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Xiang H, Van Paepegem W, Kestens LAI. Study of Microstructural Morphology of Ti-6Al-4V Alloy by Crystallographic Analysis and Phase Field Simulation. MATERIALS 2022; 15:ma15155325. [PMID: 35955256 PMCID: PMC9369925 DOI: 10.3390/ma15155325] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Revised: 07/26/2022] [Accepted: 07/30/2022] [Indexed: 01/27/2023]
Abstract
Formation of a habit plane during martensitic transformation is related to an invariant plane strain transformation, which involves dislocation glide and twins. In the current work, the Phenomenological Theory of Martensitic Transformation (PTMT) is employed to study the crystallographic features while the phase field simulation is used to study the microstructure evolution for martensitic transformation of Ti-6Al-4V alloy. Results show that mechanical constraints play a key role in the microstructure evolution. It is shown that a twinned structure with very small twinned variants is geometrically difficult to form due to the lattice parameters of Ti-6Al-4V alloy. It is concluded that the predicted habit plane from the PTMT is consistent with results of the micro-elastic theory. The formation of a triangular morphology is favored geometrically and elastically.
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Affiliation(s)
- Hao Xiang
- Department of Electromechanical, Systems and Metal Engineering, Faculty of Engineering and Architecture, Ghent University, Tech-Lane Ghent Science Park-Campus A, Technologiepark Zwijnaarde 46, B-9052 Ghent, Belgium
- Correspondence: (H.X.); (L.A.I.K.)
| | - Wim Van Paepegem
- Department of Materials, Textiles and Chemical Engineering (MaTCh), Faculty of Engineering and Architecture, Ghent University, Tech-Lane Ghent Science Park-Campus A, Technologiepark Zwijnaarde 46, B-9052 Ghent, Belgium;
| | - Leo A. I. Kestens
- Department of Electromechanical, Systems and Metal Engineering, Faculty of Engineering and Architecture, Ghent University, Tech-Lane Ghent Science Park-Campus A, Technologiepark Zwijnaarde 46, B-9052 Ghent, Belgium
- Correspondence: (H.X.); (L.A.I.K.)
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2
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Ronsin OJJ, Harting J. Phase‐Field Simulations of the Morphology Formation in Evaporating Crystalline Multicomponent Films. ADVANCED THEORY AND SIMULATIONS 2022. [DOI: 10.1002/adts.202200286] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Olivier J. J. Ronsin
- Helmholtz Institute Erlangen‐Nürnberg for Renewable Energy Forschungszentrum Jülich Fürther Straße 248 90429 Nürnberg Germany
- Department of Chemical and Biological Engineering Friedrich‐Alexander‐Universität Erlangen‐Nürnberg Fürther Straße 248 90429 Nürnberg Germany
| | - Jens Harting
- Helmholtz Institute Erlangen‐Nürnberg for Renewable Energy Forschungszentrum Jülich Fürther Straße 248 90429 Nürnberg Germany
- Department of Chemical and Biological Engineering Friedrich‐Alexander‐Universität Erlangen‐Nürnberg Fürther Straße 248 90429 Nürnberg Germany
- Department of Physics Friedrich‐Alexander‐Universität Erlangen‐Nürnberg Fürther Straße 248 90429 Nürnberg Germany
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3
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Utracki L. Present and Future Trends in Polymer Blends Technology. INT POLYM PROC 2022. [DOI: 10.1515/ipp-1987-0012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
The plastics industry shows the highest growth rate of all industrial materials. Within this group the engineering resins (ER) are developing fastest. The review focuses on polymer alloys and blends (PAB) of ER. After the discussion of the economic aspect of PAB the patent literature is briefly reviewed and illustrated by a summary of selected, recent patents on polyphenylene ether blends. There is little doubt that the future trend in PAB technology will require control of morphology, especially in most common multiphase systems. For this reason the last part of the article summarizes the available information of criteria for rheological and thermodynamic control of morphology. The review ends with a brief description of the methods and equipment used by industry to compound and form the PAB.
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Affiliation(s)
- L.A. Utracki
- National Research Council Canada, Industrial Materials Research Institute , Boucherville , Canada
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4
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Röckner M, Yang H, Zhu R. Conservative stochastic two-dimensional Cahn–Hilliard equation. ANN APPL PROBAB 2021. [DOI: 10.1214/20-aap1620] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Huanyu Yang
- Institute for Mathematics, Free University of Berlin
| | - Rongchan Zhu
- Department of Mathematics, University of Bielefeld
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5
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Mukherjee B, Chakrabarti B. Gelation Impairs Phase Separation and Small Molecule Migration in Polymer Mixtures. Polymers (Basel) 2020; 12:E1576. [PMID: 32708547 PMCID: PMC7407309 DOI: 10.3390/polym12071576] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 07/06/2020] [Accepted: 07/10/2020] [Indexed: 11/16/2022] Open
Abstract
Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer ( O P ) and oligomer-gel ( O G ) systems following a temperature quench that induces demixing of components. We compute equilibrium and time varying migrant (oligomer) density profiles and wetting layer thickness in these systems using coarse grained molecular dynamics (CGMD) and mesoscale hydrodynamics (MH) simulations. Such multiscale methods quantitatively describe the phenomena over a wide range of length and time scales. We show that surface migration in gel-oligomer systems is significantly reduced on account of network elasticity. Furthermore, the phase separation processes are significantly slowed in gels leading to the modification of the well known Lifshitz-Slyozov-Wagner (LSW) law ℓ ( τ ) ∼ τ 1 / 3 . Our work allows for rational design of polymer/gel-oligomer mixtures with predictable surface segregation characteristics that can be compared against experiments.
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6
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Schaefer C, Paquay S, McLeish TCB. Morphology formation in binary mixtures upon gradual destabilisation. SOFT MATTER 2019; 15:8450-8458. [PMID: 31490530 DOI: 10.1039/c9sm01344j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation is strongly affected by critical thermal fluctuations. We propose a mechanism of pretransitional structuring of a mixture that approaches the miscibility gap and predict scaling relations that describe how the characteristic feature size of the emerging morphology decreases with an increasing quench rate. These predictions quantitatively agree with our kinetic Monte Carlo and molecular dynamics simulations of a phase-separating binary mixture, as well as with previously reported experimental observations. We discuss how these predictions are affected by non-conserved order parameters (e.g., due to chemical reactions or alignment of liquid-crystalline molecules), hydrodynamics and active transport.
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Affiliation(s)
- Charley Schaefer
- Department of Physics, University of York, Heslington, York, YO10 5DD, UK.
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7
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Zhang G, Yang T, Yang S, Wang Y. Morphological-evolution pathway during phase separation in polymer solutions with highly asymmetrical miscibility gap. Phys Rev E 2017; 96:032501. [PMID: 29346882 DOI: 10.1103/physreve.96.032501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2017] [Indexed: 06/07/2023]
Abstract
Microstructural evolution during thermally induced phase separation in a polymer solution with a highly asymmetrical miscibility gap is analyzed using Flory-Huggins thermodynamics and nonlinear Cahn-Hilliard kinetics. Computer simulation results demonstrate that, in contrast to systems with symmetric miscibility gaps, interesting morphological-evolution pathways (MEPs) including cluster-to-percolation and percolation-to-cluster transitions are identified. These MEPs are rationalized according to asynchronous evolution of the two product phases. For a highly asymmetric polymer system, the initial solution composition is also found to play a critical role in determining the MEPs. According to the simulation results a map of MEPs in terms of initial solution composition and aging time of phase separation is established to guide future microstructural design in asymmetrical polymer solutions.
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Affiliation(s)
- Gang Zhang
- Frontier Institute of Science and Technology, MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
| | - Tao Yang
- Frontier Institute of Science and Technology, MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
| | - Sen Yang
- Frontier Institute of Science and Technology, MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yunzhi Wang
- Frontier Institute of Science and Technology, MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
- Department of Materials Science and Engineering, The Ohio State University, Columbus, Ohio 43210, USA
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8
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Hill JD, Millett PC. Numerical Simulations of Directed Self-Assembly in Diblock Copolymer Films using Zone Annealing and Pattern Templating. Sci Rep 2017; 7:5250. [PMID: 28701696 PMCID: PMC5507907 DOI: 10.1038/s41598-017-05565-w] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Accepted: 05/30/2017] [Indexed: 12/03/2022] Open
Abstract
Bulk fabrication of surface patterns with sub-20 nm feature sizes is immensely desirable for many existing and emerging technologies. Directed self-assembly (DSA) of block copolymers (BCPs) has been a recently demonstrated approach to achieve such feature resolution over large-scale areas with minimal defect populations. However, much work remains to understand and optimize DSA methods in order to move this field forward. This paper presents large-scale numerical simulations of zone annealing and chemo-epitaxy processing of BCP films to achieve long-range orientational order. The simulations utilize a Time-Dependent Ginzburg-Landau model and parallel processing to elucidate relationships between the magnitude and velocity of a moving thermal gradient and the resulting BCP domain orientations and defect densities. Additional simulations have been conducted to study to what degree orientational order can be further improved by combining zone annealing and chemo-epitaxy techniques. It is found that these two DSA methods do synergistically enhance long-range order with a particular relationship between thermal gradient velocity and chemical template spacing.
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Affiliation(s)
- Joseph D Hill
- Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR, 72701, USA
| | - Paul C Millett
- Department of Mechanical Engineering, University of Arkansas, Fayetteville, AR, 72701, USA.
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9
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Torabi R, Rezaei Z. Instability in reaction-superdiffusion systems. Phys Rev E 2016; 94:052202. [PMID: 27967163 DOI: 10.1103/physreve.94.052202] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2016] [Indexed: 11/07/2022]
Abstract
We study the effect of superdiffusion on the instability in reaction-diffusion systems. It is shown that reaction-superdiffusion systems close to a Turing instability are equivalent to a time-dependent Ginzburg-Landau model and the corresponding free energy is introduced. This generalized free energy which depends on the superdiffusion exponent governs the stability, dynamics, and the fluctuations of reaction-superdiffusion systems near the Turing bifurcation. In addition, we show that for a general n-component reaction-superdiffusion system, a fractional complex Ginzburg-Landau equation emerges as the amplitude equation near a Hopf instability. Numerical simulations of this equation are carried out to illustrate the effect of superdiffusion on spatiotemporal patterns. Finally, the effect of superdiffusion on the instability in the Brusselator model, as a special case of reaction-diffusion systems, is studied. In general, superdiffusion introduces a new parameter that changes the behavior of the system near the instability.
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Affiliation(s)
- Reza Torabi
- Department of Physics, Tafresh University, Tafresh 39518 79611, Iran
| | - Zahra Rezaei
- Department of Physics, Tafresh University, Tafresh 39518 79611, Iran
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10
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Schaefer C, Michels JJ, van der Schoot P. Structuring of Thin-Film Polymer Mixtures upon Solvent Evaporation. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00537] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- C. Schaefer
- Dutch Polymer
Institute, P.O. Box 902, 5600 AX Eindhoven, The Netherlands
- Theory
of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - J. J. Michels
- Holst Centre/TNO, High Tech Campus 31, 5656 AE Eindhoven, The Netherlands
- Max Planck
Institute
für Polymerforschung, Ackermannweg
10, 55128 Mainz, Germany
| | - P. van der Schoot
- Institute
for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
- Theory
of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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11
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Umantsev A. Lifetime of metastable states in a Ginzburg-Landau system: Numerical simulations at large driving forces. Phys Rev E 2016; 93:042806. [PMID: 27176373 DOI: 10.1103/physreve.93.042806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2016] [Indexed: 11/07/2022]
Abstract
We developed a "brute-force" simulation method and conducted numerical "experiments" on homogeneous nucleation in an isotropic system at large driving forces (not small supersaturations) using the stochastic Ginzburg-Landau approach. Interactions in the system are described by the asymmetric (no external field), athermal (temperature-independent driving force), tangential (simple phase diagram) Hamiltonian, which has two independent "drivers" of the phase transition: supersaturation and thermal noise. We obtained the probability distribution function of the lifetime of the metastable state and analyzed its mean value as a function of the supersaturation, noise strength, and volume. We also proved the nucleation theorem in the mean-field approximation. The results allowed us to find the thermodynamic properties of the barrier state and conclude that at large driving forces the fluctuating volumes are not independent.
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Affiliation(s)
- A Umantsev
- Department of Physical Chemistry, National University of Science and Technology MISiS, 4 Leninsky Ave, 119049 Moscow, Russia and Department of Chemistry and Physics, Fayetteville State University, Fayetteville, North Carolina 28301, USA
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12
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Paradiso SP, Delaney KT, García-Cervera CJ, Ceniceros HD, Fredrickson GH. Cyclic Solvent Annealing Improves Feature Orientation in Block Copolymer Thin Films. Macromolecules 2016. [DOI: 10.1021/acs.macromol.5b02107] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Sean P. Paradiso
- Department of Chemical Engineering, ‡Materials Research Laboratory,
Materials Department, and §Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93016, United States
| | - Kris T. Delaney
- Department of Chemical Engineering, ‡Materials Research Laboratory,
Materials Department, and §Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93016, United States
| | - Carlos J. García-Cervera
- Department of Chemical Engineering, ‡Materials Research Laboratory,
Materials Department, and §Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93016, United States
| | - Hector D. Ceniceros
- Department of Chemical Engineering, ‡Materials Research Laboratory,
Materials Department, and §Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93016, United States
| | - Glenn H. Fredrickson
- Department of Chemical Engineering, ‡Materials Research Laboratory,
Materials Department, and §Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93016, United States
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13
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Sousa RE, Ferreira JCC, Costa CM, Machado AV, Silva MM, Lanceros-Mendez S. Tailoring poly(vinylidene fluoride-co
-chlorotrifluoroethylene) microstructure and physicochemical properties by exploring its binary phase diagram with dimethylformamide. ACTA ACUST UNITED AC 2015. [DOI: 10.1002/polb.23692] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Ricardo E. Sousa
- Departamento/Centro de Física; Universidade do Minho Campus de Gualtar; 4710-057 Braga Portugal
| | - José Carlos C. Ferreira
- Departamento/Centro de Física; Universidade do Minho Campus de Gualtar; 4710-057 Braga Portugal
| | - Carlos. M. Costa
- Departamento/Centro de Física; Universidade do Minho Campus de Gualtar; 4710-057 Braga Portugal
| | - Ana V. Machado
- IPC-Institute for Polymers and Composites; Universidade do Minho, Campus de Azurém; 4800-058 Guimarães Portugal
| | - Maria M. Silva
- Departamento/Centro de Química; Universidade do Minho Campus de Gualtar; 4710-057 Braga Portugal
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14
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Schaefer C, van der Schoot P, Michels JJ. Structuring of polymer solutions upon solvent evaporation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022602. [PMID: 25768523 DOI: 10.1103/physreve.91.022602] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2014] [Indexed: 06/04/2023]
Abstract
The morphology of solution-cast, phase-separated polymers becomes finer with increasing solvent evaporation rate. We address this observation theoretically for a model polymer where demixing is induced by steady solvent evaporation. In contrast to what is the case for a classical, thermal quench involving immiscible blends, the spinodal instability initially develops slowly and the associated length scale is not time invariant but decreases with time as t(-1/2). After a time lag, phase separation accelerates. Time lag and characteristic length exhibit power-law behavior as a function of the evaporation rate with exponents of -2/3 and -1/6. Interestingly, at later stages the spinodal structure disappears completely while a second length scale develops. The associated structure coarsens but does not follow the usual Lifshitz-Slyozov-Wagner kinetics.
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Affiliation(s)
- C Schaefer
- Dutch Polymer Institute, P.O. Box 902, 5600 AX Eindhoven, The Netherlands
- Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - P van der Schoot
- Theory of Polymers and Soft Matter, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - J J Michels
- Holst Centre/TNO, High Tech Campus 31, 5656 AE Eindhoven, The Netherlands
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15
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Zhang G, Liu G, Shi Z, Qiao G. Dynamics of spinodal decomposition coupled with chemical reaction in thermosetting phenol-formaldehyde resin-based solutions and its application in monolithic porous materials. RSC Adv 2014. [DOI: 10.1039/c3ra46490c] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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16
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Zhang G, Qiao G. Polymerization-induced spinodal decomposition of ethylene glycol∕phenolic resin solutions under electric fields. J Chem Phys 2013; 139:134903. [PMID: 24116581 DOI: 10.1063/1.4822295] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Temporal evolution of polymerization-induced spinodal decomposition (PISD) under electric fields was investigated numerically in ethylene glycol∕phenolic resin solutions with different initial composition. A model composed of the nonlinear Cahn-Hilliard-Cook equation for spinodal decomposition and a rate equation for curing reaction was utilized to describe the PISD phenomenon. As initial composition varied, deformed droplet-like and aligned bi-continuous structures were observed in the presence of an electric field. Moreover, the anisotropic parameter (D), determined from the 2D-FFT power spectrum, was employed to quantitatively characterize the degree of morphology anisotropy. The value of D increased quickly in the early stage and then decreased in the intermediate stage of spinodal decomposition, which was attributed to the resistance of coarsening process to morphology deformation and the decline of electric stress caused by polymerization reaction. The results can also provide a guidance on how to control the morphology of monolithic porous polymer and carbon materials with anisotropic structures.
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Affiliation(s)
- Gang Zhang
- State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
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17
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Zhao Y, Kwan YY, Che J, Li B, McCammon JA. Phase-field approach to implicit solvation of biomolecules with Coulomb-field approximation. J Chem Phys 2013; 139:024111. [PMID: 23862933 DOI: 10.1063/1.4812839] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A phase-field variational implicit-solvent approach is developed for the solvation of charged molecules. The starting point of such an approach is the representation of a solute-solvent interface by a phase field that takes one value in the solute region and another in the solvent region, with a smooth transition from one to the other on a small transition layer. The minimization of an effective free-energy functional of all possible phase fields determines the equilibrium conformations and free energies of an underlying molecular system. All the surface energy, the solute-solvent van der Waals interaction, and the electrostatic interaction are coupled together self-consistently through a phase field. The surface energy results from the minimization of a double-well potential and the gradient of a field. The electrostatic interaction is described by the Coulomb-field approximation. Accurate and efficient methods are designed and implemented to numerically relax an underlying charged molecular system. Applications to single ions, a two-plate system, and a two-domain protein reveal that the new theory and methods can capture capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics simulations. Comparisons of the phase-field and the original sharp-interface variational approaches are discussed.
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Affiliation(s)
- Yanxiang Zhao
- Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, California 92093-0112, USA.
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18
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Thampi SP, Pagonabarraga I, Adhikari R. Lattice-Boltzmann-Langevin simulations of binary mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046709. [PMID: 22181309 DOI: 10.1103/physreve.84.046709] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2011] [Revised: 09/15/2011] [Indexed: 05/31/2023]
Abstract
We report a hybrid numerical method for the solution of the Model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes is solved using stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretization of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.
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Affiliation(s)
- Sumesh P Thampi
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
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20
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Prusty M, Keestra B, Goossens J, Anderson P. Experimental and computational study on structure development of PMMA/SAN blends. Chem Eng Sci 2007. [DOI: 10.1016/j.ces.2006.12.023] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/01/2022]
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22
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Miura T, Kishi R, Ichijo H. Effects of Temperature and Molecular Weight on the Porous Structure Formation of Polymer Chemical Gels. Polym J 1999. [DOI: 10.1295/polymj.31.447] [Citation(s) in RCA: 3] [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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23
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Kielhorn L, Muthukumar M. Spinodal decomposition of symmetric diblock copolymer/homopolymer blends at the Lifshitz point. J Chem Phys 1999. [DOI: 10.1063/1.478289] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [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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Melenkevitz J, Javadpour SH. Phase separation dynamics in mixtures containing surfactants. J Chem Phys 1997. [DOI: 10.1063/1.474422] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Teixeira PIC, Mulder BM. Numerical simulation of thermally induced phase separation in polymer‐dispersed liquid crystals. J Chem Phys 1996. [DOI: 10.1063/1.472842] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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27
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Alig I, Junker M, Schulz M, Frisch HL. Irreversible frustrated spinodal decomposition in simultaneous interpenetrating polymer networks: Small-angle x-ray scattering. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:11481-11487. [PMID: 9982766 DOI: 10.1103/physrevb.53.11481] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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28
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29
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Pätzold G, Dawson K. Numerical simulation of phase separation in the presence of surfactants and hydrodynamics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:6908-6911. [PMID: 9964212 DOI: 10.1103/physreve.52.6908] [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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Ferreira AL, Toral R. Hybrid Monte Carlo method for conserved-order-parameter systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:R3848-R3851. [PMID: 9960565 DOI: 10.1103/physreve.47.r3848] [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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Lai Z. Theory of ordering dynamics for Cu3Au. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 41:9239-9256. [PMID: 9993266 DOI: 10.1103/physrevb.41.9239] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Farrell JE, Valls OT. Spinodal decomposition in a two-dimensional fluid model. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:7027-7039. [PMID: 9991085 DOI: 10.1103/physrevb.40.7027] [Citation(s) in RCA: 70] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Furukawa H. Numerical study of multitime scaling in a solid system undergoing phase separation. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:2341-2347. [PMID: 9992117 DOI: 10.1103/physrevb.40.2341] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Elder KR, Desai RC. Role of nonlinearities in off-critical quenches as described by the Cahn-Hilliard model of phase separation. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 40:243-254. [PMID: 9990908 DOI: 10.1103/physrevb.40.243] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Rogers TM, Desai RC. Numerical study of late-stage coarsening for off-critical quenches in the Cahn-Hilliard equation of phase separation. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:11956-11964. [PMID: 9948031 DOI: 10.1103/physrevb.39.11956] [Citation(s) in RCA: 68] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Gawlinski ET, Vials J, Gunton JD. Domain growth and scaling in the two-dimensional Langevin model. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:7266-7269. [PMID: 9947383 DOI: 10.1103/physrevb.39.7266] [Citation(s) in RCA: 32] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Valls OT, Mazenko GF. Growth kinetics for a model two-dimensional fluid. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:11643-11649. [PMID: 9946048 DOI: 10.1103/physrevb.38.11643] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Valls OT, Mazenko GF. Numerical study of spinodal decomposition for Langevin equations. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:11650-11658. [PMID: 9946049 DOI: 10.1103/physrevb.38.11650] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Lau M, Dasgupta C, Valls OT. Domain growth in the field-theoretic version of the Potts model. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:9024-9030. [PMID: 9945686 DOI: 10.1103/physrevb.38.9024] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Elder KR, Rogers TM, Desai RC. Early stages of spinodal decomposition for the Cahn-Hilliard-Cook model of phase separation. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:4725-4739. [PMID: 9946862 DOI: 10.1103/physrevb.38.4725] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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