1
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Besharat A, Radkovski J, Sibiryakov S. Effective action for dissipative and nonholonomic systems. Phys Rev E 2024; 109:L052103. [PMID: 38907505 DOI: 10.1103/physreve.109.l052103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 04/04/2024] [Indexed: 06/24/2024]
Abstract
We show that the action of a dynamical system can be supplemented by an effective action for its environment to reproduce arbitrary coordinate dependent ohmic dissipation and gyroscopic forces. The action is a generalization of the harmonic bath model and describes a set of massless interacting scalar fields in an auxiliary space coupled to the original system at the boundary. A certain limit of the model implements nonholonomic constraints. In the case of dynamics with nonlinearly realized symmetries the effective action takes the form of a two-dimensional nonlinear σ model. It provides a basis for application of path integral methods to general dissipative and nonholonomic systems.
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Affiliation(s)
- Afshin Besharat
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1 and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - Jury Radkovski
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1 and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - Sergey Sibiryakov
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1 and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
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2
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Dong YX, Zhang ZT, Zhang XD, Cao BY. Orientation of graphene nanosheets in suspension under an electric field: theoretical model and molecular dynamic simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:255702. [PMID: 38457833 DOI: 10.1088/1361-648x/ad31be] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 03/08/2024] [Indexed: 03/10/2024]
Abstract
Orientation regulation of nanoparticles in a suspension by an electric field is a powerful tool to tune its mechanical, thermal, optical, electrical properties etc. However, how molecular modification can affect the orientation of two-dimensional nanoparticles is still unclear. In this paper, the influence of molecular modification on the orientation of graphene nanosheets (GNS) in water was investigated through theoretical analyses and molecular dynamics (MD) simulations. Firstly, a new orientation angle model was proposed, which considers hydration effects, dipole moments and resistance torque. Then, MD simulations were conducted to investigate the effects of position, direction, type, and number of functional groups on the orientation of GNS. The trend observed in MD simulations is consistent with the proposed theoretical model. The results reveal that, under the combined influence of the dipole moment and hydration effects, the modification with hydrophilic functional groups can reduce the orientation angle from 21.31° to 8.34°, while the modification with hydrophobic functional groups increases it to 26.43°. Among the hydrophilic functional groups, orientation of hydroxylated GNS is the best. With an increase in the number of hydroxyl groups, orientation angle is decreased from 12.61° to 8.34°. This work can provide valuable guidance for the design of high-performance suspensions and composites, such as thermal smart materials with adjustable thermal conductivity and intelligent devices with tailored capabilities.
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Affiliation(s)
- Yu-Xia Dong
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Zi-Tong Zhang
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Xu-Dong Zhang
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Bing-Yang Cao
- Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People's Republic of China
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3
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Li D, Liu Y, Luo H, Jing G. Anisotropic Diffusion of Elongated Particles in Active Coherent Flows. MICROMACHINES 2024; 15:199. [PMID: 38398928 PMCID: PMC10893016 DOI: 10.3390/mi15020199] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2023] [Revised: 01/23/2024] [Accepted: 01/26/2024] [Indexed: 02/25/2024]
Abstract
The study of particle diffusion, a classical conundrum in scientific inquiry, holds manifold implications for various real-world applications. Particularly within the domain of active flows, where the motion of self-propelled particles instigates fluid movement, extensive research has been dedicated to unraveling the dynamics of passive spherical particles. This scrutiny has unearthed intriguing phenomena, such as superdiffusion at brief temporal scales and conventional diffusion at longer intervals. In contrast to the spherical counterparts, anisotropic particles, which manifest directional variations, are prevalent in nature. Although anisotropic behavior in passive fluids has been subject to exploration, enigmatic aspects persist in comprehending the interplay of anisotropic particles within active flows. This research delves into the intricacies of anisotropic passive particle diffusion, exposing a notable escalation in translational and rotational diffusion coefficients, as well as the superdiffusion index, contingent upon bacterial concentration. Through a detailed examination of particle coordinates, the directional preference of particle diffusion is not solely dependent on the particle length, but rather determined by the ratio of the particle length to the associated length scale of the background flow field. These revelations accentuate the paramount importance of unraveling the nuances of anisotropic particle diffusion within the context of active flows. Such insights not only contribute to the fundamental understanding of particle dynamics, but also have potential implications for a spectrum of applications.
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Affiliation(s)
| | - Yanan Liu
- School of Physics, Northwest University, Xi’an 710127, China
| | | | - Guangyin Jing
- School of Physics, Northwest University, Xi’an 710127, China
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4
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Djutanta F, Brown PT, Nainggolan B, Coullomb A, Radhakrishnan S, Sentosa J, Yurke B, Hariadi RF, Shepherd DP. Decoding the hydrodynamic properties of microscale helical propellers from Brownian fluctuations. Proc Natl Acad Sci U S A 2023; 120:e2220033120. [PMID: 37235635 PMCID: PMC10235983 DOI: 10.1073/pnas.2220033120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2022] [Accepted: 04/12/2023] [Indexed: 05/28/2023] Open
Abstract
The complex motility of bacteria, ranging from single-swimmer behaviors such as chemotaxis to collective dynamics, including biofilm formation and active matter phenomena, is driven by their microscale propellers. Despite extensive study of swimming flagellated bacteria, the hydrodynamic properties of their helical-shaped propellers have never been directly measured. The primary challenges to directly studying microscale propellers are 1) their small size and fast, correlated motion, 2) the necessity of controlling fluid flow at the microscale, and 3) isolating the influence of a single propeller from a propeller bundle. To solve the outstanding problem of characterizing the hydrodynamic properties of these propellers, we adopt a dual statistical viewpoint that connects to the hydrodynamics through the fluctuation-dissipation theorem (FDT). We regard the propellers as colloidal particles and characterize their Brownian fluctuations, described by 21 diffusion coefficients for translation, rotation, and correlated translation-rotation in a static fluid. To perform this measurement, we applied recent advances in high-resolution oblique plane microscopy to generate high-speed volumetric movies of fluorophore-labeled, freely diffusing Escherichia coli flagella. Analyzing these movies with a bespoke helical single-particle tracking algorithm, we extracted trajectories, calculated the full set of diffusion coefficients, and inferred the average propulsion matrix using a generalized Einstein relation. Our results provide a direct measurement of a microhelix's propulsion matrix and validate proposals that the flagella are highly inefficient propellers, with a maximum propulsion efficiency of less than 3%. Our approach opens broad avenues for studying the motility of particles in complex environments where direct hydrodynamic approaches are not feasible.
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Affiliation(s)
- Franky Djutanta
- Biodesign Center for Molecular Design and Biomimetics at the Biodesign Institute, Arizona State University, Tempe, AZ85287
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ85287
| | - Peter T. Brown
- Center for Biological Physics and Department of Physics, Arizona State University, Tempe, AZ85287
| | - Bonfilio Nainggolan
- Center for Biological Physics and Department of Physics, Arizona State University, Tempe, AZ85287
| | - Alexis Coullomb
- Center for Biological Physics and Department of Physics, Arizona State University, Tempe, AZ85287
| | - Sritharini Radhakrishnan
- Biodesign Center for Molecular Design and Biomimetics at the Biodesign Institute, Arizona State University, Tempe, AZ85287
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ85287
| | - Jason Sentosa
- Biodesign Center for Molecular Design and Biomimetics at the Biodesign Institute, Arizona State University, Tempe, AZ85287
| | - Bernard Yurke
- Micron School of Materials Science and Electrical and Computer Engineering Department, Boise State University, Boise, ID83725
| | - Rizal F. Hariadi
- Biodesign Center for Molecular Design and Biomimetics at the Biodesign Institute, Arizona State University, Tempe, AZ85287
- Center for Biological Physics and Department of Physics, Arizona State University, Tempe, AZ85287
| | - Douglas P. Shepherd
- Center for Biological Physics and Department of Physics, Arizona State University, Tempe, AZ85287
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5
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Mauleon-Amieva A, Allen MP, Liverpool TB, Royall CP. Dynamics and interactions of Quincke roller clusters: From orbits and flips to excited states. SCIENCE ADVANCES 2023; 9:eadf5144. [PMID: 37196094 PMCID: PMC10191443 DOI: 10.1126/sciadv.adf5144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 04/13/2023] [Indexed: 05/19/2023]
Abstract
Active matter systems may be characterized by the conversion of energy into active motion, e.g., the self-propulsion of microorganisms. Artificial active colloids form models that exhibit essential properties of more complex biological systems but are amenable to laboratory experiments. While most experimental models consist of spheres, active particles of different shapes are less understood. Furthermore, interactions between these anisotropic active colloids are even less explored. Here, we investigate the motion of active colloidal clusters and the interactions between them. We focus on self-assembled dumbbells and trimers powered by an external dc electric field. For dumbbells, we observe an activity-dependent behavior of spinning, circular, and orbital motions. Moreover, collisions between dumbbells lead to the hierarchical self-assembly of tetramers and hexamers, both of which form rotational excited states. On the other hand, trimers exhibit flipping motion that leads to trajectories reminiscent of a honeycomb lattice.
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Affiliation(s)
- Abraham Mauleon-Amieva
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK
- School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, UK
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, UK
- Bristol Centre for Functional Nanomaterials, Tyndall Avenue, Bristol BS8 1FD, UK
| | - Michael P. Allen
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK
- Department of Physics, University of Warwick, Coventry CV4 7AL, UK
| | - Tanniemola B. Liverpool
- School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG UK
| | - C. Patrick Royall
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK
- School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, UK
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, UK
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
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6
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Niggel V, Bailey MR, van Baalen C, Zosso N, Isa L. 3-D rotation tracking from 2-D images of spherical colloids with textured surfaces. SOFT MATTER 2023; 19:3069-3079. [PMID: 37043248 PMCID: PMC10155603 DOI: 10.1039/d3sm00076a] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Tracking the three-dimensional rotation of colloidal particles is essential to elucidate many open questions, e.g. concerning the contact interactions between particles under flow, or the way in which obstacles and neighboring particles affect self-propulsion in active suspensions. In order to achieve rotational tracking, optically anisotropic particles are required. We synthesise here rough spherical colloids that present randomly distributed fluorescent asperities and track their motion under different experimental conditions. Specifically, we propose a new algorithm based on a 3-D rotation registration, which enables us to track the 3-D rotation of our rough colloids at short time-scales, using time series of 2-D images acquired at high frame rates with a conventional wide-field microscope. The method is based on the image correlation between a reference image and rotated 3-D prospective images to identify the most likely angular displacements between frames. We first validate our approach against simulated data and then apply it to the cases of: particles flowing through a capillary, freely diffusing at solid-liquid and liquid-liquid interfaces, and self-propelling above a substrate. By demonstrating the applicability of our algorithm and sharing the code, we hope to encourage further investigations in the rotational dynamics of colloidal systems.
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Affiliation(s)
- Vincent Niggel
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, CH-8093, Zurich, Switzerland.
| | - Maximilian R Bailey
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, CH-8093, Zurich, Switzerland.
| | - Carolina van Baalen
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, CH-8093, Zurich, Switzerland.
| | - Nino Zosso
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, CH-8093, Zurich, Switzerland.
| | - Lucio Isa
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, CH-8093, Zurich, Switzerland.
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7
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Ulbrich JA, Fernández-Rico C, Rost B, Vialetto J, Isa L, Urbach JS, Dullens RPA. Effect of curvature on the diffusion of colloidal bananas. Phys Rev E 2023; 107:L042602. [PMID: 37198802 DOI: 10.1103/physreve.107.l042602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 02/22/2023] [Indexed: 05/19/2023]
Abstract
Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods-also known as colloidal bananas-as a function of their opening angle α. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from 0^{∘} (straight rods) to nearly 360^{∘}(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when α>180^{∘}. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.
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Affiliation(s)
- Justin-Aurel Ulbrich
- Department of Chemistry, Physical and Theoretical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Carla Fernández-Rico
- Department of Chemistry, Physical and Theoretical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Brian Rost
- Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC 20057, USA
| | - Jacopo Vialetto
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Lucio Isa
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Jeffrey S Urbach
- Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC 20057, USA
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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8
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Mayer Martins J, Wittkowski R. Inertial dynamics of an active Brownian particle. Phys Rev E 2022; 106:034616. [PMID: 36266913 DOI: 10.1103/physreve.106.034616] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
Active Brownian motion commonly assumes spherical overdamped particles. However, self-propelled particles are often neither symmetric nor overdamped yet underlie random fluctuations from their surroundings. Active Brownian motion has already been generalized to include asymmetric particles. Separately, recent findings have shown the importance of inertial effects for particles of macroscopic size or in low-friction environments. We aim to consolidate the previous findings into the general description of a self-propelled asymmetric particle with inertia. We derive the Langevin equation of such a particle as well as the corresponding Fokker-Planck equation. Furthermore, a formula is presented that allows reconstructing the hydrodynamic resistance matrix of the particle by measuring its trajectory. Numerical solutions of the Langevin equation show that, independently of the particle's shape, the noise-free trajectory at zero temperature starts with an inertial transition phase and converges to a circular helix. We discuss this universal convergence with respect to the helical motion that many microorganisms exhibit.
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Affiliation(s)
- Jonas Mayer Martins
- Institute of Theoretical Physics, Center for Soft Nanoscience, University of Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institute of Theoretical Physics, Center for Soft Nanoscience, University of Münster, 48149 Münster, Germany
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9
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De Corato M, Pagonabarraga I, Natale G. Spontaneous chiralization of polar active particles. Phys Rev E 2021; 104:044607. [PMID: 34781499 DOI: 10.1103/physreve.104.044607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 09/26/2021] [Indexed: 11/07/2022]
Abstract
Polar active particles constitute a wide class of active matter that is able to propel along a preferential direction, given by their polar axis. Here, we demonstrate a generic active mechanism that leads to their spontaneous chiralization through a symmetry-breaking instability. We find that the transition of an active particle from a polar to a chiral symmetry is characterized by the emergence of active rotation and of circular trajectories. The instability is driven by the advection of a solute that interacts differently with the two portions of the particle surface and it occurs through a supercritical pitchfork bifurcation.
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Affiliation(s)
- Marco De Corato
- Aragon Institute of Engineering Research (I3A), University of Zaragoza, 50009 Zaragoza, Spain
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, C. Martí Franquès 1, 08028 Barcelona, Spain University of Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain and CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne (EPFL), Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
| | - Giovanniantonio Natale
- Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive NW, Calgary, Canada
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10
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Sprenger AR, Jahanshahi S, Ivlev AV, Löwen H. Time-dependent inertia of self-propelled particles: The Langevin rocket. Phys Rev E 2021; 103:042601. [PMID: 34005997 DOI: 10.1103/physreve.103.042601] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.
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Affiliation(s)
- Alexander R Sprenger
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Soudeh Jahanshahi
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Alexei V Ivlev
- Max-Planck-Institut für Extraterrestrische Physik, 85748 Garching, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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11
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Verweij RW, Ketzetzi S, de Graaf J, Kraft DJ. Height distribution and orientation of colloidal dumbbells near a wall. Phys Rev E 2020; 102:062608. [PMID: 33466010 DOI: 10.1103/physreve.102.062608] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles and can further contribute to the development of quantitative frameworks for arbitrarily shaped microparticle dynamics in confinement.
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Affiliation(s)
- Ruben W Verweij
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Stefania Ketzetzi
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - Joost de Graaf
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Daniela J Kraft
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
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12
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Hernández RJ, Sevilla FJ, Mazzulla A, Pagliusi P, Pellizzi N, Cipparrone G. Collective motion of chiral Brownian particles controlled by a circularly-polarized laser beam. SOFT MATTER 2020; 16:7704-7714. [PMID: 32734983 DOI: 10.1039/c9sm02404b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We demonstrate the emergence of circular collective motion in a system of spherical light-propelled Brownian particles. Light-propulsion occurs as consequence of the coupling between the chirality of polymeric particles - left (L)- or right (R)-type - and the circularly-polarized light that irradiates them. Irradiation with light that has the same helicity as the particle material leads to a circular cooperative vortical motion between the chiral Brownian particles. In contrast, opposite circular-polarization does not induce such coupling among the particles but only affects their Brownian motion. The mean angular momentum of each particle has a value and sign that distinguishes between chiral activity dynamics and typical Brownian motion. These outcomes have relevant implications for chiral separation technologies and provide new strategies for optical torque tunability in mesoscopic optical array systems, micro- and nanofabrication of light-activated engines with selective control and collective motion.
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Affiliation(s)
- Raúl Josué Hernández
- Cátedra CONACYT Consejo Nacional de Ciencia y Tecnología - Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, 04510 Cd. de México, Mexico.
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13
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Bianchi S, Carmona Sosa V, Vizsnyiczai G, Di Leonardo R. Brownian fluctuations and hydrodynamics of a microhelix near a solid wall. Sci Rep 2020; 10:4609. [PMID: 32165686 PMCID: PMC7067800 DOI: 10.1038/s41598-020-61451-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2019] [Accepted: 02/25/2020] [Indexed: 12/20/2022] Open
Abstract
We combine two-photon lithography and optical tweezers to investigate the Brownian fluctuations and propeller characteristics of a microfabricated helix. From the analysis of mean squared displacements and time correlation functions we recover the components of the full mobility tensor. We find that Brownian motion displays correlations between angular and translational fluctuations from which we can directly measure the hydrodynamic coupling coefficient that is responsible for thrust generation. By varying the distance of the microhelices from a no-slip boundary we can systematically measure the effects of a nearby wall on the resistance matrix. Our results indicate that a rotated helix moves faster when a nearby no-slip boundary is present, providing a quantitative insight on thrust enhancement in confined geometries for both synthetic and biological microswimmers.
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Affiliation(s)
- Silvio Bianchi
- NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Laboratory, Roma, I-00185, Italy.
| | | | - Gaszton Vizsnyiczai
- Physics Department, University of Rome "Sapienza", Roma, I-00185, Italy
- Institute of Biophysics, Biological Research Centre, Szeged, 6726, Hungary
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14
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Gubbiotti A, Chinappi M, Casciola CM. Confinement effects on the dynamics of a rigid particle in a nanochannel. Phys Rev E 2019; 100:053307. [PMID: 31869915 DOI: 10.1103/physreve.100.053307] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Indexed: 12/19/2022]
Abstract
The transport of nanoparticles in confined geometries plays a crucial role in several technological applications ranging from nanopore sensors to filtration membranes. Here we describe a Brownian approach to simulate the motion of a rigid-body nanoparticle of an arbitrary shape under confinement. A quaternion formulation is used for the nanoparticle orientation, and the corresponding overdamped Langevin equation, completed by the proper fluctuation-dissipation relation, is derived. The hydrodynamic mobility matrix is obtained via dissipative particle dynamics simulation equipped with a new method for enforcing the no-slip boundary condition for curved moving solid-liquid interfaces. As an application, we analyzed the motion of a nanoparticle in a cylindrical channel under the action of external fields. We show that both axial effective diffusion and rotational diffusion decrease with confinement.
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Affiliation(s)
- Alberto Gubbiotti
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, 00184 Roma, Italia
| | - Mauro Chinappi
- Dipartimento di Ingegneria Industriale, Università di Roma Tor Vergata, 00133 Roma, Italia
| | - Carlo Massimo Casciola
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, 00184 Roma, Italia
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15
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Diffusion Tensors of Arbitrary-Shaped Nanoparticles in Fluid by Molecular Dynamics Simulation. Sci Rep 2019; 9:18943. [PMID: 31831762 PMCID: PMC6908649 DOI: 10.1038/s41598-019-55042-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Accepted: 10/30/2019] [Indexed: 11/09/2022] Open
Abstract
The anisotropic diffusive behavior of nanoparticles with complex shapes attracts great interest due to its potential applications in many fields ranging from bionics to aeronautic industry. Although molecular dynamics (MD) simulations are used widely to investigate nanoparticle diffusion properties, universal methods to describe the diffusion process comprehensively are still lacking. Here, we address this problem by introducing diffusion tensor as it can describe translational and rotational diffusion in three dimensions both individually and their coupling. We take carbon triple sphere suspended in argon fluid as our model system. The consistency of our results and velocity autocorrelation function(VAF) method validates our simulations. The coupling between translational and rotational diffusion is observed directly from analyzing diffusion tensor, and quantified by coupling diffusion coefficient. Our simulation reveals non-trivial effect of some factors in diffusion at nanoscale, which was not considered in previous theories. In addition to introducing an effective method to calculate the diffusion tensor in MD simulations, our work also provides insights for understanding the diffusion process of arbitrary-shaped particles in nanoengineering.
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16
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de Buyl P. Mesoscopic simulations of anisotropic chemically powered nanomotors. Phys Rev E 2019; 100:022603. [PMID: 31574644 DOI: 10.1103/physreve.100.022603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2018] [Indexed: 11/07/2022]
Abstract
Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive L-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.
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Affiliation(s)
- Pierre de Buyl
- Instituut voor Theoretische Fysica, KU Leuven B-3001, Belgium
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17
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Volk K, Deißenbeck F, Mandal S, Löwen H, Karg M. Moiré and honeycomb lattices through self-assembly of hard-core/soft-shell microgels: experiment and simulation. Phys Chem Chem Phys 2019; 21:19153-19162. [DOI: 10.1039/c9cp03116b] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Moiré and honeycomb lattices result from the sequential double deposition of monolayers of core/shell microgels in dependence of the drying conditions.
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Affiliation(s)
- Kirsten Volk
- Institut für Physikalische Chemie I: Kolloide und Nanooptik
- Heinrich-Heine-Universität Düsseldorf
- D-40225 Düsseldorf
- Germany
| | - Florian Deißenbeck
- Institut für Theoretische Physik II: Weiche Materie
- Heinrich-Heine-Universität Düsseldorf
- D-40225 Düsseldorf
- Germany
| | - Suvendu Mandal
- Institut für Theoretische Physik II: Weiche Materie
- Heinrich-Heine-Universität Düsseldorf
- D-40225 Düsseldorf
- Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie
- Heinrich-Heine-Universität Düsseldorf
- D-40225 Düsseldorf
- Germany
| | - Matthias Karg
- Institut für Physikalische Chemie I: Kolloide und Nanooptik
- Heinrich-Heine-Universität Düsseldorf
- D-40225 Düsseldorf
- Germany
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18
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Ouhajji S, van Ravensteijn BGP, Fernández-Rico C, Lacina KS, Philipse AP, Petukhov AV. Wet-Chemical Synthesis of Chiral Colloids. ACS NANO 2018; 12:12089-12095. [PMID: 30428258 PMCID: PMC6307084 DOI: 10.1021/acsnano.8b05065] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2018] [Accepted: 11/14/2018] [Indexed: 05/22/2023]
Abstract
We disclose a method for the synthesis of chiral colloids from spontaneously formed hollow sugar-surfactant microtubes with internally confined mobile colloidal spheres. Key feature of our approach is the grafting of colloid surfaces with photoresponsive coumarin moieties, which allow for UV-induced, covalent clicking of colloids into permanent chains, with morphologies set by the colloid-to-tube diameter ratio. Subsequent dissolution of tube confinement yields aqueous suspensions that comprise bulk quantities of a variety of linear chains, including single helical chains of polystyrene colloids. These colloidal equivalents of chiral (DNA) molecules are intended for microscopic study of chiral dynamics on a single-particle level.
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Affiliation(s)
- Samia Ouhajji
- Van
’t Hoff Laboratory for Physical and Colloid Chemistry, Debye
Institute for Nanomaterials Science, Utrecht
University, Padualaan 8, 3584 CH Utrecht, The Netherlands
- E-mail:
| | - Bas G. P. van Ravensteijn
- Van
’t Hoff Laboratory for Physical and Colloid Chemistry, Debye
Institute for Nanomaterials Science, Utrecht
University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Carla Fernández-Rico
- Van
’t Hoff Laboratory for Physical and Colloid Chemistry, Debye
Institute for Nanomaterials Science, Utrecht
University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Kanvaly S. Lacina
- Van
’t Hoff Laboratory for Physical and Colloid Chemistry, Debye
Institute for Nanomaterials Science, Utrecht
University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Albert P. Philipse
- Van
’t Hoff Laboratory for Physical and Colloid Chemistry, Debye
Institute for Nanomaterials Science, Utrecht
University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Andrei V. Petukhov
- Van
’t Hoff Laboratory for Physical and Colloid Chemistry, Debye
Institute for Nanomaterials Science, Utrecht
University, Padualaan 8, 3584 CH Utrecht, The Netherlands
- Laboratory
of Physical Chemistry, Eindhoven University
of Technology, 5600 MB Eindhoven, The Netherlands
- E-mail:
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19
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Stuckert R, Plüisch CS, Wittemann A. Experimental Assessment and Model Validation on How Shape Determines Sedimentation and Diffusion of Colloidal Particles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:13339-13351. [PMID: 30350686 DOI: 10.1021/acs.langmuir.8b02999] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Understanding the hydrodynamics of colloids with complex shapes is of equal importance to widespread practical applications and fundamental scientific problems, such as gelation, crystallization, and phase behavior. Building on previous work, we present a comprehensive study of sedimentation, diffusion, intrinsic viscosities, and other shape-dependent quantities of clusters built from spherical nanoparticles. Cluster preparation is accomplished by assembling surface-modified polystyrene particles on evaporating emulsion droplets. This results in supracolloids that exhibit well-defined configurations, which are governed by the number of constituent particles. Sorting into uniform cluster fractions is achieved through centrifugation of the cluster mixture in a density gradient. Sedimentation coefficients are elucidated by differential centrifugal sedimentation. Rotational and translational diffusion of the clusters are investigated by polarized and depolarized dynamic light scattering. The experimental results are compared to data obtained via a bead-shell model suitable for predicting hydrodynamic quantities of particles with arbitrary shapes. The experimental data are in excellent agreement with the predictions from hydrodynamic modeling. The variety of investigated shapes shows the robustness of our approach and provides a complete picture of the hydrodynamic behavior of complex particles.
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Affiliation(s)
- Rouven Stuckert
- Colloid Chemistry , University of Konstanz , Universitaetsstrasse 10 , 78464 Konstanz , Germany
| | - Claudia Simone Plüisch
- Colloid Chemistry , University of Konstanz , Universitaetsstrasse 10 , 78464 Konstanz , Germany
| | - Alexander Wittemann
- Colloid Chemistry , University of Konstanz , Universitaetsstrasse 10 , 78464 Konstanz , Germany
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20
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Bukowicki M, Ekiel-Jeżewska ML. Different bending models predict different dynamics of sedimenting elastic trumbbells. SOFT MATTER 2018; 14:5786-5799. [PMID: 29974114 DOI: 10.1039/c8sm00604k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at low-Reynolds-number. We use the bead-spring approximation of a filament and the Rotne-Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or - alternatively - by the 'cosine' (also called the Kratky-Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic long-lasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky-Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky-Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads well-separated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own.
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Affiliation(s)
- Marek Bukowicki
- Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5b, 02-106 Warszaw, Poland.
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21
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Nili H, Naji A. Re-entrant bimodality in spheroidal chiral swimmers in shear flow. Sci Rep 2018; 8:8328. [PMID: 29844481 PMCID: PMC5974238 DOI: 10.1038/s41598-018-26771-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Accepted: 05/18/2018] [Indexed: 12/17/2022] Open
Abstract
We use a continuum model to report on the behavior of a dilute suspension of chiral swimmers subject to externally imposed shear in a planar channel. Swimmer orientation in response to the imposed shear can be characterized by two distinct phases of behavior, corresponding to unimodal or bimodal distribution functions for swimmer orientation along the channel. These phases indicate the occurrence (or not) of a population splitting phenomenon changing the swimming direction of a macroscopic fraction of active particles to the exact opposite of that dictated by the imposed flow. We present a detailed quantitative analysis elucidating the complexities added to the population splitting behavior of swimmers when they are chiral. In particular, the transition from unimodal to bimodal and vice versa are shown to display a re-entrant behavior across the parameter space spanned by varying the chiral angular speed. We also present the notable effects of particle aspect ratio and self-propulsion speed on system phase behavior and discuss potential implications of our results in applications such as swimmer separation/sorting.
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Affiliation(s)
- Hossein Nili
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran.
| | - Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5531, Iran
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22
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Furukawa A, Tateno M, Tanaka H. Physical foundation of the fluid particle dynamics method for colloid dynamics simulation. SOFT MATTER 2018; 14:3738-3747. [PMID: 29700543 DOI: 10.1039/c8sm00189h] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Colloid dynamics is significantly influenced by many-body hydrodynamic interactions mediated by a suspending fluid. However, theoretical and numerical treatments of such interactions are extremely difficult. To overcome this situation, we developed a fluid particle dynamics (FPD) method [H. Tanaka and T. Araki, Phys. Rev. Lett., 2000, 35, 3523], which is based on two key approximations: (i) a colloidal particle is treated as a highly viscous particle and (ii) the viscosity profile is described by a smooth interfacial profile function. Approximation (i) makes our method free from the solid-fluid boundary condition, significantly simplifying the treatment of many-body hydrodynamic interactions while satisfying the incompressible condition without the Stokes approximation. Approximation (ii) allows us to incorporate an extra degree of freedom in a fluid, e.g., orientational order and concentration, as an additional field variable. Here, we consider two fundamental problems associated with these approximations. One is the introduction of thermal noise and the other is the incorporation of coupling of the colloid surface with an order parameter introduced into a fluid component, which is crucial when considering colloidal particles suspended in a complex fluid. Here, we show that our FPD method makes it possible to simulate colloid dynamics properly while including full hydrodynamic interactions, inertia effects, incompressibility, thermal noise, and additional degrees of freedom of a fluid, which may be relevant for wide applications in colloidal and soft matter science.
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Affiliation(s)
- Akira Furukawa
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
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23
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Campbell AI, Wittkowski R, ten Hagen B, Löwen H, Ebbens SJ. Helical paths, gravitaxis, and separation phenomena for mass-anisotropic self-propelling colloids: Experiment versus theory. J Chem Phys 2017; 147:084905. [DOI: 10.1063/1.4998605] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Andrew I. Campbell
- Department of Chemical and Biological Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
| | - Borge ten Hagen
- Physics of Fluids Group and Max Planck Center Twente, Department of Science and Technology, MESA+ Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Stephen J. Ebbens
- Department of Chemical and Biological Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom
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24
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Packing, entropic patchiness, and self-assembly of non-convex colloidal particles: A simulation perspective. Curr Opin Colloid Interface Sci 2017. [DOI: 10.1016/j.cocis.2017.05.005] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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25
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Feigel A. Dynamics of a mechanical system with multiple degrees of freedom out of thermal equilibrium. Phys Rev E 2017; 95:052106. [PMID: 28618544 DOI: 10.1103/physreve.95.052106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2017] [Indexed: 11/07/2022]
Abstract
Out of thermal equilibrium, an environment imposes effective mechanical forces on nanofabricated devices as well as on microscopic chemical or biological systems. Here we address the question of how to calculate these forces together with the response of the system from first principles. We show that an ideal gaslike environment, even near thermal equilibrium, can enforce a specific steady state on the system by creating effective potentials in otherwise homogeneous space. An example of stable and unstable rectifications of thermal fluctuations is presented using a modified Feynman-Smoluchowski ratchet with two degrees of freedom. Moreover, the stability of a steady configuration depends on its chiral symmetry. The transition rate probabilities and the corresponding kinetic equations are derived for a complex mechanical system with arbitrary degrees of freedom. This work, therefore, extends the applicability of mechanical systems as a toy model playground of statistical physics for active and living matter with multiple degrees of freedom.
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Affiliation(s)
- A Feigel
- Racah Institute of Physics, Hebrew University of Jerusalem, 9190401 Israel
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26
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Koens L, Lisicki M, Lauga E. The non-Gaussian tops and tails of diffusing boomerangs. SOFT MATTER 2017; 13:2977-2982. [PMID: 28362456 DOI: 10.1039/c6sm02649d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Experiments involving the two-dimensional passive diffusion of colloidal boomerangs tracked off their centre of mobility have shown striking non-Gaussian tails in their probability distribution function [Chakrabarty et al., Soft Matter, 2016, 12, 4318]. This in turn can lead to anomalous diffusion characteristics, including mean drift. In this paper, we develop a general theoretical explanation for these measurements. The idea relies on calculating the two-dimensional probability densities at the centre of mobility of the particle, where all distributions are Gaussian, and then transforming them to a different reference point. Our model clearly captures the experimental results, without any fitting parameters, and demonstrates that the one-dimensional probability distributions may also exhibit strongly non-Gaussian tops. These results indicate that the choice of tracking point can cause a considerable departure from Gaussian statistics, potentially causing some common modelling techniques to fail.
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Affiliation(s)
- Lyndon Koens
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK.
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27
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Jahanshahi S, Löwen H, Ten Hagen B. Brownian motion of a circle swimmer in a harmonic trap. Phys Rev E 2017; 95:022606. [PMID: 28297979 DOI: 10.1103/physreve.95.022606] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Indexed: 06/06/2023]
Abstract
We study the dynamics of a Brownian circle swimmer with a time-dependent self-propulsion velocity in an external temporally varying harmonic potential. For several situations, the noise-free swimming paths, the noise-averaged mean trajectories, and the mean-square displacements are calculated analytically or by computer simulation. Based on our results, we discuss optimal swimming strategies in order to explore a maximum spatial range around the trap center. In particular, we find a resonance situation for the maximum escape distance as a function of the various frequencies in the system. Moreover, the influence of the Brownian noise is analyzed by comparing noise-free trajectories at zero temperature with the corresponding noise-averaged trajectories at finite temperature. The latter reveal various complex self-similar spiral or rosette-like patterns. Our predictions can be tested in experiments on artificial and biological microswimmers under dynamical external confinement.
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Affiliation(s)
- Soudeh Jahanshahi
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Borge Ten Hagen
- Physics of Fluids Group, Faculty of Science and Technology, University of Twente, 7500 AE Enschede, The Netherlands
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28
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van der Wel C, Kraft DJ. Automated tracking of colloidal clusters with sub-pixel accuracy and precision. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:044001. [PMID: 27875327 DOI: 10.1088/1361-648x/29/4/044001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Quantitative tracking of features from video images is a basic technique employed in many areas of science. Here, we present a method for the tracking of features that partially overlap, in order to be able to track so-called colloidal molecules. Our approach implements two improvements into existing particle tracking algorithms. Firstly, we use the history of previously identified feature locations to successfully find their positions in consecutive frames. Secondly, we present a framework for non-linear least-squares fitting to summed radial model functions and analyze the accuracy (bias) and precision (random error) of the method on artificial data. We find that our tracking algorithm correctly identifies overlapping features with an accuracy below 0.2% of the feature radius and a precision of 0.1 to 0.01 pixels for a typical image of a colloidal cluster. Finally, we use our method to extract the three-dimensional diffusion tensor from the Brownian motion of colloidal dimers.
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Affiliation(s)
- Casper van der Wel
- Soft Matter Physics, Huygens-Kamerlingh Onnes Laboratory, Leiden University, PO Box 9504, 2300 RA Leiden, The Netherlands
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29
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Löwen H. Dynamical Density Functional Theory for Brownian Dynamics of Colloidal Particles. VARIATIONAL METHODS IN MOLECULAR MODELING 2017. [DOI: 10.1007/978-981-10-2502-0_9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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30
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Ilse SE, Holm C, de Graaf J. Surface roughness stabilizes the clustering of self-propelled triangles. J Chem Phys 2016; 145:134904. [PMID: 27782450 DOI: 10.1063/1.4963804] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sven Erik Ilse
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Joost de Graaf
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
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31
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Rotational friction of dipolar colloids measured by driven torsional oscillations. Sci Rep 2016; 6:34193. [PMID: 27680399 PMCID: PMC5040963 DOI: 10.1038/srep34193] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2016] [Accepted: 09/05/2016] [Indexed: 01/02/2023] Open
Abstract
Despite its prominent role in the dynamics of soft materials, rotational friction remains a quantity that is difficult to determine for many micron-sized objects. Here, we demonstrate how the Stokes coefficient of rotational friction can be obtained from the driven torsional oscillations of single particles in a highly viscous environment. The idea is that the oscillation amplitude of a dipolar particle under combined static and oscillating fields provides a measure for the Stokes friction. From numerical studies we derive a semi-empirical analytic expression for the amplitude of the oscillation, which cannot be calculated analytically from the equation of motion. We additionally demonstrate that this expression can be used to experimentally determine the rotational friction coefficient of single particles. Here, we record the amplitudes of a field-driven dipolar Janus microsphere with optical microscopy. The presented method distinguishes itself in its experimental and conceptual simplicity. The magnetic torque leaves the local environment unchanged, which contrasts with other approaches where, for example, additional mechanical (frictional) or thermal contributions have to be regarded.
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32
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Sarmiento-Gómez E, Villanueva-Valencia JR, Herrera-Velarde S, Ruiz-Santoyo JA, Santana-Solano J, Arauz-Lara JL, Castañeda-Priego R. Short-time dynamics of monomers and dimers in quasi-two-dimensional colloidal mixtures. Phys Rev E 2016; 94:012608. [PMID: 27575180 DOI: 10.1103/physreve.94.012608] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Indexed: 06/06/2023]
Abstract
We report on the short-time dynamics in colloidal mixtures made up of monomers and dimers highly confined between two glass plates. At low concentrations, the experimental measurements of colloidal motion agree well with the solution of the Navier-Stokes equation at low Reynolds numbers; the latter takes into account the increase in the drag force on a colloidal particle due to wall-particle hydrodynamic forces. More importantly, we find that the ratio of the short-time diffusion coefficient of the monomer and that of the center of mass of the dimmer is almost independent of both the dimer molar fraction, x_{d}, and the total packing fraction, ϕ, up to ϕ≈0.5. At higher concentrations, this ratio displays a small but systematic increase. A similar physical scenario is observed for the ratio between the parallel and the perpendicular components of the short-time diffusion coefficients of the dimer. This dynamical behavior is corroborated by means of molecular dynamics computer simulations that include explicitly the particle-particle hydrodynamic forces induced by the solvent. Our results suggest that the effects of colloid-colloid hydrodynamic interactions on the short-time diffusion coefficients are almost identical and factorable in both species.
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Affiliation(s)
- Erick Sarmiento-Gómez
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, SLP, México
| | | | - Salvador Herrera-Velarde
- Subdirección de Postgrado e Investigación, Instituto Tecnológico Superior de Xalapa, Sección 5A Reserva Territorial s/n, 91096 Xalapa, Veracruz, México
| | - José Arturo Ruiz-Santoyo
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, México
| | - Jesús Santana-Solano
- Cinvestav Unidad Monterrey, Parque de Investigación e Innovación Tecnológica, Apodaca, 66629 Nuevo León, México
| | - José Luis Arauz-Lara
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, SLP, México
| | - Ramón Castañeda-Priego
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, México
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33
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Askerka M, Maurer RJ, Batista VS, Tully JC. Role of Tensorial Electronic Friction in Energy Transfer at Metal Surfaces. PHYSICAL REVIEW LETTERS 2016; 116:217601. [PMID: 27284673 DOI: 10.1103/physrevlett.116.217601] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2016] [Indexed: 05/11/2023]
Abstract
An accurate description of nonadiabatic energy relaxation is crucial for modeling atomistic dynamics at metal surfaces. Interfacial energy transfer due to electron-hole pair excitations coupled to motion of molecular adsorbates is often simulated by Langevin molecular dynamics with electronic friction. Here, we present calculations of the full electronic friction tensor by using first order time-dependent perturbation theory at the density functional theory level. We show that the friction tensor is generally anisotropic and nondiagonal, as found for hydrogen atom on Pd(100) and CO on Cu(100) surfaces. This implies that electron-hole pair induced nonadiabatic coupling at metal surfaces leads to friction-induced mode coupling, therefore, opening an additional channel for energy redistribution. We demonstrate the robustness and accuracy of our results by direct comparison to established methods and experimental data.
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Affiliation(s)
- Mikhail Askerka
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Reinhard J Maurer
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - John C Tully
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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34
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Chakrabarty A, Wang F, Sun K, Wei QH. Effects of translation-rotation coupling on the displacement probability distribution functions of boomerang colloidal particles. SOFT MATTER 2016; 12:4318-4323. [PMID: 27079870 DOI: 10.1039/c6sm00568c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with their center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arm length. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical, to bean and then to crescent shape, and the angle averaged PDFs change from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. These 2D PDF shapes provide a clear physical picture of the non-zero mean displacements observed in boomerangs particles.
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Affiliation(s)
- Ayan Chakrabarty
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Feng Wang
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Kai Sun
- Department of Material Science and Engineering, University of Michigan, Ann Harbor, MI 48109, USA
| | - Qi-Huo Wei
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
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35
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Hoell C, Löwen H. Colloidal suspensions of C-particles: Entanglement, percolation and microrheology. J Chem Phys 2016; 144:174901. [DOI: 10.1063/1.4947237] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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36
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Cichocki B, Ekiel-Jeżewska ML, Wajnryb E. Note: Brownian motion of colloidal particles of arbitrary shape. J Chem Phys 2016; 144:076101. [PMID: 26897001 DOI: 10.1063/1.4942119] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Bogdan Cichocki
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Maria L Ekiel-Jeżewska
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland
| | - Eligiusz Wajnryb
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland
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37
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Palberg T, Wette P, Herlach DM. Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres. Phys Rev E 2016; 93:022601. [PMID: 26986371 DOI: 10.1103/physreve.93.022601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2015] [Indexed: 06/05/2023]
Abstract
The interfacial free energy is a central quantity in crystallization from the metastable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from these data effective nonequilibrium values for the interfacial free energy between the emerging bcc nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory (CNT). A strictly linear increase of the interfacial free energy was observed as a function of increased metastability. Here, we further analyze these data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. This enables us to present the first systematic experimental estimates for a reduced interfacial free energy, σ(0,bcc), between the bcc-crystal phase and the coexisting equilibrium fluid. Values obtained for σ(0,bcc) are on the order of a few k(B)T. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, σ(0) also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater.
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Affiliation(s)
- Thomas Palberg
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
| | - Patrick Wette
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51147 Köln, Germany
- Space Administration, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 53227 Bonn, Germany
| | - Dieter M Herlach
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51147 Köln, Germany
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38
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Fischer LP, Peter T, Holm C, de Graaf J. The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells. J Chem Phys 2015; 143:084107. [PMID: 26328818 DOI: 10.1063/1.4928502] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The so-called "raspberry" model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.
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Affiliation(s)
- Lukas P Fischer
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Toni Peter
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Joost de Graaf
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
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39
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Delong S, Balboa Usabiaga F, Donev A. Brownian dynamics of confined rigid bodies. J Chem Phys 2015; 143:144107. [DOI: 10.1063/1.4932062] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Steven Delong
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | | | - Aleksandar Donev
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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40
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Royer JR, Burton GL, Blair DL, Hudson SD. Rheology and dynamics of colloidal superballs. SOFT MATTER 2015; 11:5656-65. [PMID: 26078036 DOI: 10.1039/c5sm00729a] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Recent advances in colloidal synthesis make it possible to generate a wide array of precisely controlled, non-spherical particles. This provides a unique opportunity to probe the role that particle shape plays in the dynamics of colloidal suspensions, particularly at higher volume fractions, where particle interactions are important. We examine the role of particle shape by characterizing both the bulk rheology and micro-scale diffusion in a suspension of pseudo-cubic silica superballs. Working with these well-characterized shaped colloids, we can disentangle shape effects in the hydrodynamics of isolated particles from shape-mediated particle interactions. We find that the hydrodynamic properties of isolated superballs are marginally different from comparably sized hard spheres. However, shape-mediated interactions modify the suspension microstructure, leading to significant differences in the self-diffusion of the superballs. While this excluded volume interaction can be captured with a rescaling of the superball volume fraction, we observe qualitative differences in the shear thickening behavior of moderately concentrated superball suspensions that defy simple rescaling onto hard sphere results. This study helps to define the unknowns associated with the effects of shape on the rheology and dynamics of colloidal solutions.
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Affiliation(s)
- John R Royer
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
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41
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Passow C, ten Hagen B, Löwen H, Wagner J. Depolarized light scattering from prolate anisotropic particles: The influence of the particle shape on the field autocorrelation function. J Chem Phys 2015; 143:044903. [DOI: 10.1063/1.4926931] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
| | - Borge ten Hagen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Joachim Wagner
- Institut für Chemie, Universität Rostock, D-18051 Rostock, Germany
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42
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Kaiser A, Popowa K, Löwen H. Active dipole clusters: From helical motion to fission. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012301. [PMID: 26274156 DOI: 10.1103/physreve.92.012301] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Indexed: 06/04/2023]
Abstract
The structure of a finite particle cluster is typically determined by total energy minimization. Here we consider the case where a cluster of soft-sphere dipoles becomes active, i.e., when the individual particles exhibit an additional self-propulsion along their dipole moments. We numerically solve the overdamped equations of motion for soft-sphere dipoles in a solvent. Starting from an initial metastable dipolar cluster, the self-propulsion generates a complex cluster dynamics. The final cluster state has in general a structure widely different to the initial one, the details depend on the model parameters and on the protocol of how the self-propulsion is turned on. The center of mass of the cluster moves on a helical path, the details of which are governed by the initial cluster magnetization. An instantaneous switch to a high self-propulsion leads to fission of the cluster. However, fission does not occur if the self-propulsion is increased slowly to high strengths. Our predictions can be verified through experiments with self-phoretic colloidal Janus particles and for macroscopic self-propelled dipoles in a highly viscous solvent.
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Affiliation(s)
- Andreas Kaiser
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Katarina Popowa
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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43
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Cichocki B, Ekiel-Jeżewska ML, Wajnryb E. Brownian motion of a particle with arbitrary shape. J Chem Phys 2015; 142:214902. [PMID: 26049519 DOI: 10.1063/1.4921729] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Bogdan Cichocki
- Faculty of Physics, Institute of Theoretical Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Maria L. Ekiel-Jeżewska
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland
| | - Eligiusz Wajnryb
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland
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44
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ten Hagen B, Wittkowski R, Takagi D, Kümmel F, Bechinger C, Löwen H. Can the self-propulsion of anisotropic microswimmers be described by using forces and torques? JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:194110. [PMID: 25923010 DOI: 10.1088/0953-8984/27/19/194110] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The self-propulsion of artificial and biological microswimmers (or active colloidal particles) has often been modelled by using a force and a torque entering into the overdamped equations for the Brownian motion of passive particles. This seemingly contradicts the fact that a swimmer is force-free and torque-free, i.e. that the net force and torque on the particle vanish. Using different models for mechanical and diffusiophoretic self-propulsion, we demonstrate here that the equations of motion of microswimmers can be mapped onto those of passive particles with the shape-dependent grand resistance matrix and formally external effective forces and torques. This is consistent with experimental findings on the circular motion of artificial asymmetric microswimmers driven by self-diffusiophoresis. The concept of effective self-propulsion forces and torques significantly facilitates the understanding of the swimming paths, e.g. for a microswimmer under gravity. However, this concept has its limitations when the self-propulsion mechanism of a swimmer is disturbed either by another particle in its close vicinity or by interactions with obstacles, such as a wall.
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Affiliation(s)
- Borge ten Hagen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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45
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Jose J, Blab GA, van Blaaderen A, Imhof A. Jammed elastic shells - a 3D experimental soft frictionless granular system. SOFT MATTER 2015; 11:1800-1813. [PMID: 25608643 DOI: 10.1039/c4sm02098g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a new experimental system of monodisperse, soft, frictionless, fluorescent labeled elastic shells for the characterization of structure, universal scaling laws and force networks in 3D jammed matter. The elastic shells in a jammed packing are deformed in such a way that at each contact one of the shells buckles with a dimple and the other remain spherical, closely resembling overlapping spheres. Using confocal microscopy, we obtained 3D stacks of images of shells at different volume fractions which were subsequently processed in ImageJ software to find their coordinates. The determination of 3D coordinates involved three steps: locating the edges of shells in all 2D slices, analyzing their shape and subsequently finding their 2D coordinates, and finally determining their 3D centers by grouping the corresponding 2D coordinates. From this analysis routine we obtained particle coordinates with sub-pixel accuracy. In a contact pair we also identified the shell that underwent buckling forming a dimple by analyzing the intensity profile of a line that connects the centers of particle pairs. The amorphous structure of the packing was analyzed as a function of distance to the jamming threshold by investigating the radial distribution function, bond order parameters, contact numbers and the number of dimples per particle (buckling number), which is a unique property of this system. We find that the power law scaling of the contact number with excess volume fraction deviated from theoretical and computer simulation predictions. In addition, the buckling number also showed a similar scaling as that of the contact number with distance to the jamming transition.
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Affiliation(s)
- Jissy Jose
- Soft Condensed Matter, Debye Institute for NanoMaterials Science, Utrecht University, Princetonplein 1, 3584 CC, Utrecht, The Netherlands.
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46
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Abstract
Motivated by recent experimental measurements, the passive diffusion of the bacterium Leptospira interrogans is investigated theoretically. By approximating the cell shape as a straight helix and using the slender-body-theory approximation of Stokesian hydrodynamics, the resistance matrix of Leptospira is first determined numerically. The passive diffusion of the helical cell is then obtained computationally using a Langevin formulation which is sampled in time in a manner consistent with the experimental procedure. Our results are in excellent quantitative agreement with the experimental results with no adjustable parameters.
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Affiliation(s)
- Lyndon Koens
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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47
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Chakrabarty A, Konya A, Wang F, Selinger JV, Sun K, Wei QH. Brownian motion of arbitrarily shaped particles in two dimensions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:13844-13853. [PMID: 25357180 DOI: 10.1021/la5037053] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.
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Affiliation(s)
- Ayan Chakrabarty
- Liquid Crystal Institute and Department of Chemical Physics, Kent State University , Kent, Ohio 44242, United States
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48
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ten Hagen B, Kümmel F, Wittkowski R, Takagi D, Löwen H, Bechinger C. Gravitaxis of asymmetric self-propelled colloidal particles. Nat Commun 2014; 5:4829. [DOI: 10.1038/ncomms5829] [Citation(s) in RCA: 181] [Impact Index Per Article: 18.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2013] [Accepted: 07/09/2014] [Indexed: 01/25/2023] Open
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49
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Kümmel F, ten Hagen B, Wittkowski R, Takagi D, Buttinoni I, Eichhorn R, Volpe G, Löwen H, Bechinger C. Kümmel et al. reply:. PHYSICAL REVIEW LETTERS 2014; 113:029802. [PMID: 25062249 DOI: 10.1103/physrevlett.113.029802] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2014] [Indexed: 06/03/2023]
Affiliation(s)
- F Kümmel
- 2. Physikalisches Institut, Universität Stuttgart, D-70569 Stuttgart, Germany
| | - B ten Hagen
- Institut für Theoretische Physik II:, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - R Wittkowski
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
| | - D Takagi
- Department of Mathematics, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA
| | - I Buttinoni
- 2. Physikalisches Institut, Universität Stuttgart, D-70569 Stuttgart, Germany
| | - R Eichhorn
- Nordita, Royal Institute of Technology, and Stockholm University, SE-10691 Stockholm, Sweden
| | - G Volpe
- 2. Physikalisches Institut, Universität Stuttgart, D-70569 Stuttgart, Germany
| | - H Löwen
- Institut für Theoretische Physik II:, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - C Bechinger
- 2. Physikalisches Institut, Universität Stuttgart, D-70569 Stuttgart, Germany and Max-Planck-Institut für Intelligente Systeme, D-70569 Stuttgart, Germany
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50
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Parra-Rojas C, Soto R. Casimir effect in swimmer suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:013024. [PMID: 25122386 DOI: 10.1103/physreve.90.013024] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2014] [Indexed: 06/03/2023]
Abstract
We show that the Casimir effect can emerge in microswimmer suspensions. In principle, two effects conspire against the development of Casimir effects in swimmer suspensions. First, at low Reynolds number, the force on any closed volume vanishes, but here the relevant effect is the drag by the flow produced by the swimmers, which can be finite. Second, the fluid velocity and the pressure are linear on the swimmer force dipoles, and averaging over the swimmer orientations would lead to a vanishing effect. However, being that the suspension is a discrete system, the noise terms of the coarse-grained equations depend on the density, which itself fluctuates, resulting in effective nonlinear dynamics. Applying the tools developed for other nonequilibrium systems to general coarse-grained equations for swimmer suspensions, the Casimir drag is computed on immersed objects, and it is found to depend on the correlation function between the rescaled density and dipolar density fields. By introducing a model correlation function with medium-range order, explicit expressions are obtained for the Casimir drag on a body. When the correlation length is much larger than the microscopic cutoff, the average drag is independent of the correlation length, with a range that depends only on the size of the immersed bodies.
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Affiliation(s)
- C Parra-Rojas
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile and Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK
| | - R Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
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