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Shastry T, Xie J, Tung CH, Lynn TY, Panda AS, Shi AC, Ho RM. Sequential Self-Assembly of Polystyrene- block-Polydimethylsiloxane for 3D Nanopatterning via Solvent Annealing. ACS APPLIED MATERIALS & INTERFACES 2024; 16:40263-40274. [PMID: 39036947 PMCID: PMC11299135 DOI: 10.1021/acsami.4c08813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2024] [Revised: 07/09/2024] [Accepted: 07/12/2024] [Indexed: 07/23/2024]
Abstract
This study aims to develop a strategy for the fabrication of multilayer nanopatterns through sequential self-assembly of lamella-forming polystyrene-block-polydimethylsiloxane (PS-b-PDMS) block copolymer (BCP) from solvent annealing. By simply tuning the solvent selectivity, a variety of self-assembled BCP thin-film morphologies, including hexagonal perforated lamellae (HPL), parallel cylinders, and spheres, can be obtained from single-composition PS-b-PDMS. By taking advantage of reactive ion etching (RIE), topographic SiO2 monoliths with well-ordered arrays of hexagonally packed holes, parallel lines, and hexagonally packed dots can be formed. Subsequently, hole-on-dot and line-on-hole hierarchical textures can be created through a layer-by-layer process with RIE treatment as evidenced experimentally and confirmed theoretically. The results demonstrated the feasibility of creating three-dimensional (3D) nanopatterning from the sequential self-assembly of single-composition PS-b-PDMS via solvent annealing, providing an appealing process for nano-MEMS manufacturing based on BCP lithography.
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Affiliation(s)
- Thanmayee Shastry
- Department
of Chemical Engineering, National Tsing
Hua University, Hsinchu 30013, Taiwan
| | - Jiayu Xie
- Department
of Physics & Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Cheng-Hsun Tung
- Department
of Chemical Engineering, National Tsing
Hua University, Hsinchu 30013, Taiwan
| | - Teoh Yen Lynn
- Department
of Chemical Engineering, National Tsing
Hua University, Hsinchu 30013, Taiwan
| | - Aum Sagar Panda
- Department
of Chemical Engineering, National Tsing
Hua University, Hsinchu 30013, Taiwan
| | - An-Chang Shi
- Department
of Physics & Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Rong-Ming Ho
- Department
of Chemical Engineering, National Tsing
Hua University, Hsinchu 30013, Taiwan
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2
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Non-Bulk Morphologies of Extremely Thin Block Copolymer Films Cast on Topographically Defined Substrates Featuring Deep Trenches: The Importance of Lateral Confinement. Polymers (Basel) 2023; 15:polym15041035. [PMID: 36850318 PMCID: PMC9958675 DOI: 10.3390/polym15041035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Revised: 02/15/2023] [Accepted: 02/16/2023] [Indexed: 02/22/2023] Open
Abstract
Directed self-assembly of block copolymers is evolving toward applications that are more defect-tolerant but still require high morphological control and could benefit from simple, inexpensive fabrication processes. Previously, we demonstrated that simply casting ultra-thin block copolymer films on topographically defined substrates leads to hierarchical structures with dual patterns in a controlled manner and unraveled the dependence of the local morphology on the topographic feature dimensions. In this article, we discuss the extreme of the ultraconfined thickness regime at the border of film dewetting. Additional non-bulk morphologies are observed at this extreme, which further elaborate the arsenal of dual patterns that could be obtained in coexistence with full placement control. It is shown that as the thickness confinement approaches its limit, lateral confinement imposed by the width of the plateaus becomes a critical factor influencing the local morphology.
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Demazy N, Argudo PG, Fleury G. Competitive Registration Fields for The Development of Complex Block Copolymer Structures by A Layer-by-Layer Approach. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2023; 19:e2205254. [PMID: 36504447 DOI: 10.1002/smll.202205254] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Revised: 11/09/2022] [Indexed: 06/17/2023]
Abstract
Block copolymer (BCP) self-assembly in thin films is an elegant method to generate nanometric features with tunable geometrical configurations. By combining directed assembly and hybridization methods, advances in nano-manufacturing have been attested over the past decades with flagship applications in lithography and optics. Nevertheless, the range of geometrical configurations is limited by the accessible morphologies inherent to the energy minimization process involved in BCP self-assembly. Layering of nanostructured BCP thin films has been recently proposed in order to enrich the span of nanostructures derived from BCP self-assembly with the formation of non-native heterostructures such as double-layered arrays of nanowires or dots-on-line and dots-in-hole hierarchical structures. In this work, the layer-by-layer method is further exploited for the generation of nano-mesh arrays using nanostructured BCP thin films. In particular, a subtle combination of chemical and topographical fields is leveraged in order to demonstrate design rules for the controlled registration of a BCP layer on top of an underneath immobilized one by the precise tuning of the interfacial chemical field between the two BCP layers.
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Affiliation(s)
- Nils Demazy
- Univ. Bordeaux, CNRS, Bordeaux INP, LCPO, UMR 5629, Pessac, F-33600, France
| | - Pablo G Argudo
- Univ. Bordeaux, CNRS, Bordeaux INP, LCPO, UMR 5629, Pessac, F-33600, France
| | - Guillaume Fleury
- Univ. Bordeaux, CNRS, Bordeaux INP, LCPO, UMR 5629, Pessac, F-33600, France
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Doerk GS, Stein A, Bae S, Noack MM, Fukuto M, Yager KG. Autonomous discovery of emergent morphologies in directed self-assembly of block copolymer blends. SCIENCE ADVANCES 2023; 9:eadd3687. [PMID: 36638174 PMCID: PMC9839324 DOI: 10.1126/sciadv.add3687] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 12/12/2022] [Indexed: 06/17/2023]
Abstract
The directed self-assembly (DSA) of block copolymers (BCPs) is a powerful approach to fabricate complex nanostructure arrays, but finding morphologies that emerge with changes in polymer architecture, composition, or assembly constraints remains daunting because of the increased dimensionality of the DSA design space. Here, we demonstrate machine-guided discovery of emergent morphologies from a cylinder/lamellae BCP blend directed by a chemical grating template, conducted without direct human intervention on a synchrotron x-ray scattering beamline. This approach maps the morphology-template phase space in a fraction of the time required by manual characterization and highlights regions deserving more detailed investigation. These studies reveal localized, template-directed partitioning of coexisting lamella- and cylinder-like subdomains at the template period length scale, manifesting as previously unknown morphologies such as aligned alternating subdomains, bilayers, or a "ladder" morphology. This work underscores the pivotal role that autonomous characterization can play in advancing the paradigm of DSA.
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Affiliation(s)
- Gregory S. Doerk
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Aaron Stein
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Suwon Bae
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Marcus M. Noack
- The Center for Advanced Mathematics for Energy Research Applications (CAMERA), Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Masafumi Fukuto
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Kevin G. Yager
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
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Michman E, Oded M, Shenhar R. Dual Block Copolymer Morphologies in Ultrathin Films on Topographic Substrates: The Effect of Film Curvature. Polymers (Basel) 2022; 14:polym14122377. [PMID: 35745955 PMCID: PMC9231016 DOI: 10.3390/polym14122377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2022] [Revised: 06/04/2022] [Accepted: 06/07/2022] [Indexed: 02/01/2023] Open
Abstract
The ability to create mixed morphologies using easily controlled parameters is crucial for the integration of block copolymers in advanced technologies. We have previously shown that casting an ultrathin block copolymer film on a topographically patterned substrate results in different deposited thicknesses on the plateaus and in the trenches, which leads to the co-existence of two patterns. In this work, we highlight the dependence of the dual patterns on the film profile. We suggest that the steepness of the film profile formed across the plateau edge affects the nucleation of microphase-separated domains near the plateau edges, which influences the morphology that develops on the plateau regions. An analysis of the local film thicknesses in multiple samples exhibiting various combinations of plateau and trench widths for different trench depths enabled the construction of phase diagrams, which unraveled the intricate dependence of the formed patterns not only on the curvature of the film profile but also on the fraction of the film that resides in the trenches. Our analysis facilitates the prediction of the patterns that would develop in the trenches and on the plateaus for a given block copolymer film of known thickness from the dimensions of the topographic features.
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6
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Tang H, Du F, Carr S, DeVault C, Mello O, Mazur E. Modeling the optical properties of twisted bilayer photonic crystals. LIGHT, SCIENCE & APPLICATIONS 2021; 10:157. [PMID: 34326315 PMCID: PMC8322106 DOI: 10.1038/s41377-021-00601-x] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 06/29/2021] [Accepted: 07/13/2021] [Indexed: 05/29/2023]
Abstract
We demonstrate a photonic analog of twisted bilayer graphene that has ultra-flat photonic bands and exhibits extreme slow-light behavior. Our twisted bilayer photonic device, which has an operating wavelength in the C-band of the telecom window, uses two crystalline silicon photonic crystal slabs separated by a methyl methacrylate tunneling layer. We numerically determine the magic angle using a finite-element method and the corresponding photonic band structure, which exhibits a flat band over the entire Brillouin zone. This flat band causes the group velocity to approach zero and introduces light localization, which enhances the electromagnetic field at the expense of bandwidth. Using our original plane-wave continuum model, we find that the photonic system has a larger band asymmetry. The band structure can easily be engineered by adjusting the device geometry, giving significant freedom in the design of devices. Our work provides a fundamental understanding of the photonic properties of twisted bilayer photonic crystals and opens the door to the nanoscale-based enhancement of nonlinear effects.
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Affiliation(s)
- Haoning Tang
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Fan Du
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Stephen Carr
- Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, RI, 02912, USA
| | - Clayton DeVault
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Olivia Mello
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Eric Mazur
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
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Jin C, Olsen BC, Luber EJ, Buriak JM. van der Waals Epitaxy of Soft Twisted Bilayers: Lattice Relaxation and Mass Density Waves. ACS NANO 2020; 14:13441-13450. [PMID: 32931263 DOI: 10.1021/acsnano.0c05310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Interfaces comprising incommensurate or twisted hexagonal lattices are ubiquitous and of great interest, from adsorbed organic/inorganic interfaces in electronic devices, to superlubricants, and more recently to van der Waals bilayer heterostructures (vdWHs) of graphene and other 2D materials that demonstrate a range of properties such as superconductivity and ferromagnetism. Here we show how growth of 2D crystalline domains of soft block copolymers (BCPs) on patterned hard hexagonal lattices provide fundamental insights into van der Waals heteroepitaxy. At moderate registration forces, it is experimentally found that these BCP-hard lattice vdWHs do not adopt a simple moiré superstructure, but instead adopt local structural relaxations known as mass density waves (MDWs). Simulations reveal that MDWs are a primary mechanism of energy minimization and are the origin of the observed preferential twist angle between the lattices.
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Affiliation(s)
- Cong Jin
- Department of Chemistry, University of Alberta, 11227 Saskatchewan Drive, Edmonton, AB T6G 2G2, Canada
| | - Brian C Olsen
- Department of Chemistry, University of Alberta, 11227 Saskatchewan Drive, Edmonton, AB T6G 2G2, Canada
| | - Erik J Luber
- Department of Chemistry, University of Alberta, 11227 Saskatchewan Drive, Edmonton, AB T6G 2G2, Canada
| | - Jillian M Buriak
- Department of Chemistry, University of Alberta, 11227 Saskatchewan Drive, Edmonton, AB T6G 2G2, Canada
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Self-template-assisted micro-phase segregation in blended liquid-crystalline block copolymers films toward three-dimensional structures. Proc Natl Acad Sci U S A 2020; 117:21070-21078. [PMID: 32820076 DOI: 10.1073/pnas.2010284117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In-plane mesopatterns derived from block-copolymer (BCP) micro-phase segregation in thin films have attracted much interest in practical applications as well as fundamental research programs. However, phase segregation along the film-normal direction has been less studied. Here, we describe a strategy to concurrently, yet independently, control in-plane micro-phase and out-of-plane macro-phase segregation in multiblended films composed of liquid-crystalline BCPs (LCBCPs), affording spontaneously layered three-dimensional (3D) mesostructures. This strategy relies on sequential liquid crystallization during the cooling process in thermal annealing as follows. The constituent LCBCP with the highest isotropic-transition temperature (T iso) first liquid-crystallizes and segregates from the other LCBCP mixture remaining in isotropic states to form a noncontaminated layer at the top surface. This preformed LCBCP layer preserves its inherent in-plane pattern and acts as a template guiding the subsequent micro-phase segregations of the other low-T iso LCBCPs underneath. This self-template-assisted micro-phase segregation (STAMPS) readily provides 3D mesostructures, the potential toward rational material design of which is also demonstrated in water-separation applications.
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Sohn H, Shin WH, Seok D, Lee T, Park C, Oh JM, Kim SY, Seubsai A. Novel Hybrid Conductor of Irregularly Patterned Graphene Mesh and Silver Nanowire Networks. MICROMACHINES 2020; 11:mi11060578. [PMID: 32526961 PMCID: PMC7345882 DOI: 10.3390/mi11060578] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Revised: 06/03/2020] [Accepted: 06/04/2020] [Indexed: 12/31/2022]
Abstract
We prepared the hybrid conductor of the Ag nanowire (NW) network and irregularly patterned graphene (GP) mesh with enhanced optical transmittance (~98.5%) and mechano-electric stability (ΔR/Ro: ~42.4% at 200,000 (200k) cycles) under 6.7% strain. Irregularly patterned GP meshes were prepared with a bottom-side etching method using chemical etchant (HNO3). The GP mesh pattern was judiciously and easily tuned by the regulation of treatment time (0–180 min) and concentration (0–20 M) of chemical etchants. As-formed hybrid conductor of Ag NW and GP mesh exhibit enhanced/controllable electrical-optical properties and mechano-electric stabilities; hybrid conductor exhibits enhanced optical transmittance (TT = 98.5%) and improved conductivity (ΔRs: 22%) compared with that of a conventional hybrid conductor at similar TT. It is also noteworthy that our hybrid conductor shows far superior mechano-electric stability (ΔR/Ro: ~42.4% at 200k cycles; TT: ~98.5%) to that of controls (Ag NW (ΔR/Ro: ~293% at 200k cycles), Ag NW-pristine GP hybrid (ΔR/Ro: ~121% at 200k cycles)) ascribed to our unique hybrid structure.
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Affiliation(s)
- Hiesang Sohn
- Department of Chemical Engineering, Kwangwoon University, Seoul 01897, Korea; (D.S.); (T.L.); (C.P.)
- Correspondence:
| | - Weon Ho Shin
- Department of Electronic Material Engineering, Kwangwoon University, Seoul 01897, Korea; (W.H.S.); (J.-M.O.)
| | - Dohyeong Seok
- Department of Chemical Engineering, Kwangwoon University, Seoul 01897, Korea; (D.S.); (T.L.); (C.P.)
| | - Taek Lee
- Department of Chemical Engineering, Kwangwoon University, Seoul 01897, Korea; (D.S.); (T.L.); (C.P.)
| | - Chulhwan Park
- Department of Chemical Engineering, Kwangwoon University, Seoul 01897, Korea; (D.S.); (T.L.); (C.P.)
| | - Jong-Min Oh
- Department of Electronic Material Engineering, Kwangwoon University, Seoul 01897, Korea; (W.H.S.); (J.-M.O.)
| | - Se Yun Kim
- Material Research Center, Samsung Advanced Institute of Technology (SAIT), Samsung Electronics, Suwon 16678, Korea;
| | - Anusorn Seubsai
- Department of Chemical Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand;
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11
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Liu Y, Deng K, Yang J, Wu X, Fan X, Tang M, Quan Z. Shape-directed self-assembly of nanodumbbells into superstructure polymorphs. Chem Sci 2020; 11:4065-4073. [PMID: 34122872 PMCID: PMC8152806 DOI: 10.1039/d0sc00592d] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 03/27/2020] [Indexed: 12/18/2022] Open
Abstract
Self-assembly of colloidal nanoparticles into ordered superstructures provides a promising route to create novel/enhanced functional materials. Much progress has been made in self-assembly of anisotropic nanoparticles, but the complexity and tunability of superstructures remain restricted by their available geometries. Here we report the controlled packing of nanodumbbells (NDs) with two spherical lobes connected by one rod-like middle bar into varied superstructure polymorphs. When assembled into two-dimensional (2D) monolayer assemblies, such NDs with specific shape parameters could form orientationally ordered degenerate crystals with a 6-fold symmetry, in which these NDs possess no translational order but three allowed orientations with a rotational symmetry of 120 degrees. Detailed analyses identify the distinct roles of subunits in the ND assembly: the spherical lobes direct NDs to closely assemble together into a hexagonal pattern, and the rod-like connection between the lobes endows NDs with this specific orientational order. Such intralayer assembly features are well maintained in the two-layer superstructures of NDs; however, the interlayer stackings could be adjusted to produce stable bilayer superstructures and a series of metastable moiré patterns. Moreover, in addition to horizontal alignment, these NDs could gradually stand up to form tilted or even vertical packing based on the delicate control over the liquid-liquid interface and ND dimensions. This study provides novel insights into creating superstructures by controlling geometric features of nanoscale building blocks and may spur their novel applications.
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Affiliation(s)
- Yulian Liu
- Department of Chemistry, Shenzhen Engineering Research Center for Frontier Materials Synthesis at High Pressures, Southern University of Science and Technology (SUSTech) Shenzhen Guangdong 518055 China
- School of Chemistry and Chemical Engineering, Southwest University Chongqing 400715 China
| | - Kerong Deng
- Department of Chemistry, Shenzhen Engineering Research Center for Frontier Materials Synthesis at High Pressures, Southern University of Science and Technology (SUSTech) Shenzhen Guangdong 518055 China
| | - Jun Yang
- School of Chemistry and Chemical Engineering, Southwest University Chongqing 400715 China
| | - Xiaotong Wu
- Department of Chemistry, Shenzhen Engineering Research Center for Frontier Materials Synthesis at High Pressures, Southern University of Science and Technology (SUSTech) Shenzhen Guangdong 518055 China
| | - Xiaokun Fan
- Department of Chemistry, Shenzhen Engineering Research Center for Frontier Materials Synthesis at High Pressures, Southern University of Science and Technology (SUSTech) Shenzhen Guangdong 518055 China
| | - Min Tang
- Department of Chemistry, Shenzhen Engineering Research Center for Frontier Materials Synthesis at High Pressures, Southern University of Science and Technology (SUSTech) Shenzhen Guangdong 518055 China
| | - Zewei Quan
- Department of Chemistry, Shenzhen Engineering Research Center for Frontier Materials Synthesis at High Pressures, Southern University of Science and Technology (SUSTech) Shenzhen Guangdong 518055 China
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Bunje H, Glotzer S, Li Y, Samori P, Weil T, Shmakov SN, Weiss PS. Announcing the 2020 ACS Nano Award Lecture Laureates. ACS NANO 2020; 14:1213-1215. [PMID: 32098015 DOI: 10.1021/acsnano.0c01221] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
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13
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Michman E, Langenberg M, Stenger R, Oded M, Schvartzman M, Müller M, Shenhar R. Controlled Spacing between Nanopatterned Regions in Block Copolymer Films Obtained by Utilizing Substrate Topography for Local Film Thickness Differentiation. ACS APPLIED MATERIALS & INTERFACES 2019; 11:35247-35254. [PMID: 31482698 DOI: 10.1021/acsami.9b12817] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Various types of devices require hierarchically nanopatterned substrates, where the spacing between patterned domains is controlled. Ultraconfined films exhibit extreme morphological sensitivity to slight variations in film thickness when the substrate is highly selective toward one of the blocks. Here, it is shown that using the substrate's topography as a thickness differentiating tool enables the creation of domains with different surface patterns in a fully controlled fashion from a single, unblended block copolymer. This approach is applicable to block copolymers of different compositions and to different topographical patterns and thus opens numerous possibilities for the hierarchical construction of multifunctional devices.
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Affiliation(s)
- Elisheva Michman
- The Institute of Chemistry and the Center for Nanoscience and Nanotechnology , The Hebrew University of Jerusalem , Jerusalem 9190401 , Israel
| | - Marcel Langenberg
- Institute for Theoretical Physics , Georg-August-University Göttingen , Friedrich-Hund-Platz 1 , 37077 Göttingen , Germany
| | - Roland Stenger
- Institute for Theoretical Physics , Georg-August-University Göttingen , Friedrich-Hund-Platz 1 , 37077 Göttingen , Germany
| | - Meirav Oded
- The Institute of Chemistry and the Center for Nanoscience and Nanotechnology , The Hebrew University of Jerusalem , Jerusalem 9190401 , Israel
| | - Mark Schvartzman
- Department of Materials Engineering and Ilse Katz Institute for Nanoscale Science and Technology , Ben Gurion University of the Negev , Beer Sheva 8410501 , Israel
| | - Marcus Müller
- Institute for Theoretical Physics , Georg-August-University Göttingen , Friedrich-Hund-Platz 1 , 37077 Göttingen , Germany
| | - Roy Shenhar
- The Institute of Chemistry and the Center for Nanoscience and Nanotechnology , The Hebrew University of Jerusalem , Jerusalem 9190401 , Israel
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