1
|
Avalos E, Teramoto T, Hirai Y, Yabu H, Nishiura Y. Controlling the Formation of Polyhedral Block Copolymer Nanoparticles: Insights from Process Variables and Dynamic Modeling. ACS OMEGA 2024; 9:17276-17288. [PMID: 38645350 PMCID: PMC11025090 DOI: 10.1021/acsomega.3c10302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/23/2023] [Revised: 02/20/2024] [Accepted: 02/26/2024] [Indexed: 04/23/2024]
Abstract
This study delves into the formation of nanoscale polyhedral block copolymer particles (PBCPs) exhibiting cubic, octahedral, and variant geometries. These structures represent a pioneering class that has never been fabricated previously. PBCP features distinct variations in curvature on the outer surface, aligning with the edges and corners of polyhedral shapes. This characteristic sharply contrasts with previous block copolymers (BCPs), which displayed a smooth spherical surface. The emergence of these cornered morphologies presents an intriguing and counterintuitive phenomenon and is linked to process parameters, such as evaporation rates and initial concentration, while keeping other variables constant. Using a system of coupled Cahn-Hillard (CCH) equations, we uncover the mechanisms driving polyhedral particle formation, emphasizing the importance of controlling relaxation parameters for shape variable u and microphase separation v. This unconventional approach, differing from traditional steepest descent method, allows for precise control and diverse polyhedral particle generation. Accelerating the shape variable u proves crucial for expediting precipitation and aligns with experimental observations. Employing the above theoretical model, we achieve shape predictions for particles and the microphase separation within them, which overcomes the limitations of ab initio computations. Additionally, a numerical stability analysis discerns the transient nature versus local minimizer characteristics. Overall, our findings contribute to understanding the complex interplay between process variables and the morphology of polyhedral BCP nanoparticles.
Collapse
Affiliation(s)
- Edgar Avalos
- Advanced
Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan
| | - Takashi Teramoto
- Faculty
of Data Science, Kyoto Women’s University, 35 Kitahiyoshi-cho, Imakumano, Higashiyama-ku, Kyoto 605-8501, Japan
| | - Yutaro Hirai
- Advanced
Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan
| | - Hiroshi Yabu
- Advanced
Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan
| | - Yasumasa Nishiura
- Advanced
Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan
- Research
Center of Mathematics for Social Creativity, Research Institute for
Electronic Science, Hokkaido University, N12W7, Kita-Ward, Mid-Campus Open
Laboratory Building No. 2, Sapporo 060-0812, Japan
| |
Collapse
|
2
|
Singh J, Gupta S, Chokshi P. Confinement-induced self-assembly of a diblock copolymer within a non-uniform cylindrical nanopore. SOFT MATTER 2024; 20:1543-1553. [PMID: 38268494 DOI: 10.1039/d3sm01348k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2024]
Abstract
The self-assembly of a diblock copolymer melt confined within a non-uniform cylindrical nanopore is studied using the self-consistent field theory. The non-uniformity manifests in the form of a converging-diverging cylindrical nanopore. The axial variation in pore diameter presents a range of curvatures within the same confinement pore as opposed to a single curvature in a uniform-diameter cylindrical pore. The introduction of multiple curvatures leads to the formation of novel microstructures not accessible in uniform cylindrical confinement. The well-known equilibrium structures like a single helix, double helices, and concentric lamella under cylindrical confinement transition into new morphologies such as hyperboloidal phases, microstructures containing rings with a bead, rings with spheres, and a squeezed helical phase as the pore diameter varies axially. The converging-diverging geometry of the confining pore renders the helical phases seen in the cylindrical pore less favorable. A phase diagram in the parametric space of the block fraction and the ratio of the smallest and largest pore radii has been constructed to depict the order-order transition of various microstructures. The ratio of radii, a measure of the non-uniformity of the pore, along with the pore length brings out some interesting morphologies. The mechanism of these structural transitions is understood as the interplay between the variation in pore curvature attributed to the non-uniformity, the spontaneous curvature of the block copolymer interface, and the enthalpic interaction between the segregated blocks.
Collapse
Affiliation(s)
- Jagat Singh
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India.
| | - Supriya Gupta
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India.
| | - Paresh Chokshi
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India.
| |
Collapse
|
3
|
Li N, Li J, Qing L, Ma S, Li Y, Li B. Self-assembly of colloids with competing interactions confined in spheres. SOFT MATTER 2024; 20:304-314. [PMID: 38050746 DOI: 10.1039/d3sm01227a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/06/2023]
Abstract
At low temperatures, colloidal particles with short-range attractive and long-range repulsive interactions can form various periodic microphases in bulk. In this paper, we investigate the self-assembly behaviour of colloids with competing interactions under spherical confinement by conducting molecular dynamics simulations. We find that the cluster, mixture, cylindrical, perforated lamellar and lamellar structures can be obtained, but the details of the ordered structures are different from those in bulk systems. Interestingly, the system tends to form more perforated structures when confined in smaller spheres. The mechanism behind this phenomenon is driven by the relationship between the energy of the ordered structures and the bending of the confinement wall, which is different from the mechanism in copolymer systems.
Collapse
Affiliation(s)
- Ningyi Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Junhong Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Lijingting Qing
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Shicheng Ma
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Yao Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| | - Baohui Li
- School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China.
| |
Collapse
|
4
|
Wu J, Chen ST, Li SB, Liu LM, Wang XH, Lang WC. Simulation of Surface-Induced Morphology Transition and Phase Diagram of Linear Triblock Copolymers under Spherical Confinement. CHINESE JOURNAL OF POLYMER SCIENCE 2022. [DOI: 10.1007/s10118-022-2812-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
5
|
Chen K, Wang F, Liu M, Wang X. Tunable helical structures formed by blending
ABC
triblock copolymers and C homopolymers in nanopores. POLYM INT 2021. [DOI: 10.1002/pi.6253] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Ka Chen
- Department of Chemistry, Key Laboratory of Surface and Interface Science of Polymer Materials of Zhejiang Province Zhejiang Sci‐Tech University Hangzhou China
| | - Feng Wang
- Department of Chemistry, Key Laboratory of Surface and Interface Science of Polymer Materials of Zhejiang Province Zhejiang Sci‐Tech University Hangzhou China
| | - Meijiao Liu
- Department of Chemistry, Key Laboratory of Surface and Interface Science of Polymer Materials of Zhejiang Province Zhejiang Sci‐Tech University Hangzhou China
- State Key Laboratory of Molecular Engineering of Polymers Fudan University Shanghai China
| | - Xinping Wang
- Department of Chemistry, Key Laboratory of Surface and Interface Science of Polymer Materials of Zhejiang Province Zhejiang Sci‐Tech University Hangzhou China
| |
Collapse
|
6
|
Gupta S, Chokshi P. Self-Assembly of Polymer Grafted Nanoparticles within Spherically Confined Diblock Copolymers. J Phys Chem B 2020; 124:11738-11749. [PMID: 33319558 DOI: 10.1021/acs.jpcb.0c08279] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Geometric confinement plays an important role in the generation of interesting microstructures on account of structural frustration and confinement-induced entropy loss. In the present study, self-consistent field calculations have been performed to examine the self-assembly behavior of a mixture of diblock copolymers and polymer grafted nanoparticles within a spherical confinement. The analysis is aimed at obtaining the equilibrium distribution of nanoparticles with a high degree of order. The ordered mesophases of diblock copolymers provide useful templates to achieve ordering of nanoparticles in a selective domain. Self-assembly of nanoparticles within frustrated diblock copolymers is found to be very different from the bulk. A rich variety of equilibrium morphologies are observed depending on the degree of confinement and the extent of particle loading. In addition, the role of particle size and selectivity along with the length and the number of polymer chains grafted onto the surface of nanoparticles are analyzed to understand the self-assembly behavior. The specific interest is to obtain the chiral structures out of achiral block copolymers subjected to spherical confinement. The realization of various captivating microstructures, such as chiral ordering of nanoparticles, is highly essential to produce advanced nanomaterials with superior physical properties.
Collapse
Affiliation(s)
- Supriya Gupta
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India
| | - Paresh Chokshi
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India
| |
Collapse
|
7
|
Schneider L, Lichtenberg G, Vega D, Müller M. Symmetric Diblock Copolymers in Cylindrical Confinement: A Way to Chiral Morphologies? ACS APPLIED MATERIALS & INTERFACES 2020; 12:50077-50095. [PMID: 33079515 DOI: 10.1021/acsami.0c16987] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We investigate the confinement-induced formation and stability of helix morphologies in lamella-forming AB diblock copolymers via large-scale, particle-based, single-chain-in-mean-field simulations. Such helix structures are rarely observed in bulk or thin films. Structure formation is induced by quenching incompatibility, χN, from a disordered morphology. If the surfaces of the cylindrical confinement do not prefer one component over the other, we observe that stacked lamellae, with their normals along the cylinder axis, are the preferred morphology. Kinetically, this morphology initially forms close to the cylinder surface, whereas the spontaneous, spinodal microphase separation in the cylinder's interior gives rise to a microemulsion-like morphology, riddled with defects and no directional order. Subsequently, the ordered morphology on the cylinder surface progresses inward, pervading the entire volume. In case that the cylindrical pore is only partially filled, the additional confinement along the cylinder axis generally gives rise to incommensurability between the equilibrium spacing of stacked lamellae and the cylinder height. To accommodate this mismatch, the lamella normals will tilt away from the cylinder axis and generate helices of lamellae on the surface of the cylinder. Again, this order progresses from the cylinder surface inward, generating a chiral morphology. Because the spacing between the internal AB interfaces decreases upon approaching the helix center, the concomitant stress results in a decrease in the number of lamellae and the formation of unique dislocation defects. This type of chiral defect morphology is reproducibly formed by the kinetics of structure formation in partly filled cylindrical pores with nonpreferential surfaces and may find applications in photonic applications.
Collapse
Affiliation(s)
- Ludwig Schneider
- Institute for Theoretical Physics, Georg-August University Göttingen, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
| | - Georg Lichtenberg
- Institute for Theoretical Physics, Georg-August University Göttingen, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
| | - Daniel Vega
- Instituto de Fı́sica del Sur (IFISUR), Consejo Nacional de Investigaciones Cientı́ficas y Técnicas (CONICET), Universidad Nacional de Sur, 8000 Bahı́a Blanca, Argentina
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University Göttingen, Friedrich-Hund Platz 1, 37077 Göttingen, Germany
| |
Collapse
|
8
|
Gupta S, Chokshi P. Diblock copolymer templated self-assembly of grafted nanoparticles under circular pore confinement. SOFT MATTER 2020; 16:3522-3535. [PMID: 32215433 DOI: 10.1039/d0sm00124d] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Geometrical confinement plays an important role in generating novel molecular organization arising out of structural frustration and confinement-induced entropy loss. In the present study, we perform self-consistent mean-field theoretical calculations to examine a mixture of a diblock copolymer and polymer grafted nanoparticles confined in a cylindrical nanopore. The two-dimensional analysis is aimed at constructing the equilibrium nanostructures decorated with particles in an ordered manner. The rich variety of ordered mesophases of the diblock copolymer under confinement provide a template to achieve the self-assembly of nanoparticles in a selective domain. The localization behavior of nanoparticles under confinement is found to be qualitatively different from that in a bulk system. In particular, for the concentric lamellar phase the particles tend to localize predominantly in the region of greater curvature within the curved lamella. The incorporation of grafted nanoparticles also results in a transition in ordered phases. Various equilibrium morphologies are observed depending upon the degree of confinement, particle loading, density of grafted segments and selectivity of the particle core to the polymeric species. The ordering of particles and the ensuing equilibrium nanostructures are analyzed. The comprehensive understanding of the self-assembly behavior of particles enables one to design novel nanomaterials with desirable material properties.
Collapse
Affiliation(s)
- Supriya Gupta
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India.
| | - Paresh Chokshi
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110 016, India.
| |
Collapse
|
9
|
Liu M, Chen K, Li W, Wang X. Tunable helical structures formed by ABC triblock copolymers under cylindrical confinement. Phys Chem Chem Phys 2019; 21:26333-26341. [PMID: 31782439 DOI: 10.1039/c9cp04978a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Block copolymers confined in nanopores provide unique achiral systems for the formation of helical structures. With AB diblock copolymers, stable single and double helical structures are observed. Aiming to obtain more different helical structures, we replace the AB diblock copolymer with linear ABC triblock copolymers. We speculate that a core-shell superstructure is formed within the nanopore, which is composed of a C-core cylinder wrapped by B-helices within the A-shell. Accordingly, the pore surface is set to be most attractive to the majority A-block and a typical set of interaction parameters is chosen as χACN ≪ χABN = χBCN = 80 to generate the frustrated interfaces. Furthermore, the volume fraction of B-block is fixed as fB = 0.1 to form helical cylinders. A number of helical structures with strands ranging from 1 to 5 are predicted by self-consistent field theory, and in general, the number of strands decreases as the volume fraction of C-block fC increases in a given nanopore. More surprisingly, the variation of helical strand in the confined system has an opposite trend to that in the bulk, which mainly results from the constraint of the cylindrical confinement on the change of the curvature between the outer A-layer and the inner B/C-superdomain. Our work demonstrates a facile way to fabricate different helical superstructures.
Collapse
Affiliation(s)
- Meijiao Liu
- Department of Chemistry, Zhejiang Sci-Tech University, Hangzhou 310018, China.
| | | | | | | |
Collapse
|
10
|
Yang T, Xue H, Cao R, Li W. Formation of homochiral helical nanostructures in diblock copolymers under the confinement of nanopores. Phys Chem Chem Phys 2019; 21:7067-7074. [DOI: 10.1039/c9cp00227h] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The control of the homochirality of helical structures formed in achiral systems is of great interest as it is helpful for understanding the origin of homochirality in life.
Collapse
Affiliation(s)
- Tao Yang
- Ningxia Key Laboratory of Information Sensing & Intelligent Desert
- School of Physics and Electronic-Electrical Engineering
- Ningxia University
- Yinchuan 750021
- China
| | - Haiyan Xue
- Ningxia Key Laboratory of Information Sensing & Intelligent Desert
- School of Physics and Electronic-Electrical Engineering
- Ningxia University
- Yinchuan 750021
- China
| | - Ruifang Cao
- Xinhua College of Ningxia University
- Yinchuan 750021
- China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers
- Department of Macromolecular Science
- Fudan University
- Shanghai 200433
- China
| |
Collapse
|
11
|
Wu J, Huang Z, Lang W, Wang X, Li S. Surface-Induced Nanostructures and Phase Diagrams of ABC Linear Triblock Copolymers under Spherical Confinement: A Self-Consistent Field Theory Simulation. Polymers (Basel) 2018; 10:E1276. [PMID: 30961201 PMCID: PMC6401785 DOI: 10.3390/polym10111276] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Revised: 11/08/2018] [Accepted: 11/14/2018] [Indexed: 11/23/2022] Open
Abstract
We investigate the nanostructures and phase diagrams of ABC linear triblock copolymers confined in spherical cavities by using real-space self-consistent field theory. Various 3D morphologies, such as spherical concentric lamellae, dumbbell-like cylinder, and rotational structures, are identified in the phase diagrams, which are constructed on the basis of the diameters of spherical cavities and the interaction between the polymers and preferential surfaces. We designate specific monomer-monomer interactions and block compositions, with which the polymers spontaneously form a cylindrical morphology in bulk, and firstly study morphology transformation with a neutral surface when a confining radius progressively increases. We then focus on phase morphologies under the preferential surfaces and consolidate them into phase diagrams. The spherical radius and the degree of preferential interactions can obviously induce the formation of a cylindrical morphology. Theoretical results correspond to an amount of recent experimental observations to a high degree and contribute to synthesising functional materials.
Collapse
Affiliation(s)
- Ji Wu
- Department of Physics, Wenzhou Vocational & Technical College, Wenzhou 325035, Zhejiang, China.
| | - Zhihong Huang
- Department of Physics, Wenzhou Vocational & Technical College, Wenzhou 325035, Zhejiang, China.
| | - Wenchang Lang
- Department of Physics, Wenzhou Vocational & Technical College, Wenzhou 325035, Zhejiang, China.
| | - Xianghong Wang
- Department of Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China.
| | - Shiben Li
- Department of Physics, Wenzhou University, Wenzhou 325035, Zhejiang, China.
| |
Collapse
|
12
|
Bezik CT, Garner GP, de Pablo JJ. Mechanisms of Directed Self-Assembly in Cylindrical Hole Confinements. Macromolecules 2018. [DOI: 10.1021/acs.macromol.7b02639] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Cody T. Bezik
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Grant P. Garner
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Juan J. de Pablo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Argonne National
Laboratory, 9700 S Cass Ave., Argonne, Illinois 60439, United States
| |
Collapse
|
13
|
Yau MY, Gunkel I, Hartmann-Azanza B, Akram W, Wang Y, Thurn-Albrecht T, Steinhart M. Semicrystalline Block Copolymers in Rigid Confining Nanopores. Macromolecules 2017; 50:8637-8646. [PMID: 30174341 PMCID: PMC6114844 DOI: 10.1021/acs.macromol.7b01567] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Revised: 09/18/2017] [Indexed: 02/04/2023]
Abstract
We have investigated PLLA crystallization in lamellae-forming PS-b-PLLA confined to straight cylindrical nanopores under weak confinement (nanopore diameter D/equilibrium PS-b-PLLA period L0 ≥ 4.8). Molten PS-b-PLLA predominantly forms concentric lamellae along the nanopores, but intertwined helices occur even for D/L0 ≈ 7.3. Quenching PS-b-PLLA melts below TG(PS) results in PLLA cold crystallization strictly confined by the vitrified PS domains. Above TG(PS), PLLA crystallization is templated by the PS-b-PLLA melt domain structure in the nanopore centers, while adsorption on the nanopore walls stabilizes the outermost cylindrical PS-b-PLLA shell. In between, the nanoscopic PS-b-PLLA melt domain structure apparently ripens to reduce frustrations transmitted from the outermost immobilized PS-b-PLLA layer. The onset of PLLA crystallization catalyzes the ripening while transient ripening states are arrested by advancing PLLA crystallization. Certain helical structure motifs persist PLLA crystallization even if PS is soft. The direction of fastest PLLA crystal growth is preferentially aligned with the nanopore axes to the same degree as for PLLA homopolymer, independent of whether PS is vitreous or soft.
Collapse
Affiliation(s)
- Man Yan
Eric Yau
- Institut
für Chemie neuer Materialien, Universität
Osnabrück, Barbarastr.7, 49076 Osnabrück, Germany
| | - Ilja Gunkel
- Institut
für Physik, Martin-Luther-Universität
Halle-Wittenberg, D-06099 Halle, Germany
| | - Brigitte Hartmann-Azanza
- Institut
für Chemie neuer Materialien, Universität
Osnabrück, Barbarastr.7, 49076 Osnabrück, Germany
| | - Wajiha Akram
- Institut
für Chemie neuer Materialien, Universität
Osnabrück, Barbarastr.7, 49076 Osnabrück, Germany
| | - Yong Wang
- State
Key Lab of Materials-Oriented Chemical Engineering; College of Chemical
Engineering, Nanjing Tech University, Xin Mofan Road 5, Nanjing 210009, Jiangsu, China
| | - Thomas Thurn-Albrecht
- Institut
für Physik, Martin-Luther-Universität
Halle-Wittenberg, D-06099 Halle, Germany
| | - Martin Steinhart
- Institut
für Chemie neuer Materialien, Universität
Osnabrück, Barbarastr.7, 49076 Osnabrück, Germany
| |
Collapse
|
14
|
Liu M, Li W, Wang X. Order-order transitions of diblock copolymer melts under cylindrical confinement. J Chem Phys 2017; 147:114903. [PMID: 28938804 DOI: 10.1063/1.5004181] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
The self-assembly behavior of AB diblock copolymers under cylindrical confinement is investigated using the self-consistent field theory. We focus on the impact of the confinement on the order-order transitions of three-dimensional morphologies by constructing two types of phase diagrams with continuously varying block compositions. One type is with respect to the block composition and the immiscibility parameter for various pore sizes, in which the order-order transitions are shown to be strongly impacted by the pore curvature and thus largely different from the bulk ones. Note that the morphologies are categorized by the intrinsical geometry of their domains, i.e., that helical morphologies are regarded as one type of cylindrical phase. Another type of phase diagram is with respect to the block composition and the pore diameter, which exhibits a number of interesting order-order transitions, especially the transition sequence from a straight line of spheres, to one straight cylinder and stacked disks as the pore diameter increases. A critical point is observed at which the stability region of the straight cylinder vanishes and thereby the spheres transform into the stacked disks continuously. The mechanism of these phase transitions is rationalized in the context of the bulk factors as well as an additional factor, i.e., the competition between the spontaneous curvature of the copolymer and the imposed curvature by the nanopore.
Collapse
Affiliation(s)
- Meijiao Liu
- Department of Chemistry, Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry, Zhejiang Sci-Tech University, Hangzhou 310018, China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers, Key Laboratory of Computational Physical Sciences, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Xinping Wang
- Department of Chemistry, Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry, Zhejiang Sci-Tech University, Hangzhou 310018, China
| |
Collapse
|
15
|
Wang Y, Han Y, Cui J, Jiang W, Sun Y. Monte Carlo Study of Degenerate Behavior of AB Diblock Copolymer/Nanoparticle under Cylindrical Confinement. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:8484-8493. [PMID: 27459708 DOI: 10.1021/acs.langmuir.6b01090] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Degenerate behavior (i.e., forming different self-assembled structures for a given block copolymer (BCP) under the same confinement) commonly exists in various confined systems. Understanding degenerate behavior is crucial for precise control over the structures formed by self-assembly systems under confinement. In this study, the degenerate behavior of a self-assembled AB diblock copolymer/nanoparticle (NP) mixture in a cylindrical pore is studied using Monte Carlo simulation. We find that the degenerate behavior of such a mixture depends on the introduction of the NP. Under different pore sizes, four typical degenerate structures [i.e., single helices (S-helices), double helices (D-helices), parallel cylinders, and stacked toroids] can be obtained if the NP content is zero. However, when the NP content in the mixture is increased, it is found that the number of degenerate structures decreases, that is, only blocky structures can be obtained in the case of high NP content. Moreover, the probability of forming S-helices decreases, whereas the probability of forming D-helices increases with increase in the NP content. Analysis of the interactive enthalpy densities and the chain conformation of the systems indicates that entropy plays an important role in the degenerate structure formation. This study provides some new insights into the degenerate behavior of a BCP/NP mixture under confinement, which can offer a theoretical reference for further experiments.
Collapse
Affiliation(s)
- Yingying Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences , Changchun 130022, Jilin, China
- School of Physics, Northeast Normal University , Changchun 130024, Jilin, China
- University of Chinese Academy of Sciences , Beijing 100049, People's Republic of China
| | - Yuanyuan Han
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences , Changchun 130022, Jilin, China
| | - Jie Cui
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences , Changchun 130022, Jilin, China
| | - Wei Jiang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences , Changchun 130022, Jilin, China
| | - Yingchun Sun
- School of Physics, Northeast Normal University , Changchun 130024, Jilin, China
| |
Collapse
|
16
|
Self-assembly of tiling-forming ABC star triblock copolymers in cylindrical nanotubes: A study of self-consistent field theory. J Taiwan Inst Chem Eng 2016. [DOI: 10.1016/j.jtice.2016.05.051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
17
|
Avalos E, Higuchi T, Teramoto T, Yabu H, Nishiura Y. Frustrated phases under three-dimensional confinement simulated by a set of coupled Cahn-Hilliard equations. SOFT MATTER 2016; 12:5905-5914. [PMID: 27337660 DOI: 10.1039/c6sm00429f] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We numerically study a set of coupled Cahn-Hilliard equations as a means to find morphologies of diblock copolymers in three-dimensional spherical confinement. This approach allows us to find a variety of energy minimizers including rings, tennis balls, Janus balls and multipods among several others. Phase diagrams of confined morphologies are presented. We modify the size of the interface between microphases to control the number of holes in multipod morphologies. Comparison to experimental observation by transmission electron microtomography of multipods in polystyrene-polyisoprene diblock copolymers is also presented.
Collapse
Affiliation(s)
- Edgar Avalos
- WPI-Research Center, Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
| | - Takeshi Higuchi
- Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
| | - Takashi Teramoto
- Department of Mathematics, Asahikawa Medical University, 2-1-1-1, Midorigaoka-higashi, Asahikawa 078-8510, Japan
| | - Hiroshi Yabu
- WPI-Research Center, Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
| | - Yasumasa Nishiura
- WPI-Research Center, Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
| |
Collapse
|
18
|
Kan D, He X. Tuning phase structures of a symmetrical diblock copolymer with a patterned electric field. SOFT MATTER 2016; 12:4449-4456. [PMID: 27102422 DOI: 10.1039/c5sm03154k] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Electric fields can induce the orientation of the phase interfaces of block copolymers and provide a potential method to tune polymer phase structures for nanomaterial manufacture. In this work, we applied self-consistent field theory to study the self-assembly of a diblock copolymer confined between two parallel neutral substrates on which a set of electrodes was imposed to form a patterned electric field. The results showed that an alternatively distributed electric field can induce the formation of a parallel lamellar phase structure, which exists stably only in the system with selective substrates. The phase structure was proved to be sensitive to the characteristics of the electric field distribution, such as the strength of the electric field, the size and position of the electrodes, and the corresponding phase diagram was calculated in detail. The transition pathway of the phase structure from the perpendicular layered phase to the parallel layered phase was further analysed using the minimum energy path method. It is shown that the path and the active energy barrier of the phase transition depend on the electric field strength. Compound electric field patterns that can be designed to control the formation of novel and complex microphase structures were also examined.
Collapse
Affiliation(s)
- Di Kan
- Department of Chemistry, School of Science, Tianjin University, 300072 Tianjin, China.
| | - Xuehao He
- Department of Chemistry, School of Science, Tianjin University, 300072 Tianjin, China.
| |
Collapse
|
19
|
Effect of curvature on properties of diblock copolymers confined between two coaxial cylinders: 2. Domain adjustment in a curved bilayer. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.10.032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
20
|
Surface-induced morphologies of ABC star triblock copolymer in spherical cavities. CHINESE JOURNAL OF POLYMER SCIENCE 2015. [DOI: 10.1007/s10118-015-1706-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
21
|
Xiao X, Zhao B, Ren Y. Effect of curvature on properties of diblock copolymers confined between two coaxial cylinders: 1. Layer thickness of a curved monolayer. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.05.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
22
|
|
23
|
Zhang T, Deng H, Yang T, Li W. Defective morphologies kinetically formed in diblock copolymers under the cylindrical confinement. POLYMER 2015. [DOI: 10.1016/j.polymer.2015.03.059] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
24
|
He X, Zou Z, Kan D, Liang H. Self-assembly of diblock copolymer confined in an array-structure space. J Chem Phys 2015; 142:101912. [PMID: 25770501 DOI: 10.1063/1.4907532] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The combination of top-down and bottom-up technologies is an effective method to create the novel nanostructures with long range order in the field of advanced materials manufacture. In this work, we employed a polymeric self-consistent field theory to investigate the pattern formation of diblock copolymer in a 2D confinement system designed by filling pillar arrays with various 2D shapes such as squares, rectangles, and triangles. Our simulation shows that in such confinement system, the microphase structure of diblock copolymer strongly depends on the pitch, shape, size, and rotation of the pillar as well as the surface field of confinement. The array structures can not only induce the formation of new phase patterns but also control the location and orientation of pattern structures. Finally, several methods to tune the commensuration and frustration of array-structure confinement are proposed and examined.
Collapse
Affiliation(s)
- Xuehao He
- Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China
| | - Zhixiang Zou
- Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China
| | - Di Kan
- Department of Chemistry, School of Science, Tianjin University, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China
| | - Haojun Liang
- Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei 230026, China
| |
Collapse
|
25
|
Hao QH, Miao B, Song QG, Niu XH, Liu TJ. Phase behaviors of sphere-forming triblock copolymers confined in nanopores: A dynamic density functional theory study. POLYMER 2014. [DOI: 10.1016/j.polymer.2014.06.062] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
26
|
Xu Y, Li W, Qiu F, Lin Z. Self-assembly of 21-arm star-like diblock copolymer in bulk and under cylindrical confinement. NANOSCALE 2014; 6:6844-6852. [PMID: 24830862 DOI: 10.1039/c4nr01275e] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Phase behaviors of a 21-arm star-like diblock copolymer in bulk and under confinement were explored by using the pseudo-spectral method of a self-consistent mean field theory. An asymmetrical phase diagram in bulk was constructed by comparing the free energy of different structures. The gyroid phase was found to possess a large phase region when the inner block in the star-like diblock copolymer has a small volume fraction, suggesting the propensity to form the gyroid phase under this condition. Combined with the early experimental work, a scaling law correlating the period of lamellae D(multiarms) formed from multi-arm star-like block copolymers with the number of arms f was identified, that is, D(multiarms) = D/f(1/2), where D is the period of a linear diblock copolymer with the same degree of polymerization N as a star-like diblock copolymer. The scaling law was also substantiated by the scaling theory. The bridging fraction of the lamellae formed in a star-like diblock copolymer was nearly 100%, which is advantageous for improving its mechanical properties. Some interesting two-dimensional and three-dimensional morphologies were yielded under the cylindrical confinement, where a 3D double helix was found to be the most stable structure.
Collapse
Affiliation(s)
- Yuci Xu
- Department of Macromolecular Science and Engineering, Faculty of Materials Science and Chemical Engineering, Ningbo University, Ningbo, Zhejiang 315211, China
| | | | | | | |
Collapse
|
27
|
Maniadis P, Tsimpanogiannis I, Kober E, Lookman T. Morphology of diblock copolymers in porous media. Mol Phys 2014. [DOI: 10.1080/00268976.2014.886736] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
28
|
Li W, Liu M, Qiu F, Shi AC. Phase Diagram of Diblock Copolymers Confined in Thin Films. J Phys Chem B 2013; 117:5280-8. [DOI: 10.1021/jp309546q] [Citation(s) in RCA: 81] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Weihua Li
- State Key Laboratory of Molecular
Engineering of Polymers,
Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Meijiao Liu
- State Key Laboratory of Molecular
Engineering of Polymers,
Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Feng Qiu
- State Key Laboratory of Molecular
Engineering of Polymers,
Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada, L8S 4M1
| |
Collapse
|
29
|
Liu M, Li W, Qiu F. Segmented helical structures formed by ABC star copolymers in nanopores. J Chem Phys 2013; 138:104904. [PMID: 23514516 DOI: 10.1063/1.4794785] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Self-assembly of ABC star triblock copolymers confined in cylindrical nanopores is studied using self-consistent mean-field theory. With an ABC terpolymer forming hexagonally-arranged cylinders, segmented into alternative B and C domains, in the bulk, we observe the formation in the nanopore of a segmented single circular and non-circular cylinder, a segmented single-helix, and a segmented double-helix as stable phases, and a metastable stacked-disk phase with fourfold symmetry. The phase sequence from single-cylinder, to single-helix, and then to double-helix, is similar as that in the cylindrically-confined diblock copolymers except for the absence of an equilibrium stacked-disk phase. It is revealed that the arrangement of the three-arm junctions plays a critical role for the structure formation. One of the most interesting features in the helical structures is that there are two periods: the period of the B/C domains in the helix and the helical period. We demonstrate that the period numbers of the B/C domains contained in each helical period can be tuned by varying the pore diameter. In addition, it is predicted that the period number of B/C domains can be any rational in real helical structures whose helical period can be tuned freely.
Collapse
Affiliation(s)
- Meijiao Liu
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | | | | |
Collapse
|
30
|
Xu Y, Xie N, Li W, Qiu F, Shi AC. Phase behaviors and ordering dynamics of diblock copolymer self-assembly directed by lateral hexagonal confinement. J Chem Phys 2012. [DOI: 10.1063/1.4765098] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuci Xu
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Nan Xie
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Weihua Li
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
| | - Feng Qiu
- State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
- Key Laboratory of Computational Physical Sciences, Ministry of Education of China, Shanghai 200433, China
| | - An-Chang Shi
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| |
Collapse
|
31
|
Self-assembly of linear triblock copolymers under cylindrical nanopore confinements. CHINESE JOURNAL OF POLYMER SCIENCE 2012. [DOI: 10.1007/s10118-013-1183-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
32
|
|
33
|
Yang R, Li B, Shi AC. Phase behavior of binary blends of diblock copolymer/homopolymer confined in spherical nanopores. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2012; 28:1569-1578. [PMID: 22148840 DOI: 10.1021/la204449x] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Binary blends of a diblock copolymer (AB) and an incompatible homopolymer (C) confined in spherical cavities are studied using a simulated annealing technique. The phase behavior of the blends is examined for four typical cases, representing the different selectivity of the pore surface to the A, B, and C species. The internal morphology of the spherical polymeric particles is controlled by the homopolymer volume fraction, the degree of confinement, and the composition of the copolymer. Inside a particle, the homopolymers segregate to form one or, under some conditions, two domains; thus, the homopolymers may act as an additional controlling parameter of the shape and symmetry of the copolymer domain. A rich array of confinement-induced novel diblock copolymer morphologies is predicted. In particular, core-shell particles with the copolymers as the shell wrapping around a homopolymer core or a copolymer-homopolymer combined core and Janus-like particles with the copolymers and the homopolymers on different sides are obtained.
Collapse
Affiliation(s)
- Rongqiao Yang
- School of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, Tianjin 300071, China
| | | | | |
Collapse
|
34
|
Chi P, Wang Z, Li B, Shi AC. Soft confinement-induced morphologies of diblock copolymers. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2011; 27:11683-11689. [PMID: 21834527 DOI: 10.1021/la202448c] [Citation(s) in RCA: 79] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The self-assembly of diblock copolymers under soft confinement is studied systematically using a simulated annealing method applied to a lattice model of polymers. The soft confinement is realized by the formation of polymer droplets in a poor solvent environment. Multiple sequences of soft confinement-induced copolymer aggregates with different shapes and self-assembled internal morphologies are predicted as functions of solvent-polymer interaction and the monomer concentration. It is discovered that the self-assembled internal morphology of the aggregates is largely controlled by a competition between the bulk morphology of the copolymer and the solvent-polymer interaction, and the shape of the aggregates can be non-spherical when the internal morphology is anisotropic and the solvent-polymer interaction is weak. These results demonstrate that droplets of diblock copolymers formed in poor solvents can be used as a model system to study the self-assembly of copolymers under soft confinement.
Collapse
Affiliation(s)
- Peng Chi
- School of Physics and Key Laboratory of Functional Polymer Materials of the Ministry of Education, Nankai University, Tianjin 300071, China
| | | | | | | |
Collapse
|
35
|
|
36
|
Li S, Chen P, Zhang L, Liang H. Geometric frustration phases of diblock copolymers in nanoparticles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2011; 27:5081-5089. [PMID: 21417241 DOI: 10.1021/la200379h] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.
Collapse
Affiliation(s)
- Shiben Li
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China.
| | | | | | | |
Collapse
|
37
|
|
38
|
|