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Li C, Li J, Zhang H, Yang Y. A systematic study on immiscible binary systems undergoing thermal/photo reversible chemical reactions. Phys Chem Chem Phys 2023; 25:1642-1648. [PMID: 36510818 DOI: 10.1039/d2cp04526e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
In this work, we systematically study an immiscible binary system undergoing thermal/photo reversible reactions in theory. For the thermal reaction case, no dissipative structures can be formed and only uniform equilibrium states are observed but the dynamical evolution to these trivial states witnesses a new type of sophisticated phase amplification phenomenon-temporary phase separation (TPS). Linear analysis and light-scattering calculations confirm that TPS is predominated either by spinodal decomposition or nucleation and growth mechanism, or by both successively. For the photo reaction case, steady dissipative patterns exist and are maintained by the external energy input of lights. Linear analysis together with simulations reveals that the characteristic wavelength (ξ) of these structures shortens as the input energy density increases and they obey the relation of ln ξ∝ 1/Tb with Tb the effective temperature of lights. The TPS phenomenon and length-scale dependency of dissipative patterns observed in this simple binary system might have rich implications for the non-equilibrium thermodynamics of biological systems.
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Affiliation(s)
- Changhao Li
- The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
| | - Jianfeng Li
- The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
| | - Hongdong Zhang
- The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
| | - Yuliang Yang
- The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China.
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2
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Zwicker D. The intertwined physics of active chemical reactions and phase separation. Curr Opin Colloid Interface Sci 2022. [DOI: 10.1016/j.cocis.2022.101606] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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3
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Longo TJ, Anisimov MA. Phase transitions affected by natural and forceful molecular interconversion. J Chem Phys 2022; 156:084502. [DOI: 10.1063/5.0081180] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g., the equilibrium interconversion of enantiomers) or forcefully (e.g., via an external source of energy or matter), then the process of phase separation may drastically change. In this case, depending on the nature of interconversion, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of another stable phase, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we phenomenologically generalize the Cahn–Hilliard theory of spinodal decomposition to include the molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed phenomenology to accurately describe the simulation results of three atomistic models that demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Finally, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation.
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Affiliation(s)
- Thomas J. Longo
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Mikhail A. Anisimov
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, USA
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4
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Adachi K, Kawaguchi K. Surface wetting by kinetic control of liquid-liquid phase separation. Phys Rev E 2021; 104:L042801. [PMID: 34781488 DOI: 10.1103/physreve.104.l042801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 10/10/2021] [Indexed: 06/13/2023]
Abstract
Motivated by the observations of intracellular phase separations and the wetting of cell membranes by protein droplets, we study the nonequilibrium surface wetting by Monte Carlo simulations of a lattice gas model involving particle creation. We find that, even when complete wetting should occur in equilibrium, the fast creation of particles can hinder the surface wetting for a long time due to the bulk droplet formation. Performing molecular dynamics simulations, we show that this situation also holds in colloidal particle systems when the disorder density is sufficiently high. The results suggest an intracellular control mechanism of surface wetting by changing the speed of component synthesis.
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Affiliation(s)
- Kyosuke Adachi
- Nonequilibrium Physics of Living Matter RIKEN Hakubi Research Team, RIKEN Center for Biosystems Dynamics Research, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe 650-0047, Japan
- RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, 2-1 Hirosawa, Wako 351-0198, Japan
| | - Kyogo Kawaguchi
- Nonequilibrium Physics of Living Matter RIKEN Hakubi Research Team, RIKEN Center for Biosystems Dynamics Research, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe 650-0047, Japan
- RIKEN Cluster for Pioneering Research, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe 650-0047, Japan
- Universal Biology Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
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5
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Li YI, Cates ME. Hierarchical microphase separation in non-conserved active mixtures. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:119. [PMID: 34580768 PMCID: PMC8476393 DOI: 10.1140/epje/s10189-021-00113-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Accepted: 08/18/2021] [Indexed: 05/09/2023]
Abstract
Non-equilibrium phase separating systems with reactions, such as biomolecular condensates and bacteria colonies, can break time-reversal symmetry (TRS) in two distinct ways. Firstly, the conservative and non-conservative sectors of the dynamics can be governed by incompatible free energies; when both sectors are present, this is the leading-order TRS violation, captured in its simplest form by 'Model AB'. Second, the diffusive dynamics can break TRS in its own right. This happens only at higher order in the gradient expansion (but is the leading behaviour without reactions present) and is captured by 'Active Model B+' (AMB+). Each of the two mechanisms can lead to microphase separation, by quite different routes. Here we introduce Model AB+, for which both mechanisms are simultaneously present, and show that for slow reaction rates the system can undergo a new type of hierarchical microphase separation, which we call 'bubbly microphase separation'. In this state, small droplets of one fluid are continuously created and absorbed into large droplets, whose length-scales are controlled by the competing reactive and diffusive dynamics.
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Affiliation(s)
- Yuting I Li
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge, CB3 0WA, UK.
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge, CB3 0WA, UK
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6
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Weber CA, Zwicker D, Jülicher F, Lee CF. Physics of active emulsions. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:064601. [PMID: 30731446 DOI: 10.1088/1361-6633/ab052b] [Citation(s) in RCA: 110] [Impact Index Per Article: 22.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input, for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled, and they can divide spontaneously. In this review, we discuss the physics of phase separation and emulsions and show how the concepts that govern such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development of novel applications in chemical engineering and models for the origin of life.
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Affiliation(s)
- Christoph A Weber
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany. Center for Systems Biology Dresden, CSBD, Dresden, Germany. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, United States of America
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Guo YQ, Pan JX, Sun MN, Zhang JJ. Phase transition of a symmetric diblock copolymer induced by nanorods with different surface chemistry. J Chem Phys 2017; 146:024902. [PMID: 28088151 DOI: 10.1063/1.4973560] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
We investigate the phase transition of a symmetric diblock copolymer induced by nanorods with different surface chemistry. The results demonstrate that the system occurs the phase transition from a disordered structure to ordered parallel lamellae and then to the tilted layered structure as the number of rods increases. The dynamic evolution of the domain size and the order parameter of the microstructure are also examined. Furthermore, the influence of rod property, rod-phase interaction, rod-rod interaction, rod length, and polymerization degree on the behavior of the polymer system is also investigated systematically. Moreover, longer amphiphilic nanorods tend to make the polymer system form the hexagonal structure. It transforms into a perpendicular lamellar structure as the polymerization degree increases. Our simulations provide an efficient method for determining how to obtain the ordered structure on the nanometer scales and design the functional materials with optical, electronic, and magnetic properties.
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Affiliation(s)
- Yu-Qi Guo
- School of Physics and Information Engineering, Shanxi Normal University, Linfen 041004, China
| | - Jun-Xing Pan
- School of Chemistry and Materials Science, Shanxi Normal University, Linfen 041004, China
| | - Min-Na Sun
- School of Chemistry and Materials Science, Shanxi Normal University, Linfen 041004, China
| | - Jin-Jun Zhang
- School of Physics and Information Engineering, Shanxi Normal University, Linfen 041004, China
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Luneville L, Mallick K, Pontikis V, Simeone D. Patterning in systems driven by nonlocal external forces. Phys Rev E 2016; 94:052126. [PMID: 27967002 DOI: 10.1103/physreve.94.052126] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Indexed: 11/07/2022]
Abstract
This work focuses on systems displaying domain patterns resulting from competing external and internal dynamics. To this end, we introduce a Lyapunov functional capable of describing the steady states of systems subject to external forces, by adding nonlocal terms to the Landau Ginzburg free energy of the system. Thereby, we extend the existing methodology treating long-range order interactions, to the case of external nonlocal forces. By studying the quadratic term of this Lyapunov functional, we compute the phase diagram in the temperature versus external field and we determine all possible modulated phases (domain patterns) as a function of the external forces and the temperature. Finally, we investigate patterning in chemical reactive mixtures and binary mixtures under irradiation, and we show that the last case opens the path toward micro-structural engineering of materials.
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Affiliation(s)
- L Luneville
- DEN-Service dÉtudes et de Recherche en Mathématique Appliquée, LRC CARMEN CEA-CNRS-ECP/SPMS, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France
| | - K Mallick
- CEA/DRF/IPhT, CEA, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France
| | - V Pontikis
- CEA/DRF/IRAMIS/LSI, CEA, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France
| | - D Simeone
- DEN-Service de Recherches Métallurgiques Appliquées, LRC CARMEN CEA-CNRS-ECP/SPMS, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France
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9
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Simeone D, Demange G, Luneville L. Disrupted coarsening in complex Cahn-Hilliard dynamics. Phys Rev E 2013; 88:032116. [PMID: 24125222 DOI: 10.1103/physreve.88.032116] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2013] [Revised: 06/24/2013] [Indexed: 11/07/2022]
Abstract
Predicting the pattern formation in a system maintained far from equilibrium is a complex task. For a given dynamics governed by the evolution of a conservative order parameter, recent investigations have demonstrated that the knowledge of the long time expression of the order parameter is sufficient to predict the existence of disrupted coarsening, i.e., the pinning of the inhomogeneities wavelength to a well defined value. However, there exists some dynamics for which the asymptotic form of the order parameter remains unknown. The Cahn-Hilliard-like equation used to describe the stability of solids under irradiation belongs to this class of equations. In this paper, we present an alternative to predict the patterning induced by this equation. Based on a simple ansatz, we calculated the form factor and proved that a disrupted coarsening takes place in such dynamics. This disrupted coarsening results from the bifurcation of the implicit equation linking the characteristic length of the dynamics (k_{m}^{∞})^{-1} to a control parameter describing the irradiation. This analysis is supported by direct simulations. From this paper, it clearly appears that the bifurcation of k_{m}^{∞} is a criterion for disrupted coarsening.
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Affiliation(s)
- David Simeone
- CEA/DEN/DANS/SRMA/LA2M-LRC CARMEN, CNRS-CEA-ECP, CEN Saclay, F-91191 Gif sur Yvette, France
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10
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Liu Y, Kuksenok O, Balazs AC. Using light to guide the motion of nanorods in photoresponsive binary blends: designing hierarchically structured nanocomposites. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2013; 29:12785-12795. [PMID: 23848191 DOI: 10.1021/la401775p] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
One of the challenges in creating high-performance polymer nanocomposites is establishing effective routes for tailoring the morphology of both the polymer mixture and the dispersed nanoparticles, which contribute desirable optical, electrical, and mechanical properties. Using computational modeling, we devise an effective method for simultaneously controlling the spatial regularity of the polymer phases and the distribution of the rods within this matrix. We focus on mixtures of photosensitive AB binary blends and A-coated nanorods; in the presence of light, the binary blends undergo a reversible chemical reaction and phase separation to yield a morphology resembling that of microphase-separated diblock copolymers. We simulate the effects of illuminating this sample with a uniform background light and a higher intensity, spatially localized light, which is rastered over the sample with a velocity v. The resulting material displays a periodically ordered, essentially defect-free morphology, with the A-like nanoparticles localized in lamellar A domains. The dynamic behavior of the rods within this system can be controlled by varying the velocity v and Γ2, the reaction rate coefficient produced by the higher intensity light. Specifically, the rastering light can drive the rods to be "pushed" along the lamellar domains or oriented perpendicular to these stripes. Given these attributes, we isolate scenarios where the system encompasses a complex hierarchical structure, with rods that are simultaneously ordered along two distinct directions within the periodic matrix. Namely, the rods form long nanowires that span the length of the sample and lie perpendicular to these wires in regularly spaced A lamellae. Hence, our approach points to new routes for producing self-organized rectangular grids, which can impart remarkable optoelectronic or mechanical properties to the materials.
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Affiliation(s)
- Ya Liu
- Chemical Engineering Department, University of Pittsburgh , Pittsburgh, Pennsylvania 15261, United States
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11
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Singh C, Hu Y, Khanal BP, Zubarev ER, Stellacci F, Glotzer SC. Striped nanowires and nanorods from mixed SAMS. NANOSCALE 2011; 3:3244-3250. [PMID: 21677996 DOI: 10.1039/c1nr10215j] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We investigate the use of mixed self-assembled monolayers (SAMs) for creating nanoscale striped patterns on nanowires and nanorods. Our simulations predict that SAMs comprised of an equal composition of length-mismatched, thermodynamically incompatible surfactants adsorbed on nanowire surfaces self-organize into equilibrium stripes of alternating composition always perpendicular, rather than parallel, to the nanowire axis. We support the simulation results with preliminary experimental investigations of gold nanorods coated with binary mixtures of ligand molecules, which show stripes roughly perpendicular to the rod axis in all cases.
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Affiliation(s)
- Chetana Singh
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, USA
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12
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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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13
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Pica Ciamarra M, Coniglio A, Nicodemi M. Phenomenology and theory of horizontally oscillated granular mixtures. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2007; 22:227-34. [PMID: 17318290 DOI: 10.1140/epje/e2007-00007-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2006] [Indexed: 05/14/2023]
Abstract
We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.
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Affiliation(s)
- M Pica Ciamarra
- Universitá di Napoli Federico II, INFN, Via Cintia, Napoli, Italy.
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14
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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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15
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Nakanishi H, Satoh M, Norisuye T, Tran-Cong-Miyata Q. Phase Separation of Interpenetrating Polymer Networks Synthesized by Using an Autocatalytic Reaction. Macromolecules 2006. [DOI: 10.1021/ma061198w] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hideyuki Nakanishi
- Department of Macromolecular Science and Engineering, Graduate School of Science and Technology, Kyoto Institute of Technology, Matsugasaki, Kyoto 606-8585, Japan
| | - Masahiro Satoh
- Department of Macromolecular Science and Engineering, Graduate School of Science and Technology, Kyoto Institute of Technology, Matsugasaki, Kyoto 606-8585, Japan
| | - Tomohisa Norisuye
- Department of Macromolecular Science and Engineering, Graduate School of Science and Technology, Kyoto Institute of Technology, Matsugasaki, Kyoto 606-8585, Japan
| | - Qui Tran-Cong-Miyata
- Department of Macromolecular Science and Engineering, Graduate School of Science and Technology, Kyoto Institute of Technology, Matsugasaki, Kyoto 606-8585, Japan
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16
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Ciamarra MP, Coniglio A, Nicodemi M. Dynamically induced effective interaction in periodically driven granular mixtures. PHYSICAL REVIEW LETTERS 2006; 97:038001. [PMID: 16907544 DOI: 10.1103/physrevlett.97.038001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2006] [Indexed: 05/11/2023]
Abstract
We show that a granular mixture subject to horizontal oscillations can be reduced to a monodisperse system of particles interacting via an effective interaction. This interaction is attractive at short distances and strongly anisotropic, and its features explain the system rich phenomenology, including segregation and stripe pattern formation. Finally, we show that a modified Cahn-Hilliard equation, which takes into account the characteristics of the effective interaction, is capable of describing the dynamics of the mixture.
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Affiliation(s)
- Massimo Pica Ciamarra
- Dipartimento di Scienze Fisiche, Universitá di Napoli 'Federico II', CNR-Coherentia, INFN, 80126 Napoli, Italia.
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17
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Furtado K, Yeomans JM. Lattice Boltzmann simulations of phase separation in chemically reactive binary fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:066124. [PMID: 16906931 DOI: 10.1103/physreve.73.066124] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2006] [Indexed: 05/11/2023]
Abstract
We use a lattice Boltzmann method to study pattern formation in chemically reactive binary fluids in the regime where hydrodynamic effects are important. The coupled equations solved by the method are a Cahn-Hilliard equation, modified by the inclusion of a reactive source term, and the Navier-Stokes equations for conservation of mass and momentum. The coupling is twofold, resulting from the advection of the order parameter by the velocity field and the effect of fluid composition on pressure. We study the evolution of the system following a critical quench for a linear and for a quadratic reaction source term. Comparison is made between the high and low viscosity regimes to identify the influence of hydrodynamic flows. In both cases hydrodynamics is found to influence the pathways available for domain growth and the eventual steady states.
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Affiliation(s)
- K Furtado
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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18
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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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19
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Yandek GR, Kyu T. Theoretical Modeling of the Phase Separation Dynamics in Blends of Reactive Monomers. MACROMOL THEOR SIMUL 2005. [DOI: 10.1002/mats.200400089] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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20
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Zhang JJ, Jin G, Ma Y. Orientational order transition of the striped microphase structure of a copolymer-homopolymer mixture under oscillatory particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:051803. [PMID: 16089563 DOI: 10.1103/physreve.71.051803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2005] [Revised: 03/14/2005] [Indexed: 05/03/2023]
Abstract
Based on the three-order-parameter model, we investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-homopolymer mixtures in the presence of periodic oscillatory particles. Under suitable conditions, although the macrophase separation of a system is almost isotropic, the microphase separation of the system will be significantly perturbed by the oscillatory field, and composition fluctuations are suppressed anisotropically. The isotropy of the microphase will be broken up. By changing the oscillatory amplitude and frequency, we observe the orientational order transition of a striped microphase structure from the isotropic state to a state parallel to the oscillatory direction, and from the parallel state to a state perpendicular to the oscillatory direction. We examine, in detail, the microstructure and orientational order parameter as well as the domain size in the process of orientational order transition under the oscillatory field. We study also how the microphase structure changes with the composition ratio of homopolymers and copolymers in mixtures. The results suggest that our model system may provide a simple way to realize orientational order transition of soft materials.
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Affiliation(s)
- Jin-Jun Zhang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
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Good K, Kuksenok O, Buxton GA, Ginzburg VV, Balazs AC. Effect of hydrodynamic interactions on the evolution of chemically reactive ternary mixtures. J Chem Phys 2004; 121:6052-63. [PMID: 15367034 DOI: 10.1063/1.1783872] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the structural evolution of an A/B/C ternary mixture in which the A and B components can undergo a reversible chemical reaction to form C. We developed a lattice Boltzmann model for this ternary mixture that allows us to capture both the reaction kinetics and the hydrodynamic interactions within the system. We use this model to study a specific reactive mixture in which C acts as a surfactant, i.e., the formation of C at the A/B interface decreases the interfacial tension between the A and B domains. We found that the dynamics of the system is different for fluids in the diffusive and viscous regimes. In the diffusive regime, the formation of a layer of C at the interface leads to a freezing of the structural evolution in the fluid; the values of the reaction rate constants determine the characteristic domain size in the system. In the viscous regime, where hydrodynamic interactions are important, interfacial reactions cause a slowing down of the domain growth, but do not arrest the evolution of the mixture. The results provide guidelines for controlling the morphology of this complex ternary fluid.
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Affiliation(s)
- Kevin Good
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
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22
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Huo Y, Jiang X, Zhang H, Yang Y. Hydrodynamic effects on phase separation of binary mixtures with reversible chemical reaction. J Chem Phys 2003. [DOI: 10.1063/1.1571511] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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23
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Zhu YJ, Ma YQ. Fast growth in phase-separating A-B-copolymer ternary mixtures with a chemical reaction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:021804. [PMID: 12636705 DOI: 10.1103/physreve.67.021804] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2002] [Indexed: 05/24/2023]
Abstract
We study the dynamics of phase separation of a binary A-B- polymer mixture with copolymer C, which is produced by the reaction of two counterpart reactive polymers A and B at the interface via the chemical reaction A+B right harpoon over left harpoon C. For low interfacial energy between the A and B phases, where the copolymer prefers to locate at interfaces, we show that the chemical reaction accelerates the phase separation of the system dramatically, because the backward reaction always drives the creation of immiscible A and B pairs at interfaces, which speed up the phase separation of the system, while the forward reaction process becomes more and more difficult as the interfaces are gradually saturated by copolymers. We also indicate that for a fixed chemical reaction rate constant, as the initial concentration of the copolymers increases, the domain growth at the late stage is speeded up as a result of the backward chemical reaction. However, when the interfacial energy is high, both forward and backward reactions coexist due to the occurrence of unsaturated interfaces, but the relative strength of reaction rates has no appreciable effect on domain growth during spinodal decomposition, because the interfacial energy dominates phase separation.
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Affiliation(s)
- Yue-Jin Zhu
- National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
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24
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Tong C, Yang Y. Phase-separation dynamics of a ternary mixture coupled with reversible chemical reaction. J Chem Phys 2002. [DOI: 10.1063/1.1425820] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Kyu T, Chiu HW. Morphology development during polymerization-induced phase separation in a polymer dispersed liquid crystal. POLYMER 2001. [DOI: 10.1016/s0032-3861(01)00389-5] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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26
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Ma Y. Wetting-driven structure formation of a binary mixture in the presence of a mobile particle pinning potential. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:8207-11. [PMID: 11138119 DOI: 10.1103/physreve.62.8207] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2000] [Indexed: 11/07/2022]
Abstract
We investigate the pattern formation on the solid substrate of phase-separating films containing mobile wetting particles with a preferential attraction for one component of the mixtures. The presence of mobile particles under the surface-particle interaction modulation breaks the isotropy of the bulk phase-separating process, leading to the formation of orientational structure due to the interplay between phase separation and wetting particle ordering under a modulated pinning potential at the late stage. Simulations suggest that the phase-separation morphology can be changed through the adjustment of the wettable-phase-particle interaction and the surface-particle interaction. It provides some important insights into this "wetting-directed spinodal decomposition."
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Affiliation(s)
- Yq Ma
- National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
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27
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Corberi F, Gonnella G, Lamura A. Phase separation of binary mixtures in shear flow: A numerical study. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:8064-8070. [PMID: 11138090 DOI: 10.1103/physreve.62.8064] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2000] [Indexed: 05/23/2023]
Abstract
The phase-separation kinetics of binary fluids in shear flow is studied numerically in the framework of the continuum convection-diffusion equation based on a Ginzburg-Landau free energy. Simulations are carried out for different temperatures both in d=2 and 3. Our results confirm the qualitative picture put forward by the large-N limit equations studied by Corberi et al. [Phys. Rev. Lett. 81, 3852 (1998)]. In particular, the structure factor is characterized by the presence of four peaks whose relative oscillations give rise to a periodic modulation of the behavior of the rheological indicators and of the average domains sizes. This peculiar pattern of the structure factor corresponds to the presence of domains with two characteristic thicknesses, whose relative abundance changes with time.
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Affiliation(s)
- F Corberi
- Istituto Nazionale per la Fisica della Materia, Unita di Salerno and Dipartimento di Fisica, Universita di Salerno, 84081 Baronissi (Salerno), Italy
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28
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Henriksen JR, Sabra MC, Mouritsen OG. Phase transitions and steady-state microstructures in a two-temperature lattice-gas model with mobile active impurities. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:7070-7076. [PMID: 11102063 DOI: 10.1103/physreve.62.7070] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2000] [Indexed: 05/23/2023]
Abstract
The nonequilibrium, steady-state phase transitions and the structure of the different phases of a two-dimensional system with two thermodynamic temperatures are studied via a simple lattice-gas model with mobile active impurities ("hot/cold spots") whose activity is controlled by an external drive. The properties of the model are calculated by Monte Carlo computer-simulation techniques. The two temperatures and the external drive on the system lead to a rich phase diagram including regions of microstructured phases in addition to macroscopically ordered (phase-separated) and disordered phases. Depending on the temperatures, microstructured phases of both lamellar and droplet symmetry arise, described by a length scale that is determined by the characteristic temperature controlling the diffusive motion of the active impurities.
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Affiliation(s)
- JR Henriksen
- MEMPHYS, Department of Chemistry, Technical University of Denmark, Building 206, DK-2800 Lyngby, Denmark
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29
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Nwabunma D, Chiu HW, Kyu T. Theoretical investigation on dynamics of photopolymerization-induced phase separation and morphology development in nematic liquid crystal/polymer mixtures. J Chem Phys 2000. [DOI: 10.1063/1.1309537] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Corberi F, Gonnella G, Lamura A. Structure and rheology of binary mixtures in shear flow. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:6621-6631. [PMID: 11088342 DOI: 10.1103/physreve.61.6621] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2000] [Indexed: 05/23/2023]
Abstract
Results are presented for the phase separation process of a binary mixture subject to a uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the time-dependent Ginzburg-Landau equation with an external velocity term. The large-n approximation is used to study the evolution of the model in the presence of a stationary flow and in the case of an oscillating shear. For stationary flow we show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical length scales Rx and R( perpendicular), respectively, in the flow direction and perpendicularly to it. In the scaling regime R( perpendicular) approximately t(alpha( perpendicular)) and Rx approximately gammat(alpha(x)) (with logarithmic corrections), gamma being the shear rate, with alpha(x)=5/4 and alpha( perpendicular)=1/4. The excess viscosity Deltaeta after reaching a maximum relaxes to zero as gamma(-2)t(-3/2). Deltaeta and other observables exhibit logarithmic-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains occur cyclically. In the case of an oscillating shear a crossover phenomenon is observed: Initially the evolution is characterized by the same growth exponents as for a stationary flow. For longer times the phase-separating structure cannot align with the oscillating drift and a different regime is entered with an isotropic growth and the same exponents as in the case without shear.
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Affiliation(s)
- F Corberi
- Istituto Nazionale per la Fisica della Materia, Unita di Salerno and Dipartimento di Fisica, Universita di Salerno, 84081 Baronissi (Salerno), Italy
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31
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Siddhamalli SK, Kyu T. Toughening of thermoset/thermoplastic composites via reaction-induced phase separation: Epoxy/phenoxy blends. J Appl Polym Sci 2000. [DOI: 10.1002/1097-4628(20000808)77:6<1257::aid-app10>3.0.co;2-z] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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32
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Lee BP, Douglas JF, Glotzer SC. Filler-induced composition waves in phase-separating polymer blends. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5812-22. [PMID: 11970479 DOI: 10.1103/physreve.60.5812] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/1999] [Indexed: 04/18/2023]
Abstract
The influence of immobile filler particles (spheres, fibers, platelets) on polymer-blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective affinity of one of the polymers for the filler surface leads to the development of concentration waves about the filler particles at an early stage of phase separation in near critical composition blends. These "target" patterns are overtaken in late-stage phase separation by a growing "background" spinodal pattern characteristic of blends without filler particles. The linearized CHC model is used to estimate the number of composition oscillations emanating from isolated filler particles. In far-off-critical composition blends, an "encapsulation layer" grows at the surface of the filler rather than a target pattern. The results of these simulations compare favorably with experiments on filled phase-separating ultrathin blend films in which the filler particles are immobilized on a solid substrate.
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Affiliation(s)
- B P Lee
- Polymers Division and Center for Theoretical and Computational Materials Science, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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33
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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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34
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Lacasta AM, Sagués F, Sokolov IM, Sancho JM. Study of a bimolecular annihilation process for coarsening reactants. J Chem Phys 1999. [DOI: 10.1063/1.478548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Ohta T, Urakawa O, Tran-Cong Q. Phase Separation of Binary Polymer Blends Driven by Photoisomerization: An Example for a Wavelength-Selection Process in Polymers. Macromolecules 1998. [DOI: 10.1021/ma9803943] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Takashi Ohta
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Kyoto 606, Japan
| | - Osamu Urakawa
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Kyoto 606, Japan
| | - Qui Tran-Cong
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Kyoto 606, Japan
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36
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Harada A, Tran-Cong Q. Modulated Phases Observed in Reacting Polymer Mixtures with Competing Interactions. Macromolecules 1997. [DOI: 10.1021/ma961542x] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Asuka Harada
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606, Japan
| | - Qui Tran-Cong
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606, Japan
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37
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Christensen JJ, Elder K, Fogedby HC. Phase segregation dynamics of a chemically reactive binary mixture. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:R2212-R2215. [PMID: 9965444 DOI: 10.1103/physreve.54.r2212] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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38
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Zhu YM. Monte Carlo simulation of polymerization-induced phase separation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:1645-1651. [PMID: 9965240 DOI: 10.1103/physreve.54.1645] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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39
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Harada A, Tran-Cong Q. Experimental Verification of a Scaling Law for Phase Separation Kinetics of Reacting Polymer Mixtures. Macromolecules 1996. [DOI: 10.1021/ma951627i] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Asuka Harada
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606, Japan
| | - Qui Tran-Cong
- Department of Polymer Science and Engineering, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606, Japan
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40
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Kyu T, Lee JH. Nucleation initiated spinodal decomposition in a polymerizing system. PHYSICAL REVIEW LETTERS 1996; 76:3746-3749. [PMID: 10061099 DOI: 10.1103/physrevlett.76.3746] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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41
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Tran-Cong Q, Harada A. Reaction-induced ordering phenomena in binary polymer mixtures. PHYSICAL REVIEW LETTERS 1996; 76:1162-1165. [PMID: 10061649 DOI: 10.1103/physrevlett.76.1162] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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42
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Teixeira PI, Mulder BM. Cell dynamics model of droplet formation in polymer-dispersed liquid crystals. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:1805-1815. [PMID: 9964442 DOI: 10.1103/physreve.53.1805] [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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43
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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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44
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Glotzer SC, Stauffer D, Jan N. Glotzer, Stauffer, and Jan Reply. PHYSICAL REVIEW LETTERS 1995; 75:1675. [PMID: 10060358 DOI: 10.1103/physrevlett.75.1675] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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45
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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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46
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