforcement of polymer colloidal crystals by supercritical fluids. J Colloid Interface Sci 2020; 579:786-793. [PMID: 32673855 DOI: 10.1016/j.jcis.2020.06.104] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Revised: 06/19/2020] [Accepted: 06/24/2020] [Indexed: 01/21/2023]
Abstract
Colloidal crystals realized by self-assembled polymer nanoparticles have prominent attraction as a platform for various applications from assembling photonic and phononic crystals, acoustic metamaterials to coating applications. However, the fragility of these systems limits their application horizon. In this work the uniform mechanical reinforcement and tunability of 3D polystyrene colloidal crystals by means of cold soldering are reported. This structural strengthening is achieved by high pressure gas (N2 or Ar) plasticization at temperatures well below the glass transition. Brillouin light scattering is employed to monitor in-situ the mechanical vibrations of the crystal and thereby determine preferential pressure, temperature and time ranges for soldering, i.e. formation of physical bonding among the nanoparticles while maintaining the shape and translational order. This low-cost method is potentially useful for fabrication and tuning of durable devices including applications in photonics, phononics, acoustic metamaterials, optomechanics, surface coatings and nanolithography.
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Affiliation(s)
- Visnja Babacic
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Jeena Varghese
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Emerson Coy
- NanoBioMedical Centre, Adam Mickiewicz University, Wszechnicy Piastowskiej 3, 61-614 Poznan, Poland
| | - Eunsoo Kang
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Mikolaj Pochylski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - Jacek Gapinski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland
| | - George Fytas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Bartlomiej Graczykowski
- Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznanskiego 2, 61-614 Poznan, Poland; Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
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19
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Abstract
In the paper, a phononic crystal plate composed of a magnetorheological elastomer with adjustable band gaps in the low frequency range is constructed. The dispersion relations of Lamb waves are studied by the supercell plane wave expansion method. The transmission responses as well as the displacement fields of Lamb waves are calculated by the finite element method. The influence of geometric parameters on the band gaps, the regulation effect of the volume ratio of Fe particles and the bias magnetic field on the band gaps are analyzed. Based on the numerical results, we find that the volume ratio of Fe particles and the magnetic field affect the band gap effectively. The location and width of the band gaps can be adjusted within a broad frequency range by varying the geometric parameters and magnetic field. We can control the band gap, achieve an appropriate and wide low band gap by selecting proper geometric parameters and applying an external contactless magnetic field to deal with complicated and changeable engineering environment. The results are useful for understanding and optimizing the design of composite vibration isolation plates.
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