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Li YC, Wu ZP, Zong ZH, Cao XZ. Rheological Role of Stiff Nanorings on Concurrently Strengthening and Toughening Polymer Nanocomposites. ACS Macro Lett 2023; 12:183-188. [PMID: 36692488 DOI: 10.1021/acsmacrolett.2c00610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Nanorings, which are increasingly uncovered in natural systems and synthesized in man-made materials, exhibit dynamics distinct from those known for linear chains. We show in this study that, when immersed in a polymer melt matrix, segments of a stiff nanoring (SNR) have more facilitated subdiffusion, i.e., with a larger scaling exponent in the mean squared displacement, than those belonging to one flexible counterpart, while the whole SNR is more suppressed by its surroundings. It is revealed that adding SNRs contributes to achieving the long-anticipated rheological objective of sol- and gel-like characteristics at high and low shearing frequencies, respectively. This study suggests the promising prospect of exploiting SNRs to concurrently strengthen and toughen target polymer nanocomposites.
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Affiliation(s)
- Yu-Chao Li
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
| | - Zong-Pei Wu
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
| | - Ze-Hao Zong
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
| | - Xue-Zheng Cao
- Department of Physics and Fujian Provincial Key Laboratory for Soft Functional Materials Research, College of Physical Science and Technology, Xiamen University, Xiamen 361005, P.R. China
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2
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Liu G, Rauscher PM, Rawe BW, Tranquilli MM, Rowan SJ. Polycatenanes: synthesis, characterization, and physical understanding. Chem Soc Rev 2022; 51:4928-4948. [PMID: 35611843 DOI: 10.1039/d2cs00256f] [Citation(s) in RCA: 26] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Chemical composition and architecture are two key factors that control the physical and material properties of polymers. Some of the more unusual and intriguing polymer architectures are the polycatenanes, which are a class of polymers that contain mechanically interlocked rings. Since the development of high yielding synthetic routes to catenanes, there has been an interest in accessing their polymeric counterparts, primarily on account of the unique conformations and degrees of freedom offered by non-bonded interlocked rings. This has lead to the synthesis of a wide variety of polycatenane architectures and to studies aimed at developing structure-property relationships of these interesting materials. In this review, we provide an overview of the field of polycatenanes, exploring synthesis, architecture, properties, simulation, and modelling, with a specific focus on some of the more recent developments.
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Affiliation(s)
- Guancen Liu
- Department of Chemistry, University of Chicago, Chicago, IL, USA.
| | - Phillip M Rauscher
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Benjamin W Rawe
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | | | - Stuart J Rowan
- Department of Chemistry, University of Chicago, Chicago, IL, USA. .,Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.,Chemical and Engineering Sciences, Argonne National Laboratory, Lemont, IL, USA
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3
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Kong D, Banik S, San Francisco MJ, Lee M, Robertson Anderson RM, Schroeder CM, McKenna GB. Rheology of Entangled Solutions of Ring–Linear DNA Blends. Macromolecules 2022. [DOI: 10.1021/acs.macromol.1c01672] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Dejie Kong
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, United States
| | - Sourya Banik
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, United States
| | | | - Megan Lee
- Department of Physics and Biophysics, University of San Diego, San Diego, California 92110, United States
| | - Rae M. Robertson Anderson
- Department of Physics and Biophysics, University of San Diego, San Diego, California 92110, United States
| | - Charles M. Schroeder
- Department of Materials Science and Engineering and the Department of Chemical & Biomolecular Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Gregory B. McKenna
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, United States
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States
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4
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Morphology and growth rate of spherulite of cyclic poly(ε-caprolactone) having a triazole group at the closing point. POLYMER 2020. [DOI: 10.1016/j.polymer.2020.122660] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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5
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Ono R, Atarashi H, Yamazaki S, Kimura K. Molecular weight dependence of the growth rate of spherulite of cyclic poly(ε-caprolactone) polymerized by ring expansion reaction. POLYMER 2020. [DOI: 10.1016/j.polymer.2020.122403] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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6
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Vargas-Lara F, Pazmiño Betancourt BA, Douglas JF. Communication: A comparison between the solution properties of knotted ring and star polymers. J Chem Phys 2018; 149:161101. [PMID: 30384696 PMCID: PMC11005112 DOI: 10.1063/1.5048937] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
We computationally investigate the good solvent solution properties of knotted ring and star polymers by combining molecular dynamics (MD) simulation and path-integral calculations. We consider knotted rings having a minimal crossing number m c in the range, 0 ≤ m c ≤ 9, and star polymers having a range of f star arms, 2 ≤ f ≤ 20, attached to a common core monomer particle. After generating configurational ensembles of these polymers by MD, we use the path-integration program ZENO to calculate basic configurational properties, i.e., radius of gyration, hydrodynamic radius, intrinsic viscosity, as well as fluctuations in these properties. Our simulations indicate that the configurational properties of knotted rings and star polymers in solution show a similar decrease with increasing m c and f. Moreover, fluctuations in these properties also decrease with increasing topological complexity. Our findings should be helpful in polymer characterization and more generally for understanding the role of polymer topology in polymer material properties.
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Affiliation(s)
- Fernando Vargas-Lara
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Beatriz A. Pazmiño Betancourt
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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7
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Qian Z, McKenna GB. Expanding the application of the van Gurp-Palmen plot: New insights into polymer melt rheology. POLYMER 2018. [DOI: 10.1016/j.polymer.2018.09.036] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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8
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Zhang S, Cheng X, Wang J, Zhang Z, Zhang W, Zhu X. Synthesis of a cyclic-brush polymer with a high grafting density using activated ester chemistry via the “grafting onto” approach. Polym Chem 2018. [DOI: 10.1039/c8py01014e] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
A concept for preparing cyclic-brush polymers with high grafting densities combining a ring-closure strategy and activated ester chemistry as a post-modification method via the grafting onto approach.
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Affiliation(s)
- Shuangshuang Zhang
- Suzhou Key Laboratory of Macromolecular Design and Precision Synthesis
- Jiangsu Key Laboratory of Advanced Functional Polymer Design and Application
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials
- College of Chemistry
- Chemical Engineering and Materials Science
| | - Xiaoxiao Cheng
- Suzhou Key Laboratory of Macromolecular Design and Precision Synthesis
- Jiangsu Key Laboratory of Advanced Functional Polymer Design and Application
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials
- College of Chemistry
- Chemical Engineering and Materials Science
| | - Junzhi Wang
- Suzhou Key Laboratory of Macromolecular Design and Precision Synthesis
- Jiangsu Key Laboratory of Advanced Functional Polymer Design and Application
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials
- College of Chemistry
- Chemical Engineering and Materials Science
| | - Zhengbiao Zhang
- Suzhou Key Laboratory of Macromolecular Design and Precision Synthesis
- Jiangsu Key Laboratory of Advanced Functional Polymer Design and Application
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials
- College of Chemistry
- Chemical Engineering and Materials Science
| | - Wei Zhang
- Suzhou Key Laboratory of Macromolecular Design and Precision Synthesis
- Jiangsu Key Laboratory of Advanced Functional Polymer Design and Application
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials
- College of Chemistry
- Chemical Engineering and Materials Science
| | - Xiulin Zhu
- Suzhou Key Laboratory of Macromolecular Design and Precision Synthesis
- Jiangsu Key Laboratory of Advanced Functional Polymer Design and Application
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials
- College of Chemistry
- Chemical Engineering and Materials Science
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9
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Affiliation(s)
- Youncheol Jeong
- Division of Advanced Materials
Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Ye Jin
- Division of Advanced Materials
Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Taihyun Chang
- Division of Advanced Materials
Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Filip Uhlik
- Department of Physical and
Macromolecular Chemistry, Charles University, Prague 12843,Czech Republic
| | - Jacques Roovers
- Institute for Environmental
Chemistry, National Research Council of Canada, Ottawa, ON K1A 0R6, Canada
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10
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Abstract
The first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small-molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including chirality, strong and selective ion binding, and catalytic activity. As the number and complexity of accessible molecular knot topologies increases, it will become increasingly useful for chemists to adopt the knot terminology employed by other disciplines. Here we give an overview of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry and molecular structure.
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Affiliation(s)
| | - David A. Leigh
- School of ChemistryUniversity of ManchesterOxford RoadManchesterM13 9PLUK
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11
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Affiliation(s)
- Stephen D. P. Fielden
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - David A. Leigh
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - Steffen L. Woltering
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
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12
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Deguchi T, Uehara E. Statistical and Dynamical Properties of Topological Polymers with Graphs and Ring Polymers with Knots. Polymers (Basel) 2017; 9:E252. [PMID: 30970929 PMCID: PMC6432503 DOI: 10.3390/polym9070252] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2017] [Revised: 06/22/2017] [Accepted: 06/23/2017] [Indexed: 11/16/2022] Open
Abstract
We review recent theoretical studies on the statistical and dynamical properties of polymers with nontrivial structures in chemical connectivity and those of polymers with a nontrivial topology, such as knotted ring polymers in solution. We call polymers with nontrivial structures in chemical connectivity expressed by graphs "topological polymers". Graphs with no loop have only trivial topology, while graphs with loops such as multiple-rings may have nontrivial topology of spatial graphs as embeddings in three dimensions, e.g., knots or links in some loops. We thus call also such polymers with nontrivial topology "topological polymers", for simplicity. For various polymers with different structures in chemical connectivity, we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We evaluate the ratio of the gyration radius to the hydrodynamic radius, which we expect to be universal from the viewpoint of the renormalization group. Furthermore, we show that the short-distance intrachain correlation is much enhanced for real topological polymers (the Kremer⁻Grest model) expressed with complex graphs. We then address topological properties of ring polymers in solution. We define the knotting probability of a knot K by the probability that a given random polygon or self-avoiding polygon of N vertices has the knot K. We show a formula for expressing it as a function of the number of segments N, which gives good fitted curves to the data of the knotting probability versus N. We show numerically that the average size of self-avoiding polygons with a fixed knot can be much larger than that of no topological constraint if the excluded volume is small. We call it "topological swelling".
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Affiliation(s)
- Tetsuo Deguchi
- Department of Physics, Faculty of Core Research, Ochanomizu University, Ohtsuka 2-1-1, Bunkyo-ku, Tokyo 112-8610, Japan.
| | - Erica Uehara
- Department of Physics, Faculty of Core Research, Ochanomizu University, Ohtsuka 2-1-1, Bunkyo-ku, Tokyo 112-8610, Japan.
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13
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Cao PF, Rong LH, Mangadlao JD, Advincula RC. Synthesizing a Trefoil Knotted Block Copolymer via Ring-Expansion Strategy. Macromolecules 2017. [DOI: 10.1021/acs.macromol.6b02029] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Peng-Fei Cao
- Chemical
Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, United States
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14
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Crysup B, Shanbhag S. What Happens When Threading is Suppressed in Blends of Ring and Linear Polymers? Polymers (Basel) 2016; 8:E409. [PMID: 30974687 PMCID: PMC6432297 DOI: 10.3390/polym8120409] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2016] [Revised: 11/15/2016] [Accepted: 11/18/2016] [Indexed: 11/16/2022] Open
Abstract
Self-diffusivity of a large tracer ring polymer, D r , immersed in a matrix of linear polymers with N l monomers each shows unusual length dependence. D r initially increases, and then decreases with increasing N l . To understand the relationship between the nonmonotonic variation in D r and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the uncrossability of ring and linear polymer contours is switched on (non-crossing), or artificially turned off (crossing). The D r ≈ 6 . 2 × 10 - 7 N l 2 / 3 obtained from the crossing simulations, provides an upper bound for the D r obtained for the regular, non-crossing simulations. The center-of-mass mean-squared displacement ( g 3 ( t ) ) curves for the crossing simulations are consistent with the Rouse model; we find g 3 ( t ) = 6 D r t . Analysis of the polymer structure indicates that the smaller matrix chains are able to infiltrate the space occupied by the ring probe more effectively, which is dynamically manifested as a larger frictional drag per ring monomer.
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Affiliation(s)
- Benjamin Crysup
- Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA.
| | - Sachin Shanbhag
- Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA.
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15
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Abe H, Ida D. Mean-Square Radius of Gyration and Scattering Function of Semiflexible Ring Polymers of the Trefoil Knot. Polymers (Basel) 2016; 8:polym8080271. [PMID: 30974548 PMCID: PMC6432251 DOI: 10.3390/polym8080271] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2016] [Revised: 07/22/2016] [Accepted: 07/22/2016] [Indexed: 11/16/2022] Open
Abstract
A Monte Carlo study of the mean-square radius of gyration Rg2 and scattering function P(k) with k the magnitude of the scattering vector for semiflexible ring polymers of the trefoil knot was conducted by the use of the discrete version of the Kratky–Porod (KP) wormlike ring model. The behavior of Rg2 and P(k) as functions of the reduced contour length λL, defined as the total contour length L divided by the stiffness parameter λ−1, is clarified. A comparison is made of the results for the KP ring of the trefoil knot with those for the KP ring of the trivial knot and for the phantom KP ring without the topological constraints.
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Affiliation(s)
- Hiroki Abe
- Department of Polymer Chemistry, Kyoto University, Katsura, Kyoto 615-8510, Japan.
| | - Daichi Ida
- Department of Polymer Chemistry, Kyoto University, Katsura, Kyoto 615-8510, Japan.
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16
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Zhu L, Wang X, Li J, Wang Y. Radius of Gyration, Mean Span, and Geometric Shrinking Factors of Bridged Polycyclic Ring Polymers. MACROMOL THEOR SIMUL 2016. [DOI: 10.1002/mats.201600033] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Lijuan Zhu
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials; Department of Polymer Science and Engineering; College of Chemistry; Chemical Engineering and Materials Science; Soochow University; 199 Ren-ai Road Suzhou 215123 P. R. China
| | - Xiaoyan Wang
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials; Department of Polymer Science and Engineering; College of Chemistry; Chemical Engineering and Materials Science; Soochow University; 199 Ren-ai Road Suzhou 215123 P. R. China
| | - Jianfeng Li
- The State Key Laboratory of Molecular Engineering of Polymers; Department of Macromolecular Science; Fudan University; Shanghai 200433 P. R. China
| | - Yanwei Wang
- State and Local Joint Engineering Laboratory for Novel Functional Polymeric Materials; Department of Polymer Science and Engineering; College of Chemistry; Chemical Engineering and Materials Science; Soochow University; 199 Ren-ai Road Suzhou 215123 P. R. China
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17
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Coil to globule transition of homo- and block-copolymer with different topological constraint and chain stiffness. Sci China Chem 2015. [DOI: 10.1007/s11426-015-5430-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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18
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Doi Y, Matsubara K, Ohta Y, Nakano T, Kawaguchi D, Takahashi Y, Takano A, Matsushita Y. Melt Rheology of Ring Polystyrenes with Ultrahigh Purity. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b00076] [Citation(s) in RCA: 98] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Yuya Doi
- Department
of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Kazuki Matsubara
- Department
of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Yutaka Ohta
- Department
of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Tomohiro Nakano
- Department
of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Daisuke Kawaguchi
- Education
Center for Global Leaders in Molecular System for Devices, Kyushu University, Fukuoka 819-0395, Japan
| | - Yoshiaki Takahashi
- Institute
for Materials Chemistry and Engineering, Kyushu University, 6-1, Kasuga-koen,
Kasuga, Fukuoka 816-8580, Japan
| | - Atsushi Takano
- Department
of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
| | - Yushu Matsushita
- Department
of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
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19
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Cao PF, Mangadlao J, Advincula R. A trefoil knotted polymer produced through ring expansion. Angew Chem Int Ed Engl 2015; 54:5127-31. [PMID: 25728998 DOI: 10.1002/anie.201411623] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Revised: 01/16/2014] [Indexed: 12/29/2022]
Abstract
A synthetic strategy is reported for the production of a trefoil knotted polymer from a copper(I)-templated helical knot precursor through ring expansion. The expected changes in the properties of the knotted polymer compared to a linear analogue, for example, reduced hydrodynamic radius and lower intrinsic viscosity, together with an atomic force microscopy (AFM) image of individual molecular knots, confirmed the formation of the resulting trefoil knotted polymer. The strategies employed here could be utilized to enrich the variety of available polymers with new architectures.
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Affiliation(s)
- Peng-Fei Cao
- Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106 (USA)
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20
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Cao PF, Mangadlao J, Advincula R. A Trefoil Knotted Polymer Produced through Ring Expansion. Angew Chem Int Ed Engl 2015. [DOI: 10.1002/ange.201411623] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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21
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Suzuki J, Takano A, Matsushita Y. Chain conformations of ring polymers under theta conditions studied by Monte Carlo simulation. J Chem Phys 2013; 139:184904. [DOI: 10.1063/1.4829046] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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