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Hillery K, Hendeniya N, Abtahi S, Chittick C, Chang B. Substrate Neutrality for Obtaining Block Copolymer Vertical Orientation. Polymers (Basel) 2024; 16:1740. [PMID: 38932090 PMCID: PMC11207976 DOI: 10.3390/polym16121740] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2024] [Revised: 06/16/2024] [Accepted: 06/17/2024] [Indexed: 06/28/2024] Open
Abstract
Nanopatterning methods utilizing block copolymer (BCP) self-assembly are attractive for semiconductor fabrication due to their molecular precision and high resolution. Grafted polymer brushes play a crucial role in providing a neutral surface conducive for the orientational control of BCPs. These brushes create a non-preferential substrate, allowing wetting of the distinct chemistries from each block of the BCP. This vertically aligns the BCP self-assembled lattice to create patterns that are useful for semiconductor nanofabrication. In this review, we aim to explore various methods used to tune the substrate and BCP interface toward a neutral template. This review takes a historical perspective on the polymer brush methods developed to achieve substrate neutrality. We divide the approaches into copolymer and blended homopolymer methods. Early attempts to obtain neutral substrates utilized end-grafted random copolymers that consisted of monomers from each block. This evolved into side-group-grafted chains, cross-linked mats, and block cooligomer brushes. Amidst the augmentation of the chain architecture, homopolymer blends were developed as a facile method where polymer chains with each chemistry were mixed and grafted onto the substrate. This was largely believed to be challenging due to the macrophase separation of the chemically incompatible chains. However, innovative methods such as sequential grafting and BCP compatibilizers were utilized to circumvent this problem. The advantages and challenges of each method are discussed in the context of neutrality and feasibility.
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Affiliation(s)
| | | | | | | | - Boyce Chang
- Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, USA
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2
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Wang Z, Servio P, Rey A. Wrinkling pattern formation with periodic nematic orientation: From egg cartons to corrugated surfaces. Phys Rev E 2022; 105:034702. [PMID: 35428159 DOI: 10.1103/physreve.105.034702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 03/04/2022] [Indexed: 06/14/2023]
Abstract
Egg cartons, known as doubly sinusoidal surfaces, display a rich variety of saddles-cylinder-spherical patches organized with different spatial symmetries and connectivities. Egg carton surfaces, rich in functionalities, are observed in synthetic and biological materials, as well as across atomic and macroscopic scales. In this work we use the liquid crystal shape equation in the absence of elastic effects and normal stress jumps to predict and classify a family of uniaxial, equibiaxial, and biaxial egg cartons, according to the periodicities of the surface director field in nematic (N) and cholesteric (N*) liquid crystals under the presence of anisotropic surface tension (anchoring). Egg carton surface shape periodic solutions to the nonlinear and linearized liquid crystal shape equations predict that the mean curvature is a linear function of the orthogonal (along the surface normal) splay and bend contributions. Mixtures of egg carton surfaces (uniaxial, equibiaxial, and biaxial) emerge according to the symmetries of the nonsingular director field, and the spatial distributions of the director escape into the third dimension; pure uniaxial egg cartons emerge when the director escape has linelike geometries and mixtures of egg cartons arise under source or sink orientation lattices. Orientation symmetry and permutation analysis are incorporated into a full curvature (Casorati, shape parameter, mean curvature, and Gaussian curvature) characterization. Under a fixed anchoring parameter, conditions for maximal nanoscale curvedness and microscale maximal shape gradient diversity are identified. The present results contribute to various pathways to surface pattern formation using intrinsic anisotropic interfacial tension.
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Affiliation(s)
- Ziheng Wang
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, Canada H3A 0C5
| | - Phillip Servio
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, Canada H3A 0C5
| | - Alejandro Rey
- Department of Chemical Engineering, McGill University, 3610 University Street, Montréal, Québec, Canada H3A 0C5
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Gruhn T, Pogorelov E, Seiferling F, Emmerich H. Analyzing spinodal decomposition of an anisotropic fluid mixture. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:055103. [PMID: 27941222 DOI: 10.1088/1361-648x/aa4de0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Spinodal decomposition leads to spontaneous fluctuations of the local concentration. In the early stage, the resulting pattern provides explicit information about the material properties of the mixture. In the case of two isotropic fluids, the static structure factor shows the characteristic ring shape. If one component is a liquid crystal, the pattern is typically anisotropic and the structure factor is more complex. Using numerical methods, we investigate how structure factors can be used to extract information about material properties like the diffusion constant or the isotropic and the anisotropic contributions to the interfacial tension. The method is based on momenta taken from structure factors in the early stage of the spinodal demixing. We perform phase field calculations for an isotropic and an anisotropic spinodal decomposition. A comparison of the extracted results with analytic values is made. The calculations show that linear modes dominate in the beginning of the growth process, while non-linear modes grow monotonously in the region of the k-space for which damping is predicted by the linearized theory. As long as non-linear modes are small enough, linearized theory can be applied to extract material properties from the structure factor.
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Affiliation(s)
- Thomas Gruhn
- Materials and Process Simulation (MPS), University of Bayreuth, Germany
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Mukherjee A, Mukherjee R, Ankit K, Bhattacharya A, Nestler B. Influence of substrate interaction and confinement on electric-field-induced transition in symmetric block-copolymer thin films. Phys Rev E 2016; 93:032504. [PMID: 27078402 DOI: 10.1103/physreve.93.032504] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Indexed: 11/07/2022]
Abstract
In the present work, we study morphologies arising due to competing substrate interaction, electric field, and confinement effects on a symmetric diblock copolymer. We employ a coarse-grained nonlocal Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric-field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular, and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness, and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.
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Affiliation(s)
- Arnab Mukherjee
- Institute of Materials Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany.,Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
| | - Rajdip Mukherjee
- Department of Materials Science and Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, India
| | - Kumar Ankit
- Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
| | - Avisor Bhattacharya
- Institute of Materials Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany.,Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
| | - Britta Nestler
- Institute of Materials Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany.,Institute of Applied Materials-Computational Materials Science, Karlsruhe Institute of Technology, Haid-und-Neu strasse 7, 76131, Karlsruhe, Germany
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5
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Jeong D, Kim J. Microphase separation patterns in diblock copolymers on curved surfaces using a nonlocal Cahn-Hilliard equation. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:117. [PMID: 26577816 DOI: 10.1140/epje/i2015-15117-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2015] [Accepted: 11/02/2015] [Indexed: 06/05/2023]
Abstract
We investigate microphase separation patterns on curved surfaces in three-dimensional space by numerically solving a nonlocal Cahn-Hilliard equation for diblock copolymers. In our model, a curved surface is implicitly represented as the zero level set of a signed distance function. We employ a discrete narrow band grid that neighbors the curved surface. Using the closest point method, we apply a pseudo-Neumann boundary at the boundary of the computational domain. The boundary treatment allows us to replace the Laplace-Beltrami operator by the standard Laplacian operator. In particular, we can apply standard finite difference schemes in order to approximate the nonlocal Cahn-Hilliard equation in the discrete narrow band domain. We employ a type of unconditionally stable scheme, which was introduced by Eyre, and use the Jacobi iterative to solve the resulting implicit discrete system of equations. In addition, we use the minimum number of grid points for the discrete narrow band domain. Therefore, the algorithm is simple and fast. Numerous computational experiments are provided to study microphase separation patterns for diblock copolymers on curved surfaces in three-dimensional space.
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Affiliation(s)
- Darae Jeong
- Department of Mathematics, Korea University, 136-713, Seoul, Republic of Korea
| | - Junseok Kim
- Department of Mathematics, Korea University, 136-713, Seoul, Republic of Korea.
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Nikoubashman A, Register RA, Panagiotopoulos AZ. Self-Assembly of Cylinder-Forming Diblock Copolymer Thin Films. Macromolecules 2013. [DOI: 10.1021/ma400867s] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Arash Nikoubashman
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544,
United States
| | - Richard A. Register
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544,
United States
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Han E, Stuen KO, Leolukman M, Liu CC, Nealey PF, Gopalan P. Perpendicular Orientation of Domains in Cylinder-Forming Block Copolymer Thick Films by Controlled Interfacial Interactions. Macromolecules 2009. [DOI: 10.1021/ma9002903] [Citation(s) in RCA: 163] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eungnak Han
- Department of Materials Science and Engineering
- Department of Chemical and Biological Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Karl O. Stuen
- Department of Materials Science and Engineering
- Department of Chemical and Biological Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Melvina Leolukman
- Department of Materials Science and Engineering
- Department of Chemical and Biological Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Chi-Chun Liu
- Department of Materials Science and Engineering
- Department of Chemical and Biological Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Paul F. Nealey
- Department of Materials Science and Engineering
- Department of Chemical and Biological Engineering
- University of Wisconsin, Madison, Wisconsin 53706
| | - Padma Gopalan
- Department of Materials Science and Engineering
- Department of Chemical and Biological Engineering
- University of Wisconsin, Madison, Wisconsin 53706
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8
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Feng J, Liu H, Hu Y, Jiang J. Flow‐Induced Morphologies of Diblock Copolymers in a Nanotube Studied by Dissipative Particle Dynamics Simulation. MACROMOL THEOR SIMUL 2008. [DOI: 10.1002/mats.200800005] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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9
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Rider DA, Chen JIL, Eloi JC, Arsenault AC, Russell TP, Ozin GA, Manners I. Controlling the Morphologies of Organometallic Block Copolymers in the 3-Dimensional Spatial Confinement of Colloidal and Inverse Colloidal Crystals. Macromolecules 2008. [DOI: 10.1021/ma7020248] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- David A. Rider
- Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6, Canada, School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K., and Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Jennifer I. L. Chen
- Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6, Canada, School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K., and Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Jean-Charles Eloi
- Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6, Canada, School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K., and Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - André C. Arsenault
- Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6, Canada, School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K., and Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Thomas P. Russell
- Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6, Canada, School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K., and Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Geoffrey A. Ozin
- Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6, Canada, School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K., and Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Ian Manners
- Department of Chemistry, University of Toronto, Toronto, ON, M5S 3H6, Canada, School of Chemistry, University of Bristol, Bristol, BS8 1TS, U.K., and Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
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10
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11
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Monte Carlo Simulations of Nano-Confined Block Copolymers. ACTA ACUST UNITED AC 2007. [DOI: 10.1007/978-1-4020-6330-5_16] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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12
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Feng J, Liu H, Hu Y. Mesophase Separation of Diblock Copolymer Confined in a Cylindrical Tube Studied by Dissipative Particle Dynamics. MACROMOL THEOR SIMUL 2006. [DOI: 10.1002/mats.200600042] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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13
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Yin Y, Sun P, Jiang R, Li B, Chen T, Jin Q, Ding D, Shi AC. Simulated annealing study of asymmetric diblock copolymer thin films. J Chem Phys 2006; 124:184708. [PMID: 16709132 DOI: 10.1063/1.2194537] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report a simulated annealing study of the morphology of asymmetric diblock copolymer thin films confined between two homogeneous and identical surfaces. We have focused on copolymers that form a gyroidal morphology in the bulk. The morphological dependence of the confined films on the film thickness and the surface-polymer interaction has been systematically investigated. From the simulations it is found that much richer morphologies can form for the gyroid-forming asymmetric diblock copolymer thin films, in contrast to the lamella-forming symmetric and cylinder-forming asymmetric diblock copolymer films. Multiple morphological transitions induced by changing the film thickness and polymer-surface interactions are observed.
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Affiliation(s)
- Yuhua Yin
- College of Physics, Nankai University, Tianjin, 300071, People's Republic of China
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14
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Xu JB, Wu H, Lu DY, He XF, Zhao YH, Wen H. Dissipative particle dynamics simulation on the meso-scale structure of diblock copolymer under cylindrical confinement. MOLECULAR SIMULATION 2006. [DOI: 10.1080/08927020600702022] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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15
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16
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Ren CL, Ma YQ. Reentrant ordering transition of asymmetric copolymer solution film confined between polymer-grafted surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:051804. [PMID: 16383635 DOI: 10.1103/physreve.72.051804] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2005] [Revised: 09/21/2005] [Indexed: 05/05/2023]
Abstract
We study the equilibrium morphology of an asymmetric A-B diblock copolymer solution film confined between homopolymer-grafted substrates by using self-consistent-field calculations. We find that on decreasing the copolymer concentration, a reentrant structural transformation between hexagonal --> lamellar --> hexagonal phases occurs as a result of the competition between the wetting effect of the brush surface and the bulk phase behavior of the asymmetric copolymer driven by the A-B interfacial tension.
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Affiliation(s)
- Chun-lai Ren
- National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
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17
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Wang Q. Morphology of Symmetric Diblock Copolymers Confined Between Two Stripe-Patterned Surfaces - Tilted Lamellae and More. MACROMOL THEOR SIMUL 2005. [DOI: 10.1002/mats.200400062] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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18
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Xiang H, Shin K, Kim T, Moon SI, McCarthy TJ, Russell TP. From Cylinders to Helices upon Confinement. Macromolecules 2005. [DOI: 10.1021/ma0476036] [Citation(s) in RCA: 183] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hongqi Xiang
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Kyusoon Shin
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Taehyung Kim
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Sung In Moon
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Thomas J. McCarthy
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Thomas P. Russell
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
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Xiang H, Shin K, Kim T, Moon S, Mccarthy TJ, Russell TP. The influence of confinement and curvature on the morphology of block copolymers. ACTA ACUST UNITED AC 2005. [DOI: 10.1002/polb.20641] [Citation(s) in RCA: 123] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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20
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Xiang H, Shin K, Kim T, Moon SI, McCarthy TJ, Russell TP. Block Copolymers under Cylindrical Confinement. Macromolecules 2004. [DOI: 10.1021/ma049299m] [Citation(s) in RCA: 251] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hongqi Xiang
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Kyusoon Shin
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Taehyung Kim
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Sung In Moon
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Thomas J. McCarthy
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
| | - Thomas P. Russell
- Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003
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Horvat A, Lyakhova KS, Sevink GJA, Zvelindovsky AV, Magerle R. Phase behavior in thin films of cylinder-forming ABA block copolymers: Mesoscale modeling. J Chem Phys 2004; 120:1117-26. [PMID: 15267948 DOI: 10.1063/1.1627325] [Citation(s) in RCA: 113] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The phase behavior of cylinder-forming ABA block copolymers in thin films is modeled in detail using dynamic density functional theory and compared with recent experiments on polystyrene-block-polybutadiene-block-polystyrene triblock copolymers. Deviations from the bulk structure, such as wetting layer, perforated lamella, and lamella, are identified as surface reconstructions. Their stability regions are determined by an interplay between surface fields and confinement effects. Our results give evidence for a general mechanism governing the phase behavior in thin films of modulated phases.
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Affiliation(s)
- A Horvat
- Physikalische Chemie II, Universität Bayreuth, D-95440 Bayreuth, Germany
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Lyakhova KS, Sevink GJA, Zvelindovsky AV, Horvat A, Magerle R. Role of dissimilar interfaces in thin films of cylinder-forming block copolymers. J Chem Phys 2004; 120:1127-37. [PMID: 15267949 DOI: 10.1063/1.1632475] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the effect of dissimilar interfaces on the phase behavior of cylinder forming block copolymers in thin films by means of dynamic density-functional theory. In this article, we show that dissimilarity of the interfaces induces hybrid structures. These structures appear when the surface fields at the two interfaces stabilize different surface structures and/or reconstructions. We propose a general classification of hybrid structures and give an unifying description of phase behavior of cylinder forming block copolymer films. Our results are consistent with experimental observations.
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Affiliation(s)
- K S Lyakhova
- Leiden Institute of Chemistry, Gorlaeus Laboratory, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
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23
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24
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Podariu I, Chakrabarti A. Morphology of asymmetric diblock copolymer thin films. J Chem Phys 2003. [DOI: 10.1063/1.1574780] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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25
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Wang Q, Nealey PF, de Pablo JJ. Simulations of the Morphology of Cylinder-Forming Asymmetric Diblock Copolymer Thin Films on Nanopatterned Substrates. Macromolecules 2003. [DOI: 10.1021/ma020996t] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Qiang Wang
- Department of Chemical Engineering, University of WisconsinMadison, Madison, Wisconsin 53706-1691
| | - Paul F. Nealey
- Department of Chemical Engineering, University of WisconsinMadison, Madison, Wisconsin 53706-1691
| | - Juan J. de Pablo
- Department of Chemical Engineering, University of WisconsinMadison, Madison, Wisconsin 53706-1691
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Tasinkevych M, Ciach A, Telo Da Gama MM. Lamellar phases confined in quasicylindrical pores: lattice model results. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:031707. [PMID: 11909081 DOI: 10.1103/physreve.65.031707] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2001] [Indexed: 05/23/2023]
Abstract
A two-dimensional (2D) vector lattice model of microemulsions is applied to study the structure of lamellar phases confined in long rectangular pores. One-point distribution functions are calculated within mean field approximation. The effects of pore geometry and surface fields are considered. A 2D analog of an onion phase is favored by a pore with strongly hydrophilic walls. For neutral walls, far from the phase boundaries, the lamellar phase is stable inside the pore. By contrast, close to the lamellar-tubular phase boundary a pore with neutral walls favors a 2D tubular phase. This is the analog of capillary condensation. In all cases the excess pressure is calculated as a function of the pore geometry.
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Affiliation(s)
- M Tasinkevych
- Departamento de Física da Faculdade de Ciências and Centro de Física Teórica e Computacional, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisboa Codex, Portugal
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28
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Tasinkevych M, Ciach A. Structural transformations in confined lamellar phases in oil–water–surfactant mixtures. J Chem Phys 2001. [DOI: 10.1063/1.1412606] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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29
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Morozov AN, Zvelindovsky AV, Fraaije JG. Influence of confinement on the orientational phase transitions in the lamellar phase of a block-copolymer melt under shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:051803. [PMID: 11735954 DOI: 10.1103/physreve.64.051803] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2001] [Indexed: 05/23/2023]
Abstract
In this paper, we incorporate some real-system effects into the theory of orientational phase transitions under shear flow [M. E. Cates and S. T. Milner, Phys. Rev. Lett. 62 1856 (1989) and G. H. Fredrickson, J. Rheol. 38, 1045 (1994)]. In particular, we study the influence of the shear-cell boundaries on the orientation of the lamellar phase. We predict that at low shear rates, the parallel orientation appears to be stable. We show that there is a critical value of the shear rate at which the parallel orientation loses its stability and the perpendicular one appears immediately below the spinodal. We associate this transition with a crossover from the fluctuation to the mean-field behavior. At lower temperatures, the stability of the parallel orientation is restored. We find that the region of stability of the perpendicular orientation rapidly decreases as shear rate increases. This behavior might be misinterpreted as an additional perpendicular to parallel transition recently discussed in literature.
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Affiliation(s)
- A N Morozov
- Faculty of Mathematics and Natural Sciences, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.
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Ashok B, Muthukumar M, Russell TP. Confined thin film diblock copolymer in the presence of an electric field. J Chem Phys 2001. [DOI: 10.1063/1.1380710] [Citation(s) in RCA: 65] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chakraborty AK, Golumbfskie AJ. Polymer adsorption-driven self-assembly of nanostructures. Annu Rev Phys Chem 2001; 52:537-73. [PMID: 11326074 DOI: 10.1146/annurev.physchem.52.1.537] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Driven by prospective applications, there is much interest in developing materials that can perform specific functions in response to external conditions. One way to design such materials is to create systems which, in response to external inputs, can self-assemble to form structures that are functionally useful. This review focuses on the principles that can be employed to design macromolecules that when presented with an appropriate two-dimensional surface, will self-assemble to form nanostructures that may be functionally useful. We discuss three specific examples: (a) biomimetic recognition between polymers and patterned surfaces. (b) control and manipulation of nanomechanical motion generated by biopolymer adsorption and binding, and (c) creation of patterned nanostructuctures by exposing molten diblock copolymers to patterned surfaces. The discussion serves to illustrate how polymer sequence can be manipulated to affect self-assembly characteristics near adsorbing surfaces. The focus of this review is on theoretical and computational work aimed toward elucidating the principles underlying the phenomena pertinent to the three topics noted above. However, synergistic experiments are also described in the appropriate context.
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Affiliation(s)
- A K Chakraborty
- Department of Chemical Engineering University of California, Lawrence Berkeley National Laboratory Berkeley, California 94720, USA.
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Wang Q, Nealey PF, de Pablo JJ. Monte Carlo Simulations of Asymmetric Diblock Copolymer Thin Films Confined between Two Homogeneous Surfaces. Macromolecules 2001. [DOI: 10.1021/ma0018751] [Citation(s) in RCA: 173] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Qiang Wang
- Department of Chemical Engineering, University of WisconsinMadison, Madison, Wisconsin 53706-1691
| | - Paul F. Nealey
- Department of Chemical Engineering, University of WisconsinMadison, Madison, Wisconsin 53706-1691
| | - Juan J. de Pablo
- Department of Chemical Engineering, University of WisconsinMadison, Madison, Wisconsin 53706-1691
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Wang Q, Nath SK, Graham MD, Nealey PF, de Pablo JJ. Symmetric diblock copolymer thin films confined between homogeneous and patterned surfaces: Simulations and theory. J Chem Phys 2000. [DOI: 10.1063/1.481635] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pereira GG, Williams DRM, Chakrabarti A. Interfacial profiles of mismatched lamellae in thin diblock copolymer films. J Chem Phys 2000. [DOI: 10.1063/1.481636] [Citation(s) in RCA: 9] [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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Martins S, Morgado WA, Massunaga MS, Bahiana M. Density mismatch in thin diblock copolymer films. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:4118-4124. [PMID: 11088206 DOI: 10.1103/physreve.61.4118] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/1999] [Revised: 12/06/1999] [Indexed: 05/23/2023]
Abstract
Thin films of diblock copolymer subject to gravitational field are simulated by means of a cell dynamical system model. The difference in density of the two sides of the molecule and the presence of the field causes the formation of lamellar patterns with orientation parallel to the confining walls even when they are neutral. The concentration profile of those films is analyzed in the weak segregation regime and a functional form for the profile is proposed.
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Affiliation(s)
- S Martins
- Instituto de Fisica, UFRJ, Caixa Postal 68528, 21945-970 Rio de Janeiro, RJ, Brazil
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Affiliation(s)
- Wilfred H. Tang
- Department of Chemistry and The James Franck Institute, University of Chicago, Chicago, Illinois 60637
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Huinink HP, Brokken-Zijp JCM, van Dijk MA, Sevink GJA. Asymmetric block copolymers confined in a thin film. J Chem Phys 2000. [DOI: 10.1063/1.480811] [Citation(s) in RCA: 166] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wang Q, Yan Q, Nealey PF, de Pablo JJ. Monte Carlo simulations of diblock copolymer thin films confined between two homogeneous surfaces. J Chem Phys 2000. [DOI: 10.1063/1.480639] [Citation(s) in RCA: 139] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Huang E, Mansky P, Russell TP, Harrison C, Chaikin PM, Register RA, Hawker CJ, Mays J. Mixed Lamellar Films: Evolution, Commensurability Effects, and Preferential Defect Formation. Macromolecules 1999. [DOI: 10.1021/ma9912711] [Citation(s) in RCA: 105] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | | | | | | | | | - R. A. Register
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544
| | - C. J. Hawker
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120-6099
| | - J. Mays
- Department of Chemistry, University of Alabama at Birmingham, Birmingham, Alabama 35294-1240
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Pereira GG, Williams DR. Thin diblock copolymer films on patterned surfaces: computer simulations and the Frenkel-Kontorowa model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5841-7. [PMID: 11970483 DOI: 10.1103/physreve.60.5841] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/1999] [Revised: 07/08/1999] [Indexed: 04/18/2023]
Abstract
We study by direct numerical integration of the dynamical evolution equation the equilibrium configuration of a diblock copolymer thin film melt on a patterned surface. The surface has a large number of stripes and the mismatch between the bulk diblock spacing and the stripe width is small. We investigate primarily the formation of small discommensurations in the incommensurate phase and compare the results with the predictions of an analogous model of solid-state physics, the Frenkel-Kontorowa model.
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Affiliation(s)
- G G Pereira
- Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, Australian Capital Territory 0200, Australia
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Kielhorn L, Muthukumar M. Phase separation of polymer blend films near patterned surfaces. J Chem Phys 1999. [DOI: 10.1063/1.479497] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Phase Transitions of Polymer Blends and Block Copolymer Melts in Thin Films. POLYMERS IN CONFINED ENVIRONMENTS 1999. [DOI: 10.1007/3-540-69711-x_1] [Citation(s) in RCA: 117] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
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Petera D, Muthukumar M. Self-consistent field theory of diblock copolymer melts at patterned surfaces. J Chem Phys 1998. [DOI: 10.1063/1.477124] [Citation(s) in RCA: 86] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chen H, Chakrabarti A. Morphology of thin block copolymer films on chemically patterned substrates. J Chem Phys 1998. [DOI: 10.1063/1.476118] [Citation(s) in RCA: 69] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tang WH, Witten TA. Quenched Degrees of Freedom in Symmetric Diblock Copolymer Thin Films. Macromolecules 1998. [DOI: 10.1021/ma971524v] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wilfred H. Tang
- James Franck Institute, University of Chicago, Chicago, Illinois 60637
| | - Thomas A. Witten
- James Franck Institute, University of Chicago, Chicago, Illinois 60637
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Pickett GT, Balazs AC. Equilibrium Orientation of Confined Diblock Copolymer Films. Macromolecules 1997. [DOI: 10.1021/ma9617173] [Citation(s) in RCA: 149] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Galen T. Pickett
- Department of Chemical and Petroleum Engineering, The University of Pittsburgh, Pittsburgh, Pennsylvania 15261
| | - Anna C. Balazs
- Department of Chemical and Petroleum Engineering, The University of Pittsburgh, Pittsburgh, Pennsylvania 15261
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