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Li X, Fang H, Sankaewtong K, Li M, Chen Y, Huang J, Ni R, Tanaka H, Tan P. Phase Reentrances and Solid Deformations in Confined Colloidal Crystals. PHYSICAL REVIEW LETTERS 2024; 132:018202. [PMID: 38242650 DOI: 10.1103/physrevlett.132.018202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Revised: 11/15/2023] [Accepted: 12/18/2023] [Indexed: 01/21/2024]
Abstract
A simple geometric constraint often leads to novel, complex crystalline phases distinct from the bulk. Using thin-film charge colloidal crystals, a model system with tunable interactions, we study the effects of geometric constraints. Through a combination of experiments and simulations, we systematically explore phase reentrances and solid deformation modes concerning geometrical confinement strength, identifying two distinct categories of phase reentrances below a characteristic layer number, N_{c}: one for bcc bulk-stable and another for fcc bulk-stable systems. We further verify that the dominant thermodynamic origin is the nonmonotonic dependence of solids' free energy on the degree of spatial confinement. Moreover, we discover transitions in solid deformation modes between interface-energy and bulk-energy dominance: below a specific layer number, N_{k}, geometric constraints generate unique soft deformation modes adaptive to confinement. These findings on the N-dependent thermodynamic and kinetic behaviors offer fresh insights into understanding and manipulating thin-film crystal structures.
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Affiliation(s)
- Xiaoxia Li
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
| | - Huang Fang
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Krongtum Sankaewtong
- Chemical Engineering, School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore
| | - Minhuan Li
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Yanshuang Chen
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Jiping Huang
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Ran Ni
- Chemical Engineering, School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore
| | - Hajime Tanaka
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
- Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
| | - Peng Tan
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
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Bharti, Deb D. Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems. Phys Chem Chem Phys 2022; 24:5154-5163. [PMID: 35156967 DOI: 10.1039/d1cp04366h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the interaction between a pair of liquid crystalline (LC) particles. The underlying substrate potential with which the GB particles interact varies sinusoidally in one direction only. At a given temperature and density of the GB system, we varied the substrate's periodicity (as) but fixed the substrate strength. We observed that with a small value of as, an underlying substrate helps to stabilize a disordered LC nematic phase to a 2D solid phase. However, for an intermediate range of as, the system melts and transitions to a modulate-smectic. Finally, with a further increase in as, the system undergoes a structural depinning transition and returns to an LC nematic phase like a free system with no substrate. We argue that a three-way interplay of the energies arising from orientation-dependent particle-particle and particle-substrate interaction makes it possible for the system to undergo substrate-periodicity-dependent multiple phase transitions in the GB LC system.
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Affiliation(s)
- Bharti
- School of Physics and Materials Science, Thapar Institute of Engineering and Technology, Patiala, Punjab - 147004, India.
| | - Debabrata Deb
- School of Physics and Materials Science, Thapar Institute of Engineering and Technology, Patiala, Punjab - 147004, India.
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Pan H, Kalman GJ, Hartmann P, Donkó Z. Strongly coupled Yukawa trilayer liquid: Structure and dynamics. Phys Rev E 2020; 102:043206. [PMID: 33212692 DOI: 10.1103/physreve.102.043206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2020] [Accepted: 09/09/2020] [Indexed: 11/07/2022]
Abstract
The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional disorder becomes the governing feature. Theoretical dispersion relations are obtained by applying the quasilocalized charge approximation (QLCA) formalism, while numerical data are generated by microcanonical molecular dynamics simulations. The dispersions and polarizations of the collective excitations obtained through both of these methods are compared and discussed in detail. We find that the QLCA method is, in general, very satisfactory, but that there are phenomena not covered by the QLCA. In particular, by analyzing the dynamical longitudinal and transverse current fluctuation spectra we discover the existence of a structure not related to the collective mode spectra. This also provides insight into the long-standing problem of the gap frequency discrepancy, observed in strongly coupled layered systems in earlier studies.
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Affiliation(s)
- Hong Pan
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
| | - Gabor J Kalman
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
| | - Peter Hartmann
- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary.,Center for Astrophysics, Space Physics and Engineering Research (CASPER), Baylor University, 100 Research Pkwy, Waco, Texas 76706, USA
| | - Zoltán Donkó
- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary
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Zampetaki AV, Huang H, Du CR, Löwen H, Ivlev AV. Buckling of two-dimensional plasma crystals with nonreciprocal interactions. Phys Rev E 2020; 102:043204. [PMID: 33212619 DOI: 10.1103/physreve.102.043204] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 09/15/2020] [Indexed: 11/07/2022]
Abstract
Laboratory realizations of two-dimensional (2D) plasma crystals typically involve monodisperse microparticles confined into horizontal monolayers in radio-frequency (rf) plasma sheaths. This gives rise to the so-called plasma wakes beneath the microparticles. The presence of wakes renders the interactions in such systems nonreciprocal, a fact that can lead to a quite different behavior from the one expected for their reciprocal counterparts. Here we examine the buckling of a hexagonal 2D plasma crystal, occurring as the confinement strength is decreased, taking explicitly into account the nonreciprocity of the system via a well-established point-wake model. We observe that for a finite wake charge, the monolayer hexagonal crystal undergoes a transition first to a bilayer hexagonal structure, unrealizable in harmonically confined reciprocal Yukawa systems, and subsequently to a bilayer square structure. Our theoretical results are confirmed by molecular dynamics simulations for experimentally relevant parameters, indicating the potential of their observation in state-of-the-art experiments with 2D complex plasmas.
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Affiliation(s)
- A V Zampetaki
- Max-Planck-Institut für Extraterrestrische Physik, 85741 Garching, Germany.,Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
| | - H Huang
- College of Science, Donghua University, 201620 Shanghai, People's Republic of China
| | - C-R Du
- College of Science, Donghua University, 201620 Shanghai, People's Republic of China
| | - H Löwen
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
| | - A V Ivlev
- Max-Planck-Institut für Extraterrestrische Physik, 85741 Garching, Germany
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Šamaj L, Trulsson M, Trizac E. Strong-coupling theory of counterions with hard cores between symmetrically charged walls. Phys Rev E 2020; 102:042604. [PMID: 33212638 DOI: 10.1103/physreve.102.042604] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 09/16/2020] [Indexed: 06/11/2023]
Abstract
By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on pointlike counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two subpopulations, one for each plate, and integrates out one subpopulation to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard-sphere overlap are unavoidable, and thus rule out configurations.
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Affiliation(s)
- Ladislav Šamaj
- Institute of Physics, Slovak Academy of Sciences, 84511 Bratislava, Slovakia
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Antlanger M, Kahl G, Mazars M, Šamaj L, Trizac E. The asymmetric Wigner bilayer. J Chem Phys 2018; 149:244904. [PMID: 30599708 DOI: 10.1063/1.5053651] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates and form there ordered sublattices. Using complementary tools (analytic and numerical), we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: net charge neutrality on each of the plates on the one hand and particles' self-organization into commensurate sublattices on the other hand. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows us to study on a quantitative level phenomena such as over- and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive, complementary Monte Carlo simulations in the canonical ensemble, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy. The simple setup of the Wigner bilayer system offers an attractive possibility to study and to control complex scenarios and strategies of colloidal self-assembly, via the variation of two system parameters.
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Affiliation(s)
- Moritz Antlanger
- Institute for Theoretical Physics and Center for Computational Materials Science (CMS), TU Wien, Wien, Austria
| | - Gerhard Kahl
- Institute for Theoretical Physics and Center for Computational Materials Science (CMS), TU Wien, Wien, Austria
| | - Martial Mazars
- Laboratoire de Physique Théorique (UMR 8627), Université Paris-Sud, Université Paris-Saclay, and CNRS, Orsay, France
| | - Ladislav Šamaj
- Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
| | - Emmanuel Trizac
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, Orsay, France
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7
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Eshraghi M, Horbach J. Molecular dynamics simulation of charged colloids confined between hard walls: pre-melting and pre-freezing across the BCC-fluid coexistence. SOFT MATTER 2018; 14:4141-4149. [PMID: 29700548 DOI: 10.1039/c8sm00398j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Molecular dynamics (MD) computer simulations are used to study the structure of hard-core Yukawa systems confined between two parallel hard walls. States around the coexistence between a fluid and a body-centered cubic (BCC) crystal are considered. In all cases a pronounced layering in the vicinity of the walls is observed. Using a thermodynamic integration scheme, we determine the wall-fluid interfacial free energy γ which is negative and monotonically decreasing with increasing bulk density of the fluid. In the case of the fluid, the layers next to the walls undergo a transition from a fluid to a hexagonal structure. This pre-freezing transition occurs well below the coexistence bulk density of the fluid. The confined BCC crystal in (111) orientation shows melted regions between crystalline face-centered cubic (FCC) layers close to the wall and the BCC bulk region.
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Affiliation(s)
- Mojtaba Eshraghi
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
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8
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Šamaj L, Trulsson M, Trizac E. Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases. SOFT MATTER 2018; 14:4040-4052. [PMID: 29790889 DOI: 10.1039/c8sm00571k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance d. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner strong-coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of d comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.
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Affiliation(s)
- Ladislav Šamaj
- Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia
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9
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Travěnec I, Šamaj L. Phase diagram and critical properties of Yukawa bilayers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022306. [PMID: 26382405 DOI: 10.1103/physreve.92.022306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2015] [Indexed: 06/05/2023]
Abstract
We study the ground-state Wigner bilayers of pointlike particles with Yukawa pairwise interactions, confined to the surface of two parallel hard walls at dimensionless distance η. The model involves as limiting cases the unscreened Coulomb potential and hard spheres. The phase diagram of Yukawa particles, studied numerically by Messina and Löwen [Phys. Rev. Lett. 91, 146101 (2003)], exhibits five different staggered phases as η varies from 0 to intermediate values. We present a lattice summation method using the generalized Misra functions which permits us to calculate the energy per particle of the phases with a precision much higher than usual in computer simulations. This allows us to address some tiny details of the phase diagram. Going from the hexagonal phase I to phase II is shown to occur at η=0. All second-order phase transitions are proved to be of mean-field type. We also derive the asymptotic shape of critical lines close to the Coulomb and hard-spheres limits. In and close to the hard-spheres limit, the dependence of the internal parameters of the present phases on η is determined exactly.
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Affiliation(s)
- Igor Travěnec
- Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia
| | - Ladislav Šamaj
- Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia
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10
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Noises-induced regime shifts and -enhanced stability under a model of lake approaching eutrophication. ECOLOGICAL COMPLEXITY 2015. [DOI: 10.1016/j.ecocom.2015.02.005] [Citation(s) in RCA: 60] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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11
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Yao Z, Olvera de la Cruz M. Electrostatic repulsion-driven crystallization model arising from filament networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042605. [PMID: 23679441 DOI: 10.1103/physreve.87.042605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2013] [Revised: 03/30/2013] [Indexed: 06/02/2023]
Abstract
The crystallization of bundles in filament networks interacting via long-range repulsions in confinement is described by a phenomenological model. The model demonstrates the formation of the hexagonal crystalline order via the interplay of the confinement potential and the filament-filament repulsion. Two distinct crystallization mechanisms in the short- and large- screening length regimes are discussed, and the phase diagram is obtained. Simulation of large bundles predicts the existence of topological defects within the bundled filaments. This electrostatic repulsion-driven crystallization model arising from studying filament networks can even find a more general context extending to charged colloidal systems.
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Affiliation(s)
- Zhenwei Yao
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, USA
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12
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Kalman GJ, Hartmann P, Donkó Z, Golden KI, Kyrkos S. Collective modes in two-dimensional binary Yukawa systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:043103. [PMID: 23679526 DOI: 10.1103/physreve.87.043103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2012] [Indexed: 06/02/2023]
Abstract
We analyze via theoretical approaches and molecular dynamics simulations the collective mode structure of strongly coupled two-dimensional binary Yukawa systems, for selected density, mass, and charge ratios, both in the liquid and crystalline solid phases. Theoretically, the liquid phase is described through the quasilocalized charge approximation (QLCA) approach, while in the crystalline phase we study the centered honeycomb and the staggered rectangular crystal structures through the standard harmonic phonon approximation. We identify "longitudinal" and "transverse" acoustic and optic modes and find that the longitudinal acoustic mode evolves from its weakly coupled counterpart in a discontinuous nonperturbative fashion. The low-frequency acoustic excitations are governed by the oscillation frequency of the average atom, while the high-frequency optic excitation frequencies are related to the Einstein frequencies of the systems.
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Affiliation(s)
- Gabor J Kalman
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA.
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Oğuz EC, Reinmüller A, Schöpe HJ, Palberg T, Messina R, Löwen H. Crystalline multilayers of charged colloids in soft confinement: experiment versus theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:464123. [PMID: 23114225 DOI: 10.1088/0953-8984/24/46/464123] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We combine real-space experiments and lattice sum calculations to investigate the phase diagram of charged colloidal particles under soft confinement. In the experiments we explore the equilibrium phase diagram of charged colloidal spheres in aqueous suspensions confined between two parallel charged walls at low background salt concentrations. Motivated by the experiments, we perform lattice sum minimizations to predict the crystalline ground state of point-like Yukawa particles which are exposed to a soft confining wall potential. In the multilayered crystalline regime, we obtain good agreement between the experimental and numerical findings: upon increasing the density we recover the sequence [structure: see text].
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Affiliation(s)
- E C Oğuz
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany.
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Löwen H, Allahyarov E, Ivlev A, Morfill GE. Heterogeneous crystallization in colloids and complex plasmas: the role of binary mobilities. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:284125. [PMID: 22738924 DOI: 10.1088/0953-8984/24/28/284125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Both charged colloidal suspensions and complex (dusty) plasmas represent classical many-body strongly coupled Coulomb systems. Here we discuss their basic properties and focus on their heterogeneous crystallization from an undercooled melt. In particular, a model with different mobilities is proposed which is realizable in binary mixtures of charged particles. Within this binary-mobility model, the crystallization behaviour near a structured wall is explored by Brownian dynamics computer simulations. As a result, the propagation velocity of the crystal-fluid interface is a nonmonotonic function of the mobility ratio (if expressed in terms of an averaged mobility).
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Affiliation(s)
- H Löwen
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany.
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15
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Curk T, de Hoogh A, Martinez-Veracoechea FJ, Eiser E, Frenkel D, Dobnikar J, Leunissen ME. Layering, freezing, and re-entrant melting of hard spheres in soft confinement. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021502. [PMID: 22463214 DOI: 10.1103/physreve.85.021502] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2011] [Indexed: 05/31/2023]
Abstract
Confinement can have a dramatic effect on the behavior of all sorts of particulate systems, and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness of the confining potential. Using grand canonical Monte Carlo simulations, we determine the phase diagram of three-dimensional hard spheres that in one dimension are constrained to a plane by a harmonic potential. The phase behavior depends strongly on the density and on the stiffness of the harmonic confinement. While we find the familiar sequence of confined hexagonal and square-symmetric packings, we do not observe any of the usual intervening ordered phases. Instead, the system phase separates under strong confinement, or forms a layered re-entrant liquid phase under weaker confinement. It is plausible that this behavior is due to the larger positional freedom in a soft confining potential and to the contribution that the confinement energy makes to the total free energy. The fact that specific structures can be induced or suppressed by simply changing the confinement conditions (e.g., in a dielectrophoretic trap) is important for applications that involve self-assembled structures of colloidal particles.
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Affiliation(s)
- Tine Curk
- Faculty of Natural Sciences and Mathematics, Koroška c. 160, SI-2000 Maribor, Slovenia
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16
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17
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Colloidal Crystallization Between Two and Three Dimensions. ADVANCES IN CHEMICAL PHYSICS 2011. [DOI: 10.1002/9781118158715.ch3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/28/2023]
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18
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Samaj L, Trizac E. Wigner-crystal formulation of strong-coupling theory for counterions near planar charged interfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041401. [PMID: 22181140 DOI: 10.1103/physreve.84.041401] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2011] [Indexed: 05/31/2023]
Abstract
We present a new analytical approach to the strong electrostatic coupling regime (SC) that can be achieved equivalently at low temperatures, high charges, low dielectric permittivity, etc. Two geometries are analyzed in detail: one charged wall first, and then two parallel walls at small distances that can be likely or oppositely charged. In all cases, only one type of mobile counterions is present, and ensures electroneutrality (salt-free case). The method is based on a systematic expansion around the ground state formed by the two-dimensional Wigner crystal(s) of counterions at the plate(s). The leading SC order stems from a single-particle theory, and coincides with the virial SC approach that has been much studied in the last 10 years. The first correction has the functional form of the virial SC prediction, but the prefactor is different. The present theory is free of divergences and the obtained results, both for symmetrically and asymmetrically charged plates, are in excellent agreement with available data of Monte Carlo simulations under strong and intermediate Coulombic couplings. All results obtained represent relevant improvements over the virial SC estimates. The present SC theory starting from the Wigner crystal and therefore coined Wigner SC, sheds light on anomalous phenomena like the counterion mediated like-charge attraction, and the opposite-charge repulsion.
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Affiliation(s)
- Ladislav Samaj
- Laboratoire de Physique Théorique et Modèles Statistiques, UMR CNRS 8626, Université Paris-Sud, F-91405 Orsay, France
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19
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Deb D, Winkler A, Yamani MH, Oettel M, Virnau P, Binder K. Hard sphere fluids at a soft repulsive wall: A comparative study using Monte Carlo and density functional methods. J Chem Phys 2011; 134:214706. [DOI: 10.1063/1.3593197] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Samaj L, Trizac E. Counterions at highly charged interfaces: from one plate to like-charge attraction. PHYSICAL REVIEW LETTERS 2011; 106:078301. [PMID: 21405546 DOI: 10.1103/physrevlett.106.078301] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2010] [Indexed: 05/30/2023]
Abstract
We present an analytical approach for similarly and highly charged planar interfaces in the presence of counterions. The procedure is physically transparent and based on an exact low temperature expansion around the ground state formed by the two-dimensional Wigner crystal of counterions. The one plate problem is worked out, together with the two plates situation. Unlike previous approaches, the expansion is free of divergences, and is shown to be in excellent agreement with available data of Monte Carlo simulations under strong Coulombic couplings. In the two plates case, the present results shed light on the like-charge attraction regime.
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Affiliation(s)
- Ladislav Samaj
- Laboratoire de Physique Théorique et Modèles Statistiques, UMR CNRS, Université Paris-Sud, Orsay, France
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21
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Peng Y, Wang Z, Alsayed AM, Yodh AG, Han Y. Melting of colloidal crystal films. PHYSICAL REVIEW LETTERS 2010; 104:205703. [PMID: 20867039 DOI: 10.1103/physrevlett.104.205703] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2010] [Revised: 03/26/2010] [Indexed: 05/29/2023]
Abstract
We study melting mechanisms in single and polycrystalline colloidal films composed of diameter-tunable microgel spheres with short-ranged repulsive interactions and confined between two glass walls. Thick films (>4 layers), thin-films (≤4 layers), and monolayers exhibit different melting behaviors. Thick films melt from grain boundaries in polycrystalline solid films and from film-wall interfaces in single-crystal films; a liquid-solid coexistence regime is observed in thick films but vanishes at a critical thickness of 4 layers. Thin solid films (2 to 4 layers) melt into the liquid phase in one step from both grain boundaries and from within crystalline domains. Monolayers melt in two steps with a middle hexatic phase.
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Affiliation(s)
- Y Peng
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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Contreras-Aburto C, Méndez-Alcaraz JM, Castañeda-Priego R. Structure and effective interactions in parallel monolayers of charged spherical colloids. J Chem Phys 2010; 132:174111. [DOI: 10.1063/1.3407454] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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23
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Cao YG, Li QX, Fu GY, Liu J, Guo HZ, Hu X, Li XJ. Depinning dynamics of two-dimensional magnetized colloids on a random substrate. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:155101. [PMID: 21389546 DOI: 10.1088/0953-8984/22/15/155101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We perform Langevin simulations on the depinning dynamics of two-dimensional magnetized colloids on a random substrate. On increasing the magnetic field strength, we find for the first time a crossover from plastic to smectic flows as well as a crossover from smectic to elastic crystal flows above depinning. For both the smectic and elastic crystal flows, a power-law scaling relationship could be obtained between the average velocity and applied driving force. The scaling exponent is found to be larger than 1 for smectic flow. But, for the elastic crystal flow, the scaling exponent is found to be less than 1. For the plastic flow, no power-law scaling relationship between the average velocity and applied driving force can be derived and history dependence of the depinning occurs. Within the crossover from plastic to smectic flows, a sudden decrease in the critical driving force is observed, and a sudden increase is found in the critical driving force across the crossover from smectic to elastic crystal flows, accompanied by a crossing of the curves of average velocity versus driving force.
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Affiliation(s)
- Y G Cao
- School of Physics and Engineering, Zhengzhou University, Zhengzhou 450001, People's Republic of China.
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24
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Hartmann P, Donkó Z, Kalman GJ, Kyrkos S, Golden KI, Rosenberg M. Collective dynamics of complex plasma bilayers. PHYSICAL REVIEW LETTERS 2009; 103:245002. [PMID: 20366204 DOI: 10.1103/physrevlett.103.245002] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2009] [Indexed: 05/29/2023]
Abstract
A classical dusty plasma experiment was performed using two different dust grain sizes to form a strongly coupled asymmetric bilayer (two closely spaced interacting monolayers) of two species of charged dust particles. The observation and analysis of the thermally excited particle oscillations revealed the collective mode structure and dispersion (wave propagation) in this system; in particular, the existence of the theoretically predicted k=0 energy (frequency) gap was verified. Equilibrium molecular-dynamics simulations were performed to emulate the experiment, assuming Yukawa-type interparticle interaction. The simulations and analytic calculations based both on lattice summation and on the quasilocalized charge approximation approach are in good agreement with the experimental findings and help in identifying and characterizing the observed phenomena.
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Affiliation(s)
- P Hartmann
- Research Institute for Solid State Physics and Optics of the Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 49, Hungary
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25
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Löwen H. Twenty years of confined colloids: from confinement-induced freezing to giant breathing. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:474203. [PMID: 21832482 DOI: 10.1088/0953-8984/21/47/474203] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The physics of colloidal suspensions confined in slits and cavities has significantly advanced during the last twenty years. In particular, freezing transitions in confinement have been addressed by theory and simulations and experimental realizations were proposed to confine colloidal particles to two dimensions. After reviewing this progress, we discuss the generalization to time-dependent confinement which leads to nonequilibrium situations. This is elaborated further for unstable situations where the particles can leave the confinement. In particular, the completely overdamped Brownian motion of a colloidal particle in a time-dependent harmonic trap is considered. The analytically soluble model of a time-dependent quadratic potential is used to extract the dynamical properties of the potential if the potential undergoes periodic switching from a confining harmonic potential to an unstable one. The amplitudes of the oscillating particle response can strongly grow in time, which we refer to as 'giant breathing'. This giant breathing process occurs also in anharmonic potentials and is verifiable in real-space experiments of colloids in laser-optical fields.
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Affiliation(s)
- H Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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26
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Oğuz EC, Messina R, Löwen H. Multilayered crystals of macroions under slit confinement. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:424110. [PMID: 21715845 DOI: 10.1088/0953-8984/21/42/424110] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The crystalline ground state of macroions confined between two neutral parallel plates in the presence of their homogeneously spread counterions is calculated by lattice sum minimization of candidate phases involving up to six layers. For increasing macroion density, a cascade of solid-solid transitions is found involving various multilayered crystals. The cascade includes triangular monolayer and buckled bilayer as well as rhombic, squared and triangular phase structures.
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Affiliation(s)
- E C Oğuz
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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27
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Messina R. Electrostatics in soft matter. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:113102. [PMID: 21693906 DOI: 10.1088/0953-8984/21/11/113102] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Recent progress in understanding the effect of electrostatics in soft matter is presented. A vast number of materials contain ions, ranging from the molecular scale (e.g. electrolyte) to the meso/macroscopic one (e.g. charged colloidal particles or polyelectrolytes). Their (micro)structure and physico-chemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular, theoretical and simulational aspects, including the experimental motivations, will be discussed.
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Affiliation(s)
- René Messina
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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Assoud L, Messina R, Löwen H. Binary crystals in two-dimensional two-component Yukawa mixtures. J Chem Phys 2008; 129:164511. [DOI: 10.1063/1.2996515] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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30
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Sheu ASY, Rice S. Transient ordering in a quasi-two-dimensional liquid near freezing. J Chem Phys 2008; 128:244517. [DOI: 10.1063/1.2949797] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Klapp SHL, Zeng Y, Qu D, von Klitzing R. Surviving structure in colloidal suspensions squeezed from 3D to 2D. PHYSICAL REVIEW LETTERS 2008; 100:118303. [PMID: 18517836 DOI: 10.1103/physrevlett.100.118303] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2007] [Indexed: 05/26/2023]
Abstract
Combining colloidal-probe experiments and computer simulations, we analyze the solvation forces F of charged silica colloids confined in films of various thicknesses h. We show that the oscillations characterizing F(h), for sufficiently large h, are determined by the dominant wavelength of the bulk radial distribution function. As a consequence, both quantities display the same power-law density dependence. This is the first direct evidence, in a system treatable both by experiment and by simulation, that the structural wavelength in bulk and confinement coincide, in agreement with predictions from density functional theory. Moreover, theoretical and experimental data are in excellent quantitative agreement.
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Affiliation(s)
- Sabine H L Klapp
- Institut für Theoretische Physik, Sekr. PN 7-1, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
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32
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Fontecha AB, Palberg T, Schöpe HJ. Construction and stability of a close-packed structure observed in thin colloidal crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:050402. [PMID: 18233615 DOI: 10.1103/physreve.76.050402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2007] [Indexed: 05/25/2023]
Abstract
We have characterized a close-packed structure of confined charged colloidal spheres, which has been recently discovered. Using different microscopy experiments, the vertically arranged hexagonal planes of n - hcp perpendicular are found to continuously evolve from the horizontally oriented stacks of n hexagonal planes (nDelta) following the maximum packing criterion, but discontinuously transform to a stack of n+1 square planes [(n+1)[SHAPE OF A SQUARE]]. Large mechanically stable domains with threefold twin structures are regularly observed in the suspended state at packing fractions between 0.4 and 0.58.
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Affiliation(s)
- Ana Barreira Fontecha
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, D-55128 Mainz, Germany
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33
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Fortini A, Dijkstra M. Phase behaviour of hard spheres confined between parallel hard plates: manipulation of colloidal crystal structures by confinement. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:L371-L378. [PMID: 21690830 DOI: 10.1088/0953-8984/18/28/l02] [Citation(s) in RCA: 111] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study the phase behaviour of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five hard-sphere diameters using free energy calculations. We find a first-order fluid-solid transition, which corresponds to either capillary freezing or melting depending on the plate separation. The coexisting solid phase consists of crystalline layers with either triangular ([Formula: see text]) or square ([Formula: see text]) symmetry. Increasing the plate separation, we find a sequence of crystal structures from [Formula: see text], where n is the number of crystal layers, in agreement with experiments on colloids. At high densities, the transition between square to triangular phases is interrupted by intermediate structures, e.g., prism, buckled, and rhombic phases.
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Affiliation(s)
- Andrea Fortini
- Soft Condensed Matter, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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Ramiro-Manzano F, Meseguer F, Bonet E, Rodriguez I. Faceting and commensurability in crystal structures of colloidal thin films. PHYSICAL REVIEW LETTERS 2006; 97:028304. [PMID: 16907485 DOI: 10.1103/physrevlett.97.028304] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2006] [Indexed: 05/11/2023]
Abstract
This Letter investigates the influence of finite size effects on the particle arrangement of thin film colloidal crystals. A rich variety of crystallographic faceting with large single domain microcrystallites is shown. Optical reflectance experiments together with scanning electron microscopy permit the identification of the crystal symmetry and the facet orientation, as well as the exact number of monolayers. When the cell thickness is not commensurable with a high symmetry layering, particles arrange themselves in a periodic distribution of (111)- and (100)-orientated face centered cubic (fcc) microcrystallites separated by planar defects. These structures can be described as a fcc ordering orientated along a vicinal surface, modified by a periodic distribution of fcc (111) stacking faults.
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Affiliation(s)
- F Ramiro-Manzano
- Centro Tecnológico de Ondas-Unidad Asociada CSIC-UPV, Universidad Politécnica de Valencia, Avenida Los Naranjos, 46022 Valencia, Spain
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35
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Schöpe HJ, Barreira Fontecha A, König H, Marques Hueso J, Biehl R. Fast microscopic method for large scale determination of structure, morphology, and quality of thin colloidal crystals. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2006; 22:1828-38. [PMID: 16460114 DOI: 10.1021/la0524972] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
We present a novel fast microscopic method to analyze the crystal structures of air-dried or suspended colloidal multilayer systems. Once typical lattice spacings of such films are in the range of visible light, characteristic Bragg scattering patterns are observed. If in microscopic observations these are excluded from image construction, a unique color coding for regions of different structures, morphologies, and layer numbers results. Incoherently scattering defect structures, however, may not be excluded from image construction and thus remain visible with high resolution.
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Affiliation(s)
- H J Schöpe
- Institut f. Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany.
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36
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Ren CL, Ma YQ. Phase Behavior in Thin Films of Confined Colloid−Polymer Mixtures. J Am Chem Soc 2006; 128:2733-7. [PMID: 16492061 DOI: 10.1021/ja057569q] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Using self-consistent-field and density-functional theories, we first investigate colloidal self-assembly of colloid-polymer films confined between two soft surfaces grafted by polymers. With increasing colloidal concentrations, the film undergoes a series of transitions from disordered liquid --> sparse square --> hexagonal (or mixed square-hexagonal) --> dense square --> cylindrical structures in a plane, which results from the competition between the entropic elasticity of polymer brushes and the steric packing effect of colloidal particles. A phase diagram displays the stable regions of different in-layer ordering structures as the colloidal concentration is varied and layering transitions as the polymer-grafted density is decreased. Our results show a new control mechanism to stabilize the ordering of structures within the films.
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Affiliation(s)
- Chun-lai Ren
- National Laboratory of Solid State Microstructures, Nanjing University, China
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37
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Messina R, Löwen H. Confined colloidal bilayers under shear: steady state and relaxation back to equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:011405. [PMID: 16486138 DOI: 10.1103/physreve.73.011405] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2005] [Revised: 10/17/2005] [Indexed: 05/06/2023]
Abstract
Crystalline bilayers of charged colloidal suspensions which are confined between two parallel plates and sheared via a relative motion of the two plates are studied by extensive Brownian dynamics computer simulations. The charge-stabilized suspension is modeled by a Yukawa pair potential. The unsheared equilibrium configuration is two crystalline layers with a nested quadratic in-plane structure. For increasing shear rates (.)gamma, we find the following steady states: First, up to a threshold of the shear rate, there is a static solid which is elastically sheared. Above the threshold, there are two crystalline layers sliding on top of each other with a registration procedure. Higher shear rates melt the crystalline bilayers and even higher shear rates lead to a reentrant solid stratified in the shear direction. This qualitative scenario is similar to that found in previous bulk simulations. We have then studied the relaxation of the sheared steady state back to equilibrium after an instantaneous cessation of shear and found a nonmonotonic behavior of the typical relaxation time as a function of the shear rate (.)gamma. In particular, application of high shear rates accelerates the relaxation back to equilibrium since shear-ordering facilitates the growth of the equilibrium crystal. This mechanism can be used to grow defect-free colloidal crystals from strongly sheared suspensions. Our theoretical predictions can be verified in real-space experiments of strongly confined charged suspensions.
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Affiliation(s)
- René Messina
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
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38
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Löwen H, Esztermann A, Wysocki A, Allahyarov E, Messina R, Jusufi A, Hoffmann N, Gottwald D, Kahl G, Konieczny M, Likos CN. Charged colloids and polyelectrolytes: from statics to electrokinetics. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/1742-6596/11/1/021] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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39
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Hoogenboom JP, van Langen-Suurling AK, Romijn J, van Blaaderen A. Epitaxial growth of a colloidal hard-sphere hcp crystal and the effects of epitaxial mismatch on crystal structure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:051602. [PMID: 15244824 DOI: 10.1103/physreve.69.051602] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2003] [Indexed: 05/24/2023]
Abstract
We demonstrate the epitaxial growth of hard-sphere hcp and double hcp crystals using a surface pattern that directly dictates the stacking sequence. A detailed three-dimensional analysis based on real-space measurements is performed on crystal structure as a function of template-crystal mismatch, which demonstrates the possibilities of colloidal epitaxy as a model system for studying the effects of a patterned substrate on crystal structure. Perfect template-induced hcp-crystal growth occurs at an isotropically deformed template. At deformed lattices we observe growth of a non-close-packed superstructure and of a perfect (100)-aligned fcc crystal. Small mismatches lead to increased out-of-plane displacements followed by a structural breakup in "crystal" grains where particle positions in successive layers are strictly periodic and "defect" grains where these positions are displaced with respect to each other. Large mismatches prevent crystallization in the surface layers. The volume fraction was found to vary drastically (up to about 20% ) as a function of template deformation.
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Affiliation(s)
- J P Hoogenboom
- F O M Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands.
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