1
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Willis JD, Matsen MW. Bicontinuous microemulsion in binary blends of complementary diblock copolymers. J Chem Phys 2024; 160:024906. [PMID: 38193556 DOI: 10.1063/5.0185556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/19/2023] [Indexed: 01/10/2024] Open
Abstract
The phase behavior of binary blends of AB diblock copolymers of compositions f and 1 - f is examined using field-theoretic simulations. Highly asymmetric compositions (i.e., f ≈ 0) behave like homopolymer blends macrophase separating into coexisting A- and B-rich phases as the segregation is increased, whereas more symmetric diblocks (i.e., f ≈ 0.5) microphase separate into an ordered lamellar phase. In self-consistent field theory, these behaviors are separated by a Lifshitz critical point at f = 0.2113. However, its lower critical dimension is believed to be four, which implies that the Lifshitz point should be destroyed by fluctuations. Consistent with this, it is found to transform into a tricritical point. Furthermore, the highly swollen lamellar phase near the mean-field Lifshitz point disorders into a bicontinuous microemulsion (BμE), consisting of large interpenetrating A- and B-rich microdomains. BμE has been previously reported in ternary blends of AB diblock copolymer with its parent A- and B-type homopolymers, but in that system the homopolymers have a tendency to macrophase separate. Our alternative system for creating BμE is free of this macrophase separation.
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Affiliation(s)
- J D Willis
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - M W Matsen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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2
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Schmid F. Understanding and Modeling Polymers: The Challenge of Multiple Scales. ACS POLYMERS AU 2022. [DOI: 10.1021/acspolymersau.2c00049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Friederike Schmid
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128Mainz, Germany
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3
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Matsen MW, Beardsley TM. Field-Theoretic Simulations for Block Copolymer Melts Using the Partial Saddle-Point Approximation. Polymers (Basel) 2021; 13:2437. [PMID: 34372040 PMCID: PMC8347900 DOI: 10.3390/polym13152437] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 07/16/2021] [Accepted: 07/20/2021] [Indexed: 11/16/2022] Open
Abstract
Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, Hf[W-,W+], depends on a composition field, W-(r), that controls the segregation of the unlike components and a pressure field, W+(r), that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which W-(r) fluctuates while W+(r) tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).
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Affiliation(s)
- Mark W. Matsen
- Department of Chemical Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada
- Department of Physics & Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
- Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, ON N2L 3G1, Canada;
| | - Thomas M. Beardsley
- Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, ON N2L 3G1, Canada;
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4
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Affiliation(s)
- Russell K. W. Spencer
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Mark W. Matsen
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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5
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Vorselaars B, Spencer RKW, Matsen MW. Instability of the Microemulsion Channel in Block Copolymer-Homopolymer Blends. PHYSICAL REVIEW LETTERS 2020; 125:117801. [PMID: 32976007 DOI: 10.1103/physrevlett.125.117801] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Accepted: 08/19/2020] [Indexed: 06/11/2023]
Abstract
Field theoretic simulations are used to predict the equilibrium phase diagram of symmetric blends of AB diblock copolymer with A- and B-type homopolymers. Experiments generally observe a channel of bicontinuous microemulsion (BμE) separating the ordered lamellar (LAM) phase from coexisting homopolymer-rich (A+B) phases. However, our simulations find that the channel is unstable with respect to macrophase separation, in particular, A+B+BμE coexistence at high T and A+B+LAM coexistence at low T. The preference for three-phase coexistence is attributed to a weak attractive interaction between diblock monolayers.
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Affiliation(s)
- Bart Vorselaars
- School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln LN6 7TS, United Kingdom
| | - Russell K W Spencer
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Mark W Matsen
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Abstract
This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.
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Affiliation(s)
- M W Matsen
- Department of Chemical Engineering, Department of Physics and Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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7
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Beardsley TM, Spencer RKW, Matsen MW. Computationally Efficient Field-Theoretic Simulations for Block Copolymer Melts. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01904] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
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8
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Yadav M, Bates FS, Morse DC. Effects of Segment Length Asymmetry in Ternary Diblock Co-polymer–Homopolymer Mixtures. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b00127] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Mridul Yadav
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Frank S. Bates
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - David C. Morse
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
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9
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Beardsley TM, Matsen MW. Calibration of the Flory-Huggins interaction parameter in field-theoretic simulations. J Chem Phys 2019; 150:174902. [PMID: 31067914 DOI: 10.1063/1.5089217] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Field-theoretic simulations (FTS) offer a versatile method of dealing with complicated block copolymer systems, but unfortunately they struggle to cope with the level of fluctuations typical of experiments. Although the main obstacle, an ultraviolet divergence, can be removed by renormalizing the Flory-Huggins χ parameter, this only works for unrealistically large invariant polymerization indexes, N¯. Here, we circumvent the problem by applying the Morse calibration, where a nonlinear relationship between the bare χb used in FTS and the effective χ corresponding to the standard Gaussian-chain model is obtained by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop predictions. This calibration brings the order-disorder transition obtained from FTS into agreement with the universal results of particle-based simulations for values of N¯ characteristic of the experiment. In the limit of weak interactions, the calibration reduces to a linear approximation, χ ≈ z∞χb, consistent with the previous renormalization of χ for large N¯.
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Affiliation(s)
- T M Beardsley
- Department of Chemical Engineering, Department of Physics, and The Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - M W Matsen
- Department of Chemical Engineering, Department of Physics, and The Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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10
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Spencer RKW, Matsen MW. Fluctuation effects in blends of A + B homopolymers with AB diblock copolymer. J Chem Phys 2018; 148:204907. [DOI: 10.1063/1.5030180] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Russell K. W. Spencer
- Department of Chemical Engineering, Department of Physics and Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Mark W. Matsen
- Department of Chemical Engineering, Department of Physics and Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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11
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Affiliation(s)
- Russell K. W. Spencer
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario Canada
| | - Mark W. Matsen
- Department of Chemical Engineering, Department of Physics & Astronomy, and Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario Canada
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12
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Vorselaars B, Stasiak P, Matsen MW. Field-Theoretic Simulation of Block Copolymers at Experimentally Relevant Molecular Weights. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b02286] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Bart Vorselaars
- Department of Chemical Engineering, Department of Physics & Astronomy, and the Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pawel Stasiak
- School
of Mathematical and Physical Sciences, University of Reading, Whiteknights, Reading RG6 6AX, U.K
| | - Mark W. Matsen
- Department of Chemical Engineering, Department of Physics & Astronomy, and the Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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13
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Pandav G, Ganesan V. Fluctuation effects on the order-disorder transition in polydisperse copolymer melts. J Chem Phys 2013; 139:214905. [DOI: 10.1063/1.4833137] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
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14
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Pandav G, Ganesan V. Efficacy of Different Block Copolymers in Facilitating Microemulsion Phases in Polymer Blend Systems. Macromolecules 2013. [DOI: 10.1021/ma4016104] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Gunja Pandav
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
| | - Venkat Ganesan
- Department
of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States
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15
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16
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Gemünden P, Poelking C, Kremer K, Andrienko D, Daoulas KC. Nematic Ordering, Conjugation, and Density of States of Soluble Polymeric Semiconductors. Macromolecules 2013. [DOI: 10.1021/ma400646a] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Patrick Gemünden
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
- InnovationLab GmbH, 69115 Heidelberg, Germany
| | - Carl Poelking
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Denis Andrienko
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Kostas Ch. Daoulas
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
- InnovationLab GmbH, 69115 Heidelberg, Germany
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17
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Stuen KO, Thomas CS, Liu G, Ferrier N, Nealey PF. Dimensional Scaling of Cylinders in Thin Films of Block Copolymer−Homopolymer Ternary Blends. Macromolecules 2009. [DOI: 10.1021/ma900520v] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Karl O. Stuen
- Department of Chemical and Biological Engineering
- Department of Mechanical Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Carla S. Thomas
- Department of Chemical and Biological Engineering
- Department of Mechanical Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Guoliang Liu
- Department of Chemical and Biological Engineering
- Department of Mechanical Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Nicola Ferrier
- Department of Chemical and Biological Engineering
- Department of Mechanical Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Paul F. Nealey
- Department of Chemical and Biological Engineering
- Department of Mechanical Engineering
- University of Wisconsin, Madison, Wisconsin 53706
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18
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Liu G, Stoykovich MP, Ji S, Stuen KO, Craig GSW, Nealey PF. Phase Behavior and Dimensional Scaling of Symmetric Block Copolymer−Homopolymer Ternary Blends in Thin Films. Macromolecules 2009. [DOI: 10.1021/ma802773h] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Guoliang Liu
- Department of Chemical and Biological Engineering, University of Wisconsin—Madison, 1415 Engineering Drive, Madison, Wisconsin 53706
| | - Mark P. Stoykovich
- Department of Chemical and Biological Engineering, University of Wisconsin—Madison, 1415 Engineering Drive, Madison, Wisconsin 53706
| | - Shengxiang Ji
- Department of Chemical and Biological Engineering, University of Wisconsin—Madison, 1415 Engineering Drive, Madison, Wisconsin 53706
| | - Karl O. Stuen
- Department of Chemical and Biological Engineering, University of Wisconsin—Madison, 1415 Engineering Drive, Madison, Wisconsin 53706
| | - Gordon S. W. Craig
- Department of Chemical and Biological Engineering, University of Wisconsin—Madison, 1415 Engineering Drive, Madison, Wisconsin 53706
| | - Paul F. Nealey
- Department of Chemical and Biological Engineering, University of Wisconsin—Madison, 1415 Engineering Drive, Madison, Wisconsin 53706
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19
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Pipich V, Willner L, Schwahn D. The A-B diblock copolymer as a nonordering external field in a three-component A/B/A-B polymer blend. J Phys Chem B 2008; 112:16170-81. [PMID: 19367997 DOI: 10.1021/jp805903p] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Thermal copolymer fluctuations were explored in a three-component blend consisting of a critical (A/B) homopolymer blend and a symmetric A-B diblock copolymer using the technique of neutron small angle scattering. The copolymer has the function of an external nonordering field and thereby determines phase behavior as well as the regimes of 3d-Ising, isotropic Lifshitz, and Brasovskiî critical universality. It was found that the random phase approximation (RPA) does not correctly describe the copolymer structure function because of strong thermal fluctuations. On the other hand a weak coupling of copolymer and homopolymer was confirmed, consistent with predictions from RPA. Self-assembly of the copolymers was observed prior to the ordering of the "total" blend, e.g. inclusive of the homopolymers, into bicontinuous and lamellar ordered phases.
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Affiliation(s)
- Vitaliy Pipich
- Institute of Solid Research of the Helmholtz Research Center Jülich, D-52425 Jülich, Germany
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20
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Imperio A, Reatto L. Microphase morphology in two-dimensional fluids under lateral confinement. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:040402. [PMID: 17994924 DOI: 10.1103/physreve.76.040402] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2007] [Indexed: 05/25/2023]
Abstract
We study the effects of confinement between two parallel walls on a two dimensional fluid with competing interactions which lead to the formation of particle microdomains at the thermodynamic equilibrium (microphases or microseparation). The possibility to induce structural changes of the morphology of the microdomains is explored, under different confinement conditions and temperatures. In the presence of neutral walls, a switch from stripes of particles to circular clusters (droplets) occurs as the temperature decreases, which does not happen in bulk. While the passage from droplets to stripes, as the density increases, is a well-known phenomenon, the change of the stripes into droplets as an effect of temperature is rather unexpected. Depending on the wall separation and on the wall-fluid interaction parameters, the stripes can switch from parallel to perpendicular to the walls and also a mixed morphology can be stable.
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21
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Nunalee ML, Guo H, de la Cruz MO, Shull KR. An Interfacial Curvature Map for Homopolymer Interfaces in the Presence of Diblock Copolymers. Macromolecules 2007. [DOI: 10.1021/ma070722b] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michelle L. Nunalee
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, and Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P.R. China
| | - Hongxia Guo
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, and Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P.R. China
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, and Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P.R. China
| | - Kenneth R. Shull
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, and Beijing National Laboratory for Molecular Sciences, State Key Laboratory of Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P.R. China
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22
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Stoykovich MP, Edwards EW, Solak HH, Nealey PF. Phase behavior of symmetric ternary block copolymer-homopolymer blends in thin films and on chemically patterned surfaces. PHYSICAL REVIEW LETTERS 2006; 97:147802. [PMID: 17155291 DOI: 10.1103/physrevlett.97.147802] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2005] [Revised: 07/21/2006] [Indexed: 05/12/2023]
Abstract
The phase diagram of symmetric ternary blends of diblock copolymers and homopolymers in thin films was determined as a function of increasing volume fraction of homopolymer (phi(H)) and was similar to that for these materials in the bulk. Blends with compositions in the lamellar region of the diagram (phi(H)< or =0.4) could be directed to assemble into ordered lamellar arrays on chemically striped surfaces if the characteristic blend dimension (L(B)) and the period of the stripes (L(S)) were commensurate such that L(S)=L(B)+/-0.10L(B). Blends with compositions in the microemulsion region of the diagram (phi(H) approximately 0.6) assembled into defect-free lamellar phases on patterned surfaces with L(S)> or =L(B), but formed coexisting lamellar (with period L(S)) and homopolymer-rich phases when L(S)<L(B).
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Affiliation(s)
- Mark P Stoykovich
- Department of Chemical and Biological Engineering and Center for Nanotechnology, University of Wisconsin, Madison, Wisconsin 53706, USA
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23
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Zhou N, Lodge TP, Bates FS. Influence of Conformational Asymmetry on the Phase Behavior of Ternary Homopolymer/Block Copolymer Blends around the Bicontinuous Microemulsion Channel. J Phys Chem B 2006; 110:3979-89. [PMID: 16509686 DOI: 10.1021/jp055704f] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have developed a new ternary polymeric system, poly(ethylene-alt-propylene) (PEP)/poly(butylene oxide) (PBO)/PEP-PBO, to study the complex phase behavior near the bicontinuous microemulsion phase channel. The molecular weights of the PEP and PBO homopolymers are 2600 and 3050 g/mol, respectively, and the copolymer is 23.4 kg/mol with volume fraction composition fPBO=0.49. A combination of small-angle neutron scattering, small-angle X-ray scattering, rheology, optical microscopy, and visual oil bath measurements was employed to map out the phase diagrams at five fixed homopolymer PBO/PEP ratios, ranging from 40/60 to 60/40 by volume, with copolymer concentrations ranging from 0 to 100%. It was found that the bicontinuous microemulsion channel is consistently cut off at low temperature by a hexagonal phase. We attribute this phenomenon to the effect of the conformational asymmetry between the PEP and PBO species, whereby the more flexible PBO component induces a spontaneous curvature toward the PBO domains. These findings complement previous descriptions of the isopleth phase diagrams for A/B/A-B systems and identify a new design variable for preparing bicontinuous phases.
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Affiliation(s)
- Ning Zhou
- Department of Chemical Engineering & Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
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24
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Ruegg ML, Reynolds BJ, Lin MY, Lohse DJ, Balsara NP. Microphase and Macrophase Separation in Multicomponent A/B/A−C Polymer Blends with Attractive and Repulsive Interactions. Macromolecules 2006. [DOI: 10.1021/ma0516889] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Megan L. Ruegg
- Department of Chemical Engineering, University of California, Berkeley, California 94720, Earth Science, Materials Sciences, and Environmental Energy Technologies Divisions, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, and ExxonMobil Research and Engineering, Annandale, New Jersey 08801
| | - Benedict J. Reynolds
- Department of Chemical Engineering, University of California, Berkeley, California 94720, Earth Science, Materials Sciences, and Environmental Energy Technologies Divisions, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, and ExxonMobil Research and Engineering, Annandale, New Jersey 08801
| | - Min Y. Lin
- Department of Chemical Engineering, University of California, Berkeley, California 94720, Earth Science, Materials Sciences, and Environmental Energy Technologies Divisions, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, and ExxonMobil Research and Engineering, Annandale, New Jersey 08801
| | - David J. Lohse
- Department of Chemical Engineering, University of California, Berkeley, California 94720, Earth Science, Materials Sciences, and Environmental Energy Technologies Divisions, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, and ExxonMobil Research and Engineering, Annandale, New Jersey 08801
| | - Nitash P. Balsara
- Department of Chemical Engineering, University of California, Berkeley, California 94720, Earth Science, Materials Sciences, and Environmental Energy Technologies Divisions, Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720, and ExxonMobil Research and Engineering, Annandale, New Jersey 08801
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25
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Pipich V, Schwahn D, Willner L. Composition fluctuations in a homopolymer-diblock copolymer mixture covering the three-dimensional Ising, isotropic Lifshitz, and Brasovskiĭ classes of critical universality. J Chem Phys 2005; 123:124904. [PMID: 16392524 DOI: 10.1063/1.1997136] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The phase behavior of a three-component polymer blend consisting of a critical mixture of polybutadiene and polystyrene (PB/PS) with varying amount of a symmetric PB-PS diblock copolymer was explored with small-angle neutron scattering. Our focus were thermal composition fluctuations which we discuss in terms of mean field, three-dimensional Ising, isotropic Lifshitz, and Brasovskiĭ classes of critical universality. Particular attention is spent to the observation of a narrow reentrant two-phase regime and double critical point in the Lifshitz critical regime as well as the Lifshitz line. Critical exponents of the isotropic Lifshitz case are proposed in spite of the demonstrated nonexistence of the isotropic Lifshitz critical point. The Ginzburg number (Gi) and Flory-Huggins parameter were determined over the whole diblock concentration range; Gi changes by three orders of magnitude, two orders of magnitude of that change over a 0.03 diblock concentration interval within the isotropic Lifshitz regime.
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Affiliation(s)
- Vitaliy Pipich
- Forschungszentrum Jülich GmbH, Institut für Festkörperforschung, D-52425 Jülich, Germany
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