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Leong DW, Shao Y, Ni Z, Bhuvanesh N, Ozerov OV. A bis(PCN) palladium pincer complex with a remarkably planar 2,5-diarylpyrazine core. Dalton Trans 2024; 53:6520-6523. [PMID: 38563468 DOI: 10.1039/d3dt04248k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
A bimetallic Pd complex of a bis(pincer) with a diarylpyrazine core has been prepared. The complex demonstrates near-perfect coplanarity of the aromatic core, is fluorescent under UV irradiation, and displays two quasi-reversible reduction events.
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Affiliation(s)
- Derek W Leong
- Department of Chemistry, Texas A&M University, College Station, TX 77842, USA.
| | - Yanwu Shao
- Department of Chemistry, Texas A&M University, College Station, TX 77842, USA.
| | - Zhen Ni
- Department of Chemistry, Texas A&M University, College Station, TX 77842, USA.
| | - Nattamai Bhuvanesh
- Department of Chemistry, Texas A&M University, College Station, TX 77842, USA.
| | - Oleg V Ozerov
- Department of Chemistry, Texas A&M University, College Station, TX 77842, USA.
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2
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Li C, Pang Y, Xu Y, Lu M, Tu L, Li Q, Sharma A, Guo Z, Li X, Sun Y. Near-infrared metal agents assisting precision medicine: from strategic design to bioimaging and therapeutic applications. Chem Soc Rev 2023. [PMID: 37334831 DOI: 10.1039/d3cs00227f] [Citation(s) in RCA: 24] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/21/2023]
Abstract
Metal agents have made incredible strides in preclinical research and clinical applications in recent years, but their short emission/absorption wavelengths continue to be a barrier to their distribution, therapeutic action, visual tracking, and efficacy evaluation. Nowadays, the near-infrared window (NIR, 650-1700 nm) provides a more accurate imaging and treatment option. Thus, there has been ongoing research focusing on developing multifunctional NIR metal agents for imaging and therapy that have deeper tissue penetration. The design, characteristics, bioimaging, and therapy of NIR metal agents are covered in this overview of papers and reports published to date. To start with, we focus on describing the structure, design strategies, and photophysical properties of metal agents from the NIR-I (650-1000 nm) to NIR-II (1000-1700 nm) region, in order of molecular metal complexes (MMCs), metal-organic complexes (MOCs), and metal-organic frameworks (MOFs). Next, the biomedical applications brought by these superior photophysical and chemical properties for more accurate imaging and therapy are discussed. Finally, we explore the challenges and prospects of each type of NIR metal agent for future biomedical research and clinical translation.
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Affiliation(s)
- Chonglu Li
- Hubei Province Key Laboratory of Occupational Hazard Identification and Control, School of Medicine, School of Public Health, Wuhan University of Science and Technology, Wuhan 430065, China.
- National Key Laboratory of Green Pesticide, College of Chemistry, Central China Normal University, Wuhan 430079, China.
| | - Yida Pang
- National Key Laboratory of Green Pesticide, College of Chemistry, Central China Normal University, Wuhan 430079, China.
| | - Yuling Xu
- National Key Laboratory of Green Pesticide, College of Chemistry, Central China Normal University, Wuhan 430079, China.
| | - Mengjiao Lu
- National Key Laboratory of Green Pesticide, Key Laboratory of Green Pesticide and Agricultural Bioengineering, Ministry of Education, Guizhou University, Guiyang 550025, China.
| | - Le Tu
- National Key Laboratory of Green Pesticide, College of Chemistry, Central China Normal University, Wuhan 430079, China.
| | - Qian Li
- NHC Key Laboratory of Nuclear Medicine, Jiangsu Key Laboratory of Molecular Nuclear Medicine, Jiangsu Institute of Nuclear Medicine, Wuxi 214063, China
| | - Amit Sharma
- CSIR-Central Scientific Instruments Organisation, Sector-30C, Chandigarh 160030, India
| | - Zhenzhong Guo
- Hubei Province Key Laboratory of Occupational Hazard Identification and Control, School of Medicine, School of Public Health, Wuhan University of Science and Technology, Wuhan 430065, China.
| | - Xiangyang Li
- National Key Laboratory of Green Pesticide, Key Laboratory of Green Pesticide and Agricultural Bioengineering, Ministry of Education, Guizhou University, Guiyang 550025, China.
| | - Yao Sun
- National Key Laboratory of Green Pesticide, College of Chemistry, Central China Normal University, Wuhan 430079, China.
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3
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Yu CH, Zhu C, Ji X, Hu W, Xie H, Bhuvanesh N, Fang L, Ozerov OV. Palladium bis-pincer complexes with controlled rigidity and inter-metal distance. Inorg Chem Front 2020. [DOI: 10.1039/d0qi01111h] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
We report a series of redox-active bis(pincer) Pd(ii) complexes in which the redox active units are based on either a diarylamido or a carbazolide framework.
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Affiliation(s)
- Cheng-Han Yu
- Department of Chemistry
- Texas A&M University
- College Station
- USA
| | - Congzhi Zhu
- Department of Chemistry
- Texas A&M University
- College Station
- USA
| | - Xiaozhou Ji
- Department of Chemistry
- Texas A&M University
- College Station
- USA
| | - Wei Hu
- Department of Chemistry
- Texas A&M University
- College Station
- USA
| | - Haomiao Xie
- Department of Chemistry
- Texas A&M University
- College Station
- USA
| | | | - Lei Fang
- Department of Chemistry
- Texas A&M University
- College Station
- USA
| | - Oleg V. Ozerov
- Department of Chemistry
- Texas A&M University
- College Station
- USA
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4
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Affiliation(s)
- Nadeesha P. N. Wellala
- Department of Chemistry, University of Cincinnati, P.O. Box 210172, Cincinnati, Ohio 45221-0172, United States
| | - Hai T. Dong
- Department of Chemistry, University of Cincinnati, P.O. Box 210172, Cincinnati, Ohio 45221-0172, United States
| | - Jeanette A. Krause
- Department of Chemistry, University of Cincinnati, P.O. Box 210172, Cincinnati, Ohio 45221-0172, United States
| | - Hairong Guan
- Department of Chemistry, University of Cincinnati, P.O. Box 210172, Cincinnati, Ohio 45221-0172, United States
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5
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Langbein S, Wadepohl H, Gade LH. Ditopic N-Heterocyclic Pincer Carbene Complexes Containing a Perylene Backbone. Organometallics 2016. [DOI: 10.1021/acs.organomet.6b00049] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Susanne Langbein
- Anorganisch-Chemisches
Institut, Universität Heidelberg, Im Neuenheimer Feld 270, 69120 Heidelberg, Germany
| | - Hubert Wadepohl
- Anorganisch-Chemisches
Institut, Universität Heidelberg, Im Neuenheimer Feld 270, 69120 Heidelberg, Germany
| | - Lutz H. Gade
- Anorganisch-Chemisches
Institut, Universität Heidelberg, Im Neuenheimer Feld 270, 69120 Heidelberg, Germany
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6
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Kean ZS, Hawk JL, Lin S, Zhao X, Sijbesma RP, Craig SL. Increasing the maximum achievable strain of a covalent polymer gel through the addition of mechanically invisible cross-links. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2014; 26:6013-6018. [PMID: 25044398 DOI: 10.1002/adma.201401570] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2014] [Revised: 05/20/2014] [Indexed: 06/03/2023]
Abstract
Hydrogels and organogels made from polymer networks are widely used in biomedical applications and soft, active devices for which the ability to sustain large deformations is required. The strain at which polymer networks fracture is typically improved through the addition of elements that dissipate energy, but these materials require extra work to achieve a given, desired level of deformation. Here, the addition of mechanically "invisible" supramolecular crosslinks causes substantial increases in the ultimate gel properties without incurring the added energetic costs of dissipation.
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Affiliation(s)
- Zachary S Kean
- Department of Chemistry, Duke University, Durham, NC, 27708-0346, USA
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7
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Xu D, Craig SL. Strain Hardening and Strain Softening of Reversibly Cross-linked Supramolecular Polymer Networks. Macromolecules 2011; 44:7478-7488. [PMID: 22043083 DOI: 10.1021/ma201386t] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The large amplitude oscillatory shear behavior of metallo-supramolecular polymer networks formed by adding bis-Pd(II) cross-linkers to poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO) solution is reported. The influence of scanning frequency, dissociation rate of cross-linkers, concentration of cross-linkers, and concentration of PVP solution on the large amplitude oscillatory shear behavior is explored. In semidilute unentangled PVP solutions, above a critical scanning frequency, strain hardening of both storage moduli and loss moduli is observed. In the semidilute entangled regime of PVP solution, however, strain softening is observed for samples with faster cross-linkers (k(d) ∼ 1450 s(-1)), whereas strain hardening is observed for samples with slower cross-linkers (k(d) ∼ 17 s(-1)). The mechanism of strain hardening is attributed primarily to a strain-induced increase in the number of elastically active chains, with possible contributions from non-Gaussian stretching of polymer chains at strains approaching network fracture. The divergent strain softening of samples with faster cross-linkers in semidilute entangled PVP solutions, relative to the strain hardening of samples with slower cross-linkers, is consistent with observed shear thinning/shear thickening behavior reported previously and is attributed to the fact that the average time that a cross-linker remains detached is too short to permit the local relaxation of polymer chain segments that is necessary for a net conversion of elastically inactive to elastically active cross-linkers. These and other observations paint a picture in which strain softening and shear thinning arise from the same set of molecular mechanisms, conceptually uniting the two nonlinear responses for this system.
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Affiliation(s)
- Donghua Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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Abstract
The linear rheological properties of networks formed by adding bis-Pd(II) cross-linkers to poly(4-vinylpyridine) (PVP) solution are examined, and the scaling law relationships between the zero shear viscosity (η(0)) of the networks versus the concentration of PVP solution (C(PVP)), the concentration of cross-linkers (C(X)), and the number density of elastically active chains (v(phantom)) are experimentally determined. The scaling law relationships are compared to the theoretical expectations of the Sticky Rouse and Sticky Reptation models (Macromolecules2001, 34, 1058-1068), and both qualitative and quantitative differences are observed.
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Affiliation(s)
- Donghua Xu
- Department of Chemistry and Center for Biologically Inspired Materials and Material Systems, Duke University, Durham, North Carolina, 27708-0346
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9
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Ghorai D, Mani G. Synthesis and structural characterization of Pd(II) complexes containing 2,6-bis[(dimethylamino)methyl]-4-methylphenolate ligand. Inorganica Chim Acta 2011. [DOI: 10.1016/j.ica.2011.01.098] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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10
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Xu D, Liu CY, Craig SL. Divergent Shear Thinning and Shear Thickening Behavior of Supramolecular Polymer Networks in Semidilute Entangled Polymer Solutions. Macromolecules 2011; 44:2343-2353. [PMID: 21547008 DOI: 10.1021/ma2000916] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The steady shear behavior of metallo-supramolecular polymer networks formed by bis-Pd(II) cross-linkers and semidilute entangled solutions of poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO) or N,N-dimethyl formamide (DMF) is reported. The steady shear behavior of the networks depends on the dissociation rate and association rate of the cross-linkers, the concentration of cross-linkers, and the concentration of the polymer solution. The divergent steady shear behavior-shear thinning versus shear thickening-of samples with identical structure but different cross-linker dynamics (J. Phys. Chem. Lett. 2010, 1, 1683-1686) is further explored in this paper. The divergent steady shear behavior for networks with different cross-linkers is connected to a competition between different time scales: the average time that a cross-linker remains open (τ(1)) and the local relaxation time of a segment of polymer chain (τ(segment)). When τ(1) is larger than τ(segment), shear thickening is observed. When τ(1) is smaller than τ(segment), only shear thinning is observed.
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Affiliation(s)
- Donghua Xu
- Department of Chemistry and Center for Biologically Inspired Materials and Material Systems, Duke University, Durham, North Carolina, 27708-0346
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Jeon SL, Loveless DM, Craig SL. Main-chain dynamics in metallo-supramolecular polymers: from solution to elastomeric fibres. Supramol Chem 2010. [DOI: 10.1080/10610278.2010.500727] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sung Lan Jeon
- a Department of Chemistry and Center for Biologically Inspired Materials and Material Systems , Duke University , Durham , NC , 27708-0346 , USA
| | - David M. Loveless
- a Department of Chemistry and Center for Biologically Inspired Materials and Material Systems , Duke University , Durham , NC , 27708-0346 , USA
| | - Stephen L. Craig
- a Department of Chemistry and Center for Biologically Inspired Materials and Material Systems , Duke University , Durham , NC , 27708-0346 , USA
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Xu D, Craig SL. Multiple Dynamic Processes Contribute to the Complex Steady Shear Behavior of Cross-Linked Supramolecular Networks of Semidilute Entangled Polymer Solutions. J Phys Chem Lett 2010; 1:1683-1686. [PMID: 20606721 PMCID: PMC2894477 DOI: 10.1021/jz1004818] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Molecular theories of shear thickening and shear thinning in associative polymer networks are typically united in that they involve a single kinetic parameter that describes the network -- a relaxation time that is related to the lifetime of the associative bonds. Here we report the steady-shear behavior of two structurally identical metallo-supramolecular polymer networks, for which single-relaxation parameter models break down in dramatic fashion. The networks are formed by the addition of reversible cross-linkers to semidilute entangled solutions of PVP in DMSO, and they differ only in the lifetime of the reversible cross-links. Shear thickening is observed for cross-linkers that have a slower dissociation rate (17 s(-1)), while shear thinning is observed for samples that have a faster dissociation rate (ca. 1400 s(-1)). The difference in the steady shear behavior of the unentangled vs. entangled regime reveals an unexpected, additional competing relaxation, ascribed to topological disentanglement in the semidilute entangled regime that contributes to the rheological properties.
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13
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Xu D, Hawk JL, Loveless DM, Jeon SL, Craig SL. Mechanism of Shear Thickening in Reversibly Cross-linked Supramolecular Polymer Networks. Macromolecules 2010; 43:3556-3565. [PMID: 20479956 DOI: 10.1021/ma100093b] [Citation(s) in RCA: 86] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We report here the nonlinear rheological properties of metallo-supramolecular networks formed by the reversible cross-linking of semi-dilute unentangled solutions of poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO). The reversible cross-linkers are bis-Pd(II) or bis-Pt(II) complexes that coordinate to the pyridine functional groups on the PVP. Under steady shear, shear thickening is observed above a critical shear rate, and that critical shear rate is experimentally correlated with the lifetime of the metal-ligand bond. The onset and magnitude of the shear thickening depend on the amount of cross-linkers added. In contrast to the behavior observed in most transient networks, the time scale of network relaxation is found to increase during shear thickening. The primary mechanism of shear thickening is ascribed to the shear-induced transformation of intrachain cross-linking to interchain cross-linking, rather than nonlinear high tension along polymer chains that are stretched beyond the Gaussian range.
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Affiliation(s)
- Donghua Xu
- Department of Chemistry and Center for Biologically Inspired Materials and Material Systems, Duke University, Durham, NC, 27708-0346, USA
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14
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Yang SK, Ambade A, Weck M. Supramolecular Alternating Block Copolymers via Metal Coordination. Chemistry 2009; 15:6605-11. [DOI: 10.1002/chem.200900573] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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15
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Zhang Y, Song G, Ma G, Zhao J, Pan CL, Li X. 1,3-Dinitrone Pincer Complexes of Palladium and Nickel: Synthesis, Structural Characterizations, and Catalysis. Organometallics 2009. [DOI: 10.1021/om900009h] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Yao Zhang
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, State Key Laboratory of Pharmaceutical Biotechnology, School of Life Sciences, Nanjing University, Nanjing 210093, People’s Republic of China, State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, Jilin, People’s Republic of China
| | - Guoyong Song
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, State Key Laboratory of Pharmaceutical Biotechnology, School of Life Sciences, Nanjing University, Nanjing 210093, People’s Republic of China, State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, Jilin, People’s Republic of China
| | - Gaoyuan Ma
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, State Key Laboratory of Pharmaceutical Biotechnology, School of Life Sciences, Nanjing University, Nanjing 210093, People’s Republic of China, State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, Jilin, People’s Republic of China
| | - Jing Zhao
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, State Key Laboratory of Pharmaceutical Biotechnology, School of Life Sciences, Nanjing University, Nanjing 210093, People’s Republic of China, State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, Jilin, People’s Republic of China
| | - Cheng-Ling Pan
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, State Key Laboratory of Pharmaceutical Biotechnology, School of Life Sciences, Nanjing University, Nanjing 210093, People’s Republic of China, State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, Jilin, People’s Republic of China
| | - Xingwei Li
- Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, State Key Laboratory of Pharmaceutical Biotechnology, School of Life Sciences, Nanjing University, Nanjing 210093, People’s Republic of China, State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, Jilin, People’s Republic of China
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Desai LV, Stowers KJ, Sanford MS. Insights into directing group ability in palladium-catalyzed C-H bond functionalization. J Am Chem Soc 2008; 130:13285-93. [PMID: 18781752 PMCID: PMC2733373 DOI: 10.1021/ja8045519] [Citation(s) in RCA: 318] [Impact Index Per Article: 19.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This paper describes a detailed investigation of factors controlling the dominance of a directing group in Pd-catalyzed ligand-directed arene acetoxylation. Mechanistic studies, involving reaction kinetics, Hammett analysis, kinetic isotope effect experiments, and the kinetic order in oxidant, have been conducted for a series of different substrates. Initial rates studies of substrates bearing different directing groups showed that these transformations are accelerated by the use of electron-withdrawing directing groups. However, in contrast, under conditions where two directing groups are in competition with one another in the same reaction flask, substrates with electron-donating directing groups react preferentially. These results are discussed in the context of the proposed mechanism for Pd-catalyzed arene acetoxylation.
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Affiliation(s)
- Lopa V. Desai
- University of Michigan, Chemistry Department, 930 North University Ave, Ann Arbor, MI 48109
| | - Kara J. Stowers
- University of Michigan, Chemistry Department, 930 North University Ave, Ann Arbor, MI 48109
| | - Melanie S. Sanford
- University of Michigan, Chemistry Department, 930 North University Ave, Ann Arbor, MI 48109
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Zhao CQ, Jennings MC, Puddephatt RJ. A hemilabile binucleating pincer ligand for self-assembly of coordination oligomers and polymers. Dalton Trans 2008:1243-50. [DOI: 10.1039/b716035f] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Kersey FR, Loveless DM, Craig SL. A hybrid polymer gel with controlled rates of cross-link rupture and self-repair. J R Soc Interface 2007; 4:373-80. [PMID: 17251135 PMCID: PMC2359846 DOI: 10.1098/rsif.2006.0187] [Citation(s) in RCA: 119] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A family of hybrid polymer gels is described, in which covalent cross-links create a permanent, stiff scaffold onto which reversible metal-ligand coordinative cross-links are added. The reversible metal-ligand interactions are shown to bear mechanical stress within the hybrid gel, and relaxations in response to that applied stress are consistent with the stress-free kinetics of ligand exchange in systems that model the reversible cross-links. The stress-induced dissociation of a model metal-ligand complex is examined by a single-molecule force spectroscopy, and its mechanical response is compared with a previously studied complex. The mechanical response of the individual interactions is relevant to those found in the family of hybrid gels, and the modular platform is therefore suitable for the study of stress-induced molecular dissociations, and their subsequent repair, within a macroscopic material of fixed structure.
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