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Xu X, Tang T, Gu M. Structural transitions in two-dimensional modulated systems under triangular confinement. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:72. [PMID: 36070024 DOI: 10.1140/epje/s10189-022-00229-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Accepted: 08/24/2022] [Indexed: 06/15/2023]
Abstract
We study numerically the structural transitions of two-dimensional systems of classic particles with competing interactions under a triangular confinement with two different types of soft-wall potentials. We observe a variety of novel confinement-induced equilibrium configurations as a function of particle density and confinement steepness for each considered confinement potential. The specific role played by the confining potentials on the ordering of the particle clusters is revealed. These findings allow us to control the self-organization of modulated systems through using external confinements.
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Affiliation(s)
- Xibin Xu
- Collaborative Innovation Center of Advanced Microstructures, School of physics, Nanjing University, Nanjing, China.
| | - Tao Tang
- Collaborative Innovation Center of Advanced Microstructures, School of physics, Nanjing University, Nanjing, China
| | - Min Gu
- Collaborative Innovation Center of Advanced Microstructures, School of physics, Nanjing University, Nanjing, China
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2
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Xu XB, Tang T, Wang ZH, Xu XN, Fang GY, Gu M. Nonequilibrium pattern formation in circularly confined two-dimensional systems with competing interactions. Phys Rev E 2021; 103:012604. [PMID: 33601588 DOI: 10.1103/physreve.103.012604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 12/19/2020] [Indexed: 11/07/2022]
Abstract
We numerically investigate the nonequilibrium behaviors of classic particles with competing interactions confined in a two-dimensional logarithmic trap. We reveal a quench-induced surprising dynamics exhibiting rich dynamic patterns depending upon confinement strength and trap size, which is attributed to the time-dependent competition between interparticle repulsions and attractions under a circular confinement. Moreover, in the collectively diffusive motions of the particles, we find that the emergence of dynamic structure transformation coincides with a diffusive mode transition from superdiffusion to subdiffusion. These findings are likely useful in understanding the pattern selection and evolution in various chemical and biological systems in addition to modulated systems, and add a new route to tailoring the morphology of pattern-forming systems.
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Affiliation(s)
- X B Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - T Tang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - Z H Wang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - X N Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - G Y Fang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
| | - M Gu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
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Xu XB, Wang ZH, Xu XN, Fang GY, Gu M. Structural transitions for 2D systems with competing interactions in logarithmic traps. J Chem Phys 2020; 152:054906. [DOI: 10.1063/1.5140816] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- X. B. Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - Z. H. Wang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - X. N. Xu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - G. Y. Fang
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
| | - M. Gu
- Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
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Tripathi AK, Kumar D, Puri S. Coarsening dynamics in the Swift-Hohenberg equation with an external field. Phys Rev E 2019; 99:022136. [PMID: 30934234 DOI: 10.1103/physreve.99.022136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Indexed: 11/07/2022]
Abstract
We study the Swift-Hohenberg equation (SHE) in the presence of an external field. The application of the field leads to a phase diagram with three phases, i.e., stripe, hexagon, and uniform. We focus on coarsening after a quench from the uniform to stripe or hexagon regions. For stripe patterns, we find that the length scale associated with the order-parameter structure factor has the same growth exponent (≃1/4) as for the SHE with zero field. The growth process is slower in the case of hexagonal patterns, with the effective growth exponent varying between 1/6 and 1/9, depending on the quench parameters. For deep quenches in the hexagonal phase, the growth process stops at late stages when defect boundaries become pinned.
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Affiliation(s)
- Ashwani K Tripathi
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India.,Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, Republic of Korea
| | - Deepak Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India
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Bupathy A, Banerjee V, Puri S. Columnar domains and anisotropic growth laws in dipolar systems. Phys Rev E 2017; 95:060103. [PMID: 28709210 DOI: 10.1103/physreve.95.060103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2016] [Indexed: 11/07/2022]
Abstract
Magnetic and dielectric solids are well-represented by the Ising model with dipolar interactions (IM+DI). The latter are long-ranged, fluctuating in sign, and anisotropic. Equilibrium studies have revealed novel consequences of these complicated interactions, but their effect on nonequilibrium behavior is not explored. We perform a deep temperature quench to study the kinetics of domain growth in the d=3 IM+DI. Our main observations are (i) the emergence of columnar domains along the z axis (Ising axis) with a transient periodicity in the xy plane; (ii) anisotropic growth laws: ℓ_{ρ}(t)∼t^{ϕ}; ℓ_{z}(t)∼t^{ψ}, where ρ[over ⃗]=(x,y) and ℓ is the characteristic length scale; (iii) generalized dynamical scaling for the correlation function: C(ρ,z;t)=g(ρ/ℓ_{ρ},z/ℓ_{z}); and (iv) an asymptotic Porod tail in the corresponding structure factor: S(k_{ρ},0;t)∼k_{ρ}^{-3}; S(0,k_{z};t)∼k_{z}^{-2}. Our results explain the experimentally observed columnar morphologies in a wide range of dipolar systems, and they have important technological implications.
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Affiliation(s)
- Arunkumar Bupathy
- Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Santos A, Singh C, Glotzer SC. Coarse-grained models of tethers for fast self-assembly simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011113. [PMID: 20365329 DOI: 10.1103/physreve.81.011113] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2009] [Indexed: 05/29/2023]
Abstract
Long molecular ligands or "tethers" play an important role in the self-assembly of many nanoscale systems. These tethers, whose only interaction may be a hard-core repulsion, contribute significantly to the free energy of the system because of their large conformational entropy. Here, we investigate how simple approximate models can be developed and used to quickly determine the configurations into which tethers will self assemble in nanoscale systems. We derive criteria that determine when these models are expected to be accurate. Finally, we propose a generalized two-body approximation that can be used as a toy model for the self-assembly of tethers in systems of arbitrary geometry and apply this to the self-assembly of self-assembled monolayers on a planar surface. We compare our results to those in the literature obtained via atomistic and dissipative particle dynamics simulations.
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Affiliation(s)
- Aaron Santos
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA
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Dominguez R, Barros K, Klein W. Early time kinetics of systems with spatial symmetry breaking. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:041121. [PMID: 19518187 DOI: 10.1103/physreve.79.041121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2008] [Revised: 02/20/2009] [Indexed: 05/27/2023]
Abstract
In this paper we present a study of the early stages of unstable state evolution of systems with spatial symmetry changes. In contrast to the early time linear theory of unstable evolution described by Cahn, Hilliard, and Cook, we develop a generalized theory that predicts two distinct stages of the early evolution for symmetry-breaking phase transitions. In the first stage the dynamics is dominated by symmetry-preserving evolution. In the second stage, which shares some characteristics with the Cahn-Hilliard-Cook theory, noise-driven fluctuations break the symmetry of the initial phase on a time scale which is large compared to the first stage for systems with long interaction ranges. To test the theory we present the results of numerical simulations of the initial evolution of a long-range antiferromagnetic Ising model quenched into an unstable region. We investigate two types of symmetry-breaking transitions in this system: disorder-to-order and order-to-order transitions. For the order-to-order case, the Fourier modes evolve as a linear combination of exponentially growing or decaying terms with different time scales.
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Affiliation(s)
- Rachele Dominguez
- Department of Physics, Center for Computational Science, Boston University, Boston, Massachusetts 02215, USA.
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Tarzia M, Coniglio A. Lamellar order, microphase structures, and glassy phase in a field theoretic model for charged colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011410. [PMID: 17358153 DOI: 10.1103/physreve.75.011410] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2006] [Indexed: 05/06/2023]
Abstract
In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation.
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Affiliation(s)
- Marco Tarzia
- Dipartimento di Scienze Fisiche and INFN sezione di Napoli, Università degli Studi di Napoli "Federico II," Complesso Universitario di Monte Sant'Angelo, via Cinthia, 80126 Napoli, Italy
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Xu A, Gonnella G, Lamura A. Morphologies and flow patterns in quenching of lamellar systems with shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011505. [PMID: 16907098 DOI: 10.1103/physreve.74.011505] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Revised: 03/02/2006] [Indexed: 05/11/2023]
Abstract
We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with the pressure tensor and the chemical potential derived by the Brazovskii free energy. Our simulations are based on a mixed numerical method with the lattice Boltzmann equation and a finite difference scheme for Navier-Stokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects, and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one, and the system looks like a mixture of tilted lamellae, droplets, and small elongated domains. We refer to this as a region with a shear-induced structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered. The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose the presence of the applied flow.
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Affiliation(s)
- Aiguo Xu
- Dipartimento di Fisica, Università di Bari, via Amendola 173, 70126 Bari, Italy
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Tarzia M, Coniglio A. Pattern formation and glassy phase in the phi4 theory with a screened electrostatic repulsion. PHYSICAL REVIEW LETTERS 2006; 96:075702. [PMID: 16606111 DOI: 10.1103/physrevlett.96.075702] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2005] [Indexed: 05/08/2023]
Abstract
We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar, and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.
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Affiliation(s)
- Marco Tarzia
- Dipartimento di Scienze Fisiche, INFN sezione di Napoli, Università degli Studi di Napoli Federico II, Complesso Universitario di Monte Sant' Angelo, via Cinthia, 80126 Napoli, Italy
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Asciutto E, Roland C, Sagui C. Self-assembled patterns and strain-induced instabilities for modulated systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:021504. [PMID: 16196570 DOI: 10.1103/physreve.72.021504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2005] [Indexed: 05/04/2023]
Abstract
The self-assembled domain patterns of modulated systems are characteristic of a wide variety of chemical and physical systems, and are the result of competing interactions. From a technological point of view, there is considerable interest in these domain patterns, as they form suitable templates for the fabrication of nanostructures. We have analyzed the domains and instabilities that form in modulated systems, and show that a large variety of patterns--based on long-lived metastable or glassy states--may be formed as a compromise between the required equilibrium modulation period and the strain present in the system. The strain results from topologically constrained trajectories in phase space, that effectively preclude the equilibrium configuration.
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Affiliation(s)
- Eliana Asciutto
- Center for High Performance Simulations and Department of Physics, The North Carolina State University, Raleigh, North Carolina 27695-8202 USA
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Sagui C, Asciutto E, Roland C. New and exotic self-organized patterns for modulated nanoscale systems. NANO LETTERS 2005; 5:389-395. [PMID: 15794631 DOI: 10.1021/nl048224t] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The self-assembled domain patterns of modulated systems are the result of competing short-range attractive and long-range repulsive interactions found in diverse physical and chemical systems. From an application point of view, there is considerable interest in these domain patterns, as they form templates suitable for the fabrication of nanostructures. In this work we have generated a variety of new and exotic patterns, which represent either metastable or glassy states. These patterns arise as a compromise between the required equilibrium modulation period and the strain resulting from topologically constrained trajectories in phase space that effectively preclude the equilibrium configuration.
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Affiliation(s)
- Celeste Sagui
- Center for High Performance Simulation and Department of Physics, The North Carolina State University, Raleigh, NC 27695-8202, USA.
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González-Segredo N, Coveney PV. Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: Lattice-Boltzmann simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061501. [PMID: 15244570 DOI: 10.1103/physreve.69.061501] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2003] [Indexed: 05/24/2023]
Abstract
By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-assembly of sponge mesophases and gyroid liquid-crystalline cubic mesophases, hence confirming that (a) amphiphile-amphiphile interactions need not be long-ranged in order for periodically modulated structures to arise in a dynamics of competing interactions, and (b) a chemically specific model of the amphiphile is not required for the self-assembly of cubic mesophases, contradicting claims in the literature. We also observe a structural order-disorder transition between sponge and gyroid phases driven by amphiphile concentration alone or, independently, by the amphiphile-amphiphile and the amphiphile-binary fluid coupling parameters. For the growth-arrested mesophases, we also observe temporal oscillations in the structure function at all length scales; most of the wave numbers show slow decay, and long-term stationarity or growth for the others. We ascribe this behavior to a combination of complex amphiphile dynamics leading to Marangoni flows.
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Affiliation(s)
- Nélido González-Segredo
- Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street,London WC1H 0AJ, United Kingdom.
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Corberi F, Gonnella G, Lamura A. Ordering of the lamellar phase under a shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:016114. [PMID: 12241433 DOI: 10.1103/physreve.66.016114] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2001] [Indexed: 05/23/2023]
Abstract
The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free energy and the evolution follows a convection-diffusion equation. Lamellas order preferentially with the normal along the vorticity direction. Typical lengths grow as gamma t(5/4) (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3.
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Affiliation(s)
- F Corberi
- Istituto Nazionale per la Fisica della Materia, Unità di Salerno and Dipartimento di Fisica, Università di Salerno, 84081 Baronissi Salerno, Italy
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Tran-Cong Q, Kawai J, Endoh K. Modes selection in polymer mixtures undergoing phase separation by photochemical reactions. CHAOS (WOODBURY, N.Y.) 1999; 9:298-307. [PMID: 12779827 DOI: 10.1063/1.166406] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Phase separation kinetics and morphology of binary polymer mixtures (A/B) in the presence of photochemical reactions were investigated by using phase-contrast optical microscopy combined with digital image analysis. The polymers were chemically designed in such a way that two types of chemical reactions, intermolecular photodimerization and intramolecular photoisomerization, of polymer segments can be induced and controled by irradiation with ultraviolet light. Unlike the conventional case, the phase separation in the presence of these reactions is spontaneously frozen due to the suppression of the long-wavelength instabilities, resulting in stationary spatial structures with intrinsic periodicities. These characteristic length scales are determined by the competition between the two antagonistic interactions: phase separation as a relatively short-range activation and the photochemical reaction as a long-range inhibition. Furthermore, it was found that the spatial symmetry breaking of concentration fluctuations can emerge from the elastic stress associated with the nonhomogeneous kinetics of the reactions. Experimental data obtained with three types of reactions: A-A only cross-link, A-A and B-B simultaneous cross-links and the reversible A<-->B photoisomerization are described. These results do not only indicate that combination of chemical reactions and phase separation could provide a novel method to control the morphology of multiphase polymer materials, but also suggest that photoreactive polymers can be used as a chemical system to study the mode-selection process in polymers far from thermodynamic equilibrium. (c) 1999 American Institute of Physics.
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Affiliation(s)
- Qui Tran-Cong
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Kyoto 606, Japan
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Arlett J, Whitehead JP, MacIsaac AB, De'Bell K. Phase diagram for the striped phase in the two-dimensional dipolar Ising model. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:3394-3402. [PMID: 9986239 DOI: 10.1103/physrevb.54.3394] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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17
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Verdasca J, Borckmans P, Dewel G. Chemically frozen phase separation in an adsorbed layer. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:R4616-R4619. [PMID: 9964088 DOI: 10.1103/physreve.52.r4616] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ohta T, Ito A. Dynamics of phase separation in copolymer-homopolymer mixtures. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:5250-5260. [PMID: 9964024 DOI: 10.1103/physreve.52.5250] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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19
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Sagui C, Desai RC. Effects of long-range repulsive interactions on Ostwald ripening. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:2822-2840. [PMID: 9963729 DOI: 10.1103/physreve.52.2822] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Sagui C, Desai RC. Late-stage kinetics of systems with competing interactions quenched into the hexagonal phase. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:2807-2821. [PMID: 9963728 DOI: 10.1103/physreve.52.2807] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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21
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Booth I, MacIsaac AB, Whitehead JP, De'Bell K. Domain structures in ultrathin magnetic films. PHYSICAL REVIEW LETTERS 1995; 75:950-953. [PMID: 10060159 DOI: 10.1103/physrevlett.75.950] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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22
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Glotzer SC, Muthukumar M. Reaction-controlled morphology of phase-separating mixtures. PHYSICAL REVIEW LETTERS 1995; 74:2034-2037. [PMID: 10057825 DOI: 10.1103/physrevlett.74.2034] [Citation(s) in RCA: 163] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
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Abstract
A wide variety of two- and three-dimensional physical-chemical systems display domain patterns in equilibrium. The phenomenology of these patterns, and of the shapes of their constituent domains, is reviewed here from a point of view that interprets these patterns as a manifestation of modulated phases. These phases are stabilized by competing interactions and are characterized by periodic spatial variations of the pertinent order parameter, the corresponding modulation period generally displaying a dependence on temperature and other external fields. This simple picture provides a unifying framework to account for striking and substantial similarities revealed in the prevalent "stripe" and "bubble" morphologies as well as in commonly observed, characteristic domain-shape instabilities. Several areas of particular current interest are discussed.
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Glotzer SC, Coniglio A. Self-consistent solution of phase separation with competing interactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:4241-4244. [PMID: 9962483 DOI: 10.1103/physreve.50.4241] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
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Hagberg A, Meron E. Complex patterns in reaction-diffusion systems: A tale of two front instabilities. CHAOS (WOODBURY, N.Y.) 1994; 4:477-484. [PMID: 12780123 DOI: 10.1063/1.166047] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatiotemporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.
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Affiliation(s)
- Aric Hagberg
- Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721Arizona Center for Mathematical Sciences, Department of Mathematics, University of Arizona, Tucson, Arizona 85721
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Glotzer SC, Stauffer D, Jan N. Monte Carlo simulations of phase separation in chemically reactive binary mixtures. PHYSICAL REVIEW LETTERS 1994; 72:4109-4112. [PMID: 10056384 DOI: 10.1103/physrevlett.72.4109] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
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Hagberg A, Meron E. From labyrinthine patterns to spiral turbulence. PHYSICAL REVIEW LETTERS 1994; 72:2494-2497. [PMID: 10055894 DOI: 10.1103/physrevlett.72.2494] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Schönborn O, Puri S, Desai RC. Singular perturbation analysis for unstable systems with convective nonlinearity. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:3480-3483. [PMID: 9961617 DOI: 10.1103/physreve.49.3480] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Sagui C, Desai RC. Kinetics of phase separation in two-dimensional systems with competing interactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:2225-2244. [PMID: 9961465 DOI: 10.1103/physreve.49.2225] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Sagui C, Desai RC. Kinetics of topological defects in systems with competing interactions. PHYSICAL REVIEW LETTERS 1993; 71:3995-3998. [PMID: 10055127 DOI: 10.1103/physrevlett.71.3995] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Chen LQ, Khachaturyan AG. Dynamics of simultaneous ordering and phase separation and effect of long-range Coulomb interactions. PHYSICAL REVIEW LETTERS 1993; 70:1477-1480. [PMID: 10053302 DOI: 10.1103/physrevlett.70.1477] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Hayakawa H, Rácz Z, Tsuzuki T. Ordering kinetics in systems with long-range interactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:1499-1505. [PMID: 9960168 DOI: 10.1103/physreve.47.1499] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chakrabarti A, Gunton JD. Lamellar phase in a model for block copolymers. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:R792-R795. [PMID: 9960163 DOI: 10.1103/physreve.47.r792] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Elder KR, Viñals J, Grant M. Dynamic scaling and quasiordered states in the two-dimensional Swift-Hohenberg equation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:7618-7629. [PMID: 9908113 DOI: 10.1103/physreva.46.7618] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Dworschak K. Locking of optical and thermodynamic length scales in laser-induced melt-solid patterns on silicon. PHYSICAL REVIEW LETTERS 1992; 69:3487-3490. [PMID: 10046834 DOI: 10.1103/physrevlett.69.3487] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Hurley MM, Singer SJ. Domain-array melting in the dipolar lattice gas. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:5783-5786. [PMID: 10004380 DOI: 10.1103/physrevb.46.5783] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wang ZG. Mean-field approximations and coupled maps for kinetic lattice models. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:692-700. [PMID: 9907034 DOI: 10.1103/physreva.45.692] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Elder KR, Morin B, Grant M, Desai RC. Late-time theory for the effects of a conserved field on the kinetics of an order-disorder transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:6673-6688. [PMID: 9998540 DOI: 10.1103/physrevb.44.6673] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Thomson JR, Cowan WM, Elder KR, Daviet P, Soga G, Zhang Z, Grant M, Zuckermann MJ. Neural networks with constrained inputs as models for pattern formation in primate visual cortex. J Biol Phys 1991. [DOI: 10.1007/bf00417810] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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