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Tree DR, F Dos Santos L, Wilson CB, Scott TR, Garcia JU, Fredrickson GH. Mass-transfer driven spinodal decomposition in a ternary polymer solution. SOFT MATTER 2019; 15:4614-4628. [PMID: 31025034 DOI: 10.1039/c9sm00355j] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Nonsolvent induced phase separation (NIPS) is a widely occuring process used in industrial membrane production, nanotechnology and Nature to produce microstructured polymer materials. A variety of process-dependent morphologies are produced when a polymer solution is exposed to a nonsolvent that, following a period where mass is exchanged, precipitates and solidifies the polymer. Despite years of investigation, both experimental and theoretical, many questions surround the pathways to the microstructures that NIPS can produce. Here, we provide simulation results from a model that simultaneously captures both the processess of solvent/nonsolvent exchange and phase separation. We show that the time it takes the nonsolvent to diffuse to the bottom of the film is an important timescale, and that phase separation is possible at times both much smaller and much larger than this scale. Our results include both one-dimensional simulations of the mass transfer kinetics and two- and three-dimensional simulations of morphologies at both short and long times. We find good qualitative agreement with experimental heuristics, but we conclude that an additional model for the vitrification process will be key for fully explaining experimental observations of microstructure formation.
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Affiliation(s)
- Douglas R Tree
- Chemical Engineering Department, Brigham Young University, Provo, Utah, USA.
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2
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Tree DR, Delaney KT, Ceniceros HD, Iwama T, Fredrickson GH. A multi-fluid model for microstructure formation in polymer membranes. SOFT MATTER 2017; 13:3013-3030. [PMID: 28367562 DOI: 10.1039/c6sm02839j] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We develop a multi-fluid model for a ternary polymer solution using the Rayleighian formalism of Doi and Onuki, and give an efficient pseudo-spectral method for solving both the diffusion and momentum equations that result. Subsequently, we find that the numerical simulation is capable of describing systems at the micron length-scale and easily reaches millisecond time-scales. In addition, we characterize the model thermodynamics and kinetics including the (i) phase behavior, (ii) structure of the interfaces, (iii) mutual diffusion coefficients, (iv) bulk spinodal decomposition kinetics with and without hydrodynamics and (v) spinodal decomposition in the presence of an interface with a non-solvent bath. We obtain good qualitative agreement with the expected thermodynamic and kinetic behavior. We also show that a linear stability analysis of the diffusion equation quantitatively predicts the fastest growing mode obtained from simulation and gives insight into the phase separation process relevant for the evolution of microstructure in phase-separating ternary polymer solutions.
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Affiliation(s)
- Douglas R Tree
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106-5121, USA
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3
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Gan Y, Xu A, Zhang G, Li Y, Li H. Phase separation in thermal systems: a lattice Boltzmann study and morphological characterization. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046715. [PMID: 22181315 DOI: 10.1103/physreve.84.046715] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2010] [Revised: 09/11/2011] [Indexed: 05/31/2023]
Abstract
We investigate thermal and isothermal symmetric liquid-vapor separations via a fast Fourier transform thermal lattice Boltzmann (FFT-TLB) model. Structure factor, domain size, and Minkowski functionals are employed to characterize the density and velocity fields, as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the spinodal decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth, while the exponent for thermal system is lower than that for isothermal system. With respect to the density field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction, and lower interfacial stresses are the main reasons for the differences in thermal system. Different from the isothermal case, the release of latent heat causes the changing of local temperature, which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium much more quickly. The increasing of mean temperature makes the interfacial stress lower in the following way: σ=σ(0)[(T(c)-T)/(T(c)-T(0))](3/2), where T(c) is the critical temperature and σ(0) is the interfacial stress at a reference temperature T(0), which is the main reason for the prolonged SD stage and the lower growth exponent in the thermal case. Besides thermodynamics, we probe how the local viscosities influence the morphology of the phase separating system. We find that, for both the isothermal and thermal cases, the growth exponents and local flow velocities are inversely proportional to the corresponding viscosities. Compared with the isothermal case, the local flow velocity depends not only on viscosity but also on temperature.
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Affiliation(s)
- Yanbiao Gan
- State Key Laboratory for GeoMechanics and Deep Underground Engineering, SMCE, China University of Mining and Technology (Beijing), Beijing 100083, PR China
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4
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Li S, Zhang X, Wang W. Coarse-grained model for mechanosensitive ion channels. J Phys Chem B 2010; 113:14431-8. [PMID: 19845409 DOI: 10.1021/jp9053567] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this work, a coarse-grained model for a kind of membrane protein, the mechanosensitive channel of small conductance (MscS), is proposed. The basic structure of the MscS is preserved when the protein is coarse-grained. For the coarse-grained model, the channels show two different states, namely the open and closed states, depending on the model parameters. Under the same membrane tension, the state of the ion channel is found to be critically determined by the protein structure, especially the length of the transmembrane alpha-helix. It is also found that for the protein with certain size, the gating transition occurs when the membrane tension is applied, resembling in a real mechanosensitive channel.
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Affiliation(s)
- Shuangyang Li
- Division of Molecular and Materials Simulation, Key Laboratory for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, China
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5
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Aoki H, Tanaka N, Kubo T, Hosoya K. Polymer-based monolithic columns in capillary format tailored by using controlledin situpolymerization. J Sep Sci 2009; 32:341-58. [DOI: 10.1002/jssc.200800508] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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6
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Fiałkowski M, Hołyst R. Dynamics of Phase Separation in Polymer Blends Revisited: Morphology, Spinodal, Noise, and Nucleation. MACROMOL THEOR SIMUL 2008. [DOI: 10.1002/mats.200800020] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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7
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Rehse S, Mecke K, Magerle R. Characterization of the dynamics of block copolymer microdomains with local morphological measures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051805. [PMID: 18643095 DOI: 10.1103/physreve.77.051805] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2007] [Revised: 02/15/2008] [Indexed: 05/26/2023]
Abstract
We investigate the structure formation in thin films of cylinder forming block copolymers. With in situ scanning probe microscopy image sequences can be recorded with high temporal (2 min per frame) and spatial (10 nm) resolution. We compare different image processing methods for quantitative analysis of the large amount of data. Computing local Minkowski functionals yields local geometrical and morphological information about the observed structures and enables us to track their evolution with time. An alternative characterization method is to reduce the gray scale images to their skeleton and to classify and count the branching points of the skeletonized structure. We tracked the temporal evolution of these measures and computed correlation functions.
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Affiliation(s)
- S Rehse
- Chemische Physik, Technische Universität Chemnitz, Reichenhainer Strasse 70, D-09126 Chemnitz, Germany.
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8
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9
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Kwon Y, Thornton K, Voorhees PW. Coarsening of bicontinuous structures via nonconserved and conserved dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:021120. [PMID: 17358326 DOI: 10.1103/physreve.75.021120] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2006] [Indexed: 05/14/2023]
Abstract
Coarsening subsequent to phase separations occurs in many two-phase mixtures. While unique scaled particle size distributions have been determined for highly asymmetric mixtures in which spherical particles form in a matrix, it is not known if a unique scaled structure exists for symmetric mixtures, which yield bicontinuous structures having intricately interpenetrating phase domains. Using large-scale simulations, we have established that unique scaled microstructures exist in symmetric mixtures evolving via nonconserved and conserved dynamics. We characterize their morphologies by the interfacial shape distribution, a counterpart to the particle size distribution, and their topologies by the genus. We find that the two dynamics result in unique, but different, scaled interfacial shape distributions, with conserved dynamics yielding a narrower distribution around zero mean curvature. In contrast, the two scaled structures are topologically similar, having nearly equal values of the scaled genus.
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Affiliation(s)
- Yongwoo Kwon
- Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, Illinois 60208-3108, USA
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10
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Tanaka H, Nishikawa Y. Viscoelastic phase separation of protein solutions. PHYSICAL REVIEW LETTERS 2005; 95:078103. [PMID: 16196827 DOI: 10.1103/physrevlett.95.078103] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2005] [Indexed: 05/04/2023]
Abstract
In addition to the known behavior of normal phase separation and gelation, we report novel phase-separation behavior of protein solutions as their intermediate case. A network structure of the protein-rich phase may be formed even if it is the minority phase, contrary to the conventional wisdom. This behavior is characteristic of viscoelastic phase separation found in polymer solutions. This kinetic pathway may play crucial roles in the complex phase ordering of protein solutions, in particular, protein network formation in biological systems and foods.
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Affiliation(s)
- Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, Japan
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11
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Rysz J. Monte Carlo simulations of phase separation in thin polymer blend films: scaling properties of morphological measures. POLYMER 2005. [DOI: 10.1016/j.polymer.2004.11.084] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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12
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Sevink GJA, Zvelindovsky AV. Kinetic pathways of sheared block copolymer systems derived from Minkowski functionals. J Chem Phys 2004; 121:3864-73. [PMID: 15303955 DOI: 10.1063/1.1774982] [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 employ Minkowski functionals to analyze the kinetics of pattern formation under an applied external shear flow. The considered pattern formation model describes the dynamics of phase separating block copolymer systems. For our purpose, we have chosen two block copolymer systems (a melt and a solution) that exhibit a hexagonal cylindrical morphology as an equilibrium structure. Our main objective is the determination of efficient choices for the treshold values that are required for the calculation of the Minkowski functionals. We find that a minimal set of two treshold values (one from which should be equal to an average density value and another to a higher density value) is sufficient to unraffle the phase separation kinetics. Given these choices, we focus on the influence of the degree of phase separation, and the instance at which the shear is applied, on the kinetic pathways. We also found a remarkable similarity of the time evolution of Euler characteristic and the segregation parameter for the average density choice.
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Affiliation(s)
- G J A Sevink
- LIC, Leiden University, P.O. Box 9502, 2300 RA, Leiden, The Netherlands
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13
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Fiałkowski M, Garstecki P, Hołyst R. Liquids with internal surfaces at and out of equilibrium: the homogeneity index. J Mol Liq 2004. [DOI: 10.1016/j.molliq.2003.11.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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14
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Fiałkowski M, Hołyst R. The unphysical pinning of the domain growth during the separation of homopolymer blends near the spinodal. J Chem Phys 2004; 120:5802-8. [PMID: 15267460 DOI: 10.1063/1.1649731] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We simulate model B of mesoscopic dynamic with the Flory-Huggins free energy for the homopolymer blend. We concentrate the study on the rescaling of the spatial coordinates in the model. We show that the commonly used rescaling of the spatial coordinates, by the function vanishing at the spinodal, leads to the unphysical freezing of the domains. We study the evolution of the system in two different processes: One is the growth process induced by the temperature quench to the metastable or unstable region of the phase diagram and the second is the quench-jump process in which we first allow the system to separate below the spinodal and next heat it up below or above the spinodal. The proper rescaling avoiding the unphysical pinning of the domain growth at the spinodal is proposed.
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Affiliation(s)
- Marcin Fiałkowski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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Raczkowska J, Rysz J, Budkowski A, Lekki J, Lekka M, Bernasik A, Kowalski K, Czuba P. Surface Patterns in Solvent-Cast Polymer Blend Films Analyzed with an Integral-Geometry Approach. Macromolecules 2003. [DOI: 10.1021/ma020870w] [Citation(s) in RCA: 58] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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16
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Graca M, Wieczorek SA, Fiałkowski M, Hołyst R. Demixing/Mixing of Polystyrene with Poly(methylphenylsiloxane) in a Two-Step Cooling/Heating Process: Jump Spinodal Specification Method. Macromolecules 2002. [DOI: 10.1021/ma020499c] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Graca
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland; Department of Mathematics and Natural Sciences−College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland; and Ecole Normale Superieure, Labo de Physique, 46 Allee d'Italie, Lyon, France
| | - S. A. Wieczorek
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland; Department of Mathematics and Natural Sciences−College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland; and Ecole Normale Superieure, Labo de Physique, 46 Allee d'Italie, Lyon, France
| | - M. Fiałkowski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland; Department of Mathematics and Natural Sciences−College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland; and Ecole Normale Superieure, Labo de Physique, 46 Allee d'Italie, Lyon, France
| | - R. Hołyst
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland; Department of Mathematics and Natural Sciences−College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland; and Ecole Normale Superieure, Labo de Physique, 46 Allee d'Italie, Lyon, France
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17
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Fiałkowski M, Hołyst R. Morphological changes during the order-disorder transition in the two- and three-dimensional systems of scalar nonconserved order parameters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:046121. [PMID: 12443273 DOI: 10.1103/physreve.66.046121] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2002] [Indexed: 05/24/2023]
Abstract
The order-disorder transition is studied in a system of a scalar nonconserved order parameter. We use this well studied system to show that the application of the methods of topology and geometry reveals that our knowledge of the kinetic pathways by which the order-disorder transition proceeds is far from being complete. We show that in two-dimensional (2D) and 3D systems there are three dynamical regimes in the evolution of the system: early, intermediate, and late. In the intermediate regime two length scales govern the behavior of the system, whereas in the early and intermediate regime there is only one length scale. The size distribution of the domain area indicates the pathway by which the domains change their size. There are only two types of domains in a 2D system: circular and elongated with well defined characteristics (scaling of the area with the contour length) which in the late regime do not depend on time after rescaling by the average area and contour in the system. The elongated domains continuously change into circular domains reducing in this way the overall dissipation in the system. In order to reach a Lifshitz-Cahn-Allen (LCA) late stage regime the number of elongated domains must be strongly reduced. In the intermediate regime the number of elongated domains is large and simple LCA scaling does not hold. In a 3D symmetric system we always have a bicontinuous structure that evolves by cutting small connections. The late stage regime seems to be associated with the appearance of the preferred nonzero mean curvature. The early-intermediate regime crossover is associated with the saturation of the order parameter inside the domains, while the intermediate-late stage regime crossover is related to the global breaking of the +/- order parameter symmetry (marked by the appearance of the nonzero mean curvature but still zero average magnetization). The times for the occurrence of these crossovers do not depend on the size of the system.
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Affiliation(s)
- Marcin Fiałkowski
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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18
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Fiałkowski M, Hołyst R. Quench–jump sequence in phase separation in polymer blends. J Chem Phys 2002. [DOI: 10.1063/1.1487375] [Citation(s) in RCA: 17] [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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19
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Ishikawa A, Ogawa T. Dynamics of spinodal decomposition in finite-lifetime systems: Nonlinear statistical theory based on a coarse-grained lattice-gas model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:026131. [PMID: 11863611 DOI: 10.1103/physreve.65.026131] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2001] [Revised: 07/18/2001] [Indexed: 05/23/2023]
Abstract
We study theoretically dynamics of the spinodal decomposition in finite-lifetime systems to clarify effects of the interparticle interactions beyond the Ginzburg-Landau-Wilson phenomenology. Our theory is based on the coarse-grained Hamiltonian derived from the interacting lattice-gas model with a finite lifetime. The information of a system is reduced to closed-form coupled integrodifferential equations for the single-point distribution function and the dynamical structure factor. These equations involve explicitly the interparticle interactions. The finite lifetime prevents the phase separation and the order formation in the cw creation case; domains cannot grow to be larger than an asymptotic characteristic size [k(max)(t --> infinity)](-1). Power-law dependence of k(max)(t --> infinity) on the interparticle interaction and the particle lifetime is also found numerically. The finite lifetime prevents the phase separation, i.e., the lower critical wave number k((1))(c) appears and domains of size larger than [k((1))(c)](-1) cannot grow.
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Affiliation(s)
- Akira Ishikawa
- Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan.
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20
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Lorén N, Altskär A, Hermansson AM. Structure Evolution during Gelation at Later Stages of Spinodal Decomposition in Gelatin/Maltodextrin Mixtures. Macromolecules 2001. [DOI: 10.1021/ma010722q] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Niklas Lorén
- SIKThe Swedish Institute for Food and Biotechnology, PO Box 5401, SE-402 29 Göteborg, Sweden
| | - Annika Altskär
- SIKThe Swedish Institute for Food and Biotechnology, PO Box 5401, SE-402 29 Göteborg, Sweden
| | - Anne-Marie Hermansson
- SIKThe Swedish Institute for Food and Biotechnology, PO Box 5401, SE-402 29 Göteborg, Sweden
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21
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Araki T, Tanaka H. Three-Dimensional Numerical Simulations of Viscoelastic Phase Separation: Morphological Characteristics. Macromolecules 2001. [DOI: 10.1021/ma001569n] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Takeaki Araki
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
| | - Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
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22
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Fialkowski M, Aksimentiev A, Hołyst R. Scaling of the Euler characteristic, surface area, and curvatures in the phase separating or ordering systems. PHYSICAL REVIEW LETTERS 2001; 86:240-243. [PMID: 11177801 DOI: 10.1103/physrevlett.86.240] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2000] [Indexed: 05/23/2023]
Abstract
We present robust scaling laws for the Euler characteristic and curvatures applicable to any symmetric system undergoing phase separating or ordering kinetics. We apply it to the phase ordering in a system of the nonconserved scalar order parameter and find three scaling regimes. The appearance of the preferred nonzero curvature of an interface separating +/- domains marks the crossover to the late stage regime characterized by the Lifshitz-Cahn-Allen scaling.
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Affiliation(s)
- M Fialkowski
- Institute of Physical Chemistry PAS and College of Science, Department III, Warsaw, Poland
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23
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Aksimentiev A, Holyst R. Influence of the free-energy functional form on simulated morphology of spinodally decomposing blends. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:6821-6830. [PMID: 11102035 DOI: 10.1103/physreve.62.6821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2000] [Indexed: 05/23/2023]
Abstract
The spinodal decomposition of a binary mixture has been studied within several mesoscopic models. It has been found that the form of the equilibrium free energy has a crucial effect on the morphological development in asymmetric blends. We have shown that the principal quantity that determines the topology of the interface (and type of morphology) is the equilibrium minority phase volume fraction, while the transition from bicontinuous to droplet morphology can be treated as a percolation. The concentration dependence of the square gradient coefficient attributed for the Flory-Huggins-de Gennes free energy has no significant influences on the average domain growth, but can be distinguished experimentally from its constant-coefficient alternative by measuring the maximum wave vector of the scattering intensity as a function of the minority phase volume fraction for spinodally decomposing asymmetric blends. The concentration dependence of the Onsager coefficient has the weak, systematic effect of slowing down the morphological development. The local shape of the interface is not affected considerably by the concentration dependence of the square gradient and Onsager coefficient.
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Affiliation(s)
- A Aksimentiev
- Material Science Laboratory, R&D Center, Mitsui Chemicals, Inc., 580-32 Nagaura, Sodegaura-City, Chiba 299-0265, Japan
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