20 results on '"Soumalya Bhattacharyya"'
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2. Fluorescence enhancement via structural rigidification inside a self-assembled Pd4 molecular vessel
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Shakil Ahmed, Prodip Howlader, Soumalya Bhattacharyya, Surajit Mondal, Ennio Zangrando, and Partha Sarathi Mukherjee
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Materials Chemistry ,Metals and Alloys ,Ceramics and Composites ,General Chemistry ,Catalysis ,Surfaces, Coatings and Films ,Electronic, Optical and Magnetic Materials - Abstract
RIM is fundamental for the high emission of AIEgens in concentrated solution/solid-state. Confinement of such an AIEgen (SG) in the confined nanospace of a Pd4 molecular pocket caused RIM leading to high emission even in a dilute solution.
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- 2022
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3. Self-Assembly of Octanuclear PtII/PdII Coordination Barrels and Uncommon Structural Isomerization of a Photochromic Guest in Molecular Space
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Soumalya Bhattacharyya, Pallab Bhandari, Ritwik Modak, Partha Sarathi Mukherjee, and Ennio Zangrando
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Photochromism ,Crystallography ,Chemistry ,Self-assembly ,Space (mathematics) ,Isomerization ,QD1-999 - Published
- 2021
4. Fluorescence enhancement
- Author
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Shakil, Ahmed, Prodip, Howlader, Soumalya, Bhattacharyya, Surajit, Mondal, Ennio, Zangrando, and Partha Sarathi, Mukherjee
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Restriction of intramolecular motion (RIM) is fundamental for the high emission of aggregation-induced emission (AIE)-active molecules in aggregates or the solid-state. However, they are weakly emissive in dilute solution, which limits their application in dilute solutions. A Pd
- Published
- 2022
5. A Self‐Assembled Palladium(II) Barrel for Binding of Fullerenes and Photosensitization Ability of the Fullerene‐Encapsulated Barrel
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Soumalya Bhattacharyya, Prioti Choudhury Purba, Manoranjan Maity, and Partha Sarathi Mukherjee
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Fullerene ,010405 organic chemistry ,Singlet oxygen ,Supramolecular chemistry ,chemistry.chemical_element ,General Medicine ,General Chemistry ,010402 general chemistry ,Ligand (biochemistry) ,01 natural sciences ,Combinatorial chemistry ,Catalysis ,0104 chemical sciences ,Barrel ,chemistry.chemical_compound ,chemistry ,Self-assembly ,Host–guest chemistry ,Palladium - Abstract
Fullerene extracts obtained from fullerene soot lack their real application due to their poor solubility in common solvents and difficulty in purification. Encapsulation of these extracts in a suitable host is an important approach to address these issues. We present a new Pd6 barrel (1), which is composed of three 1,4-dihydropyrrolo[3,2-b]pyrrole panels, clipped through six cis-PdII acceptors. Large open windows and cavity make it an efficient host for a large guest. Favorable interactions between the ligand and fullerene (C60 and C70 ) allows the barrel to encapsulate fullerene efficiently. Thorough investigation reveals that barrel 1 has a stronger binding affinity towards C70 over C60 , resulting in the predominant extraction of C70 from a mixture of the two. Finally, the fullerene encapsulated barrels C60 ⊂1 and C70 ⊂1 were found to be efficient for visible-light-induced singlet oxygen generation. Such preferential binding of C70 and photosensitizing ability of C60 ⊂1 and C70 ⊂1 are noteworthy.
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- 2021
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6. Self-Assembled Pd12 Coordination Cage as Photoregulated Oxidase-Like Nanozyme
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M. Venkateswarulu, Mrinmoy De, Sk Rajab Ali, Ennio Zangrando, Prodip Howlader, Soumalya Bhattacharyya, and Partha Sarathi Mukherjee
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Supramolecular chemistry ,Ethylenediamine ,General Chemistry ,010402 general chemistry ,01 natural sciences ,Biochemistry ,Combinatorial chemistry ,Acceptor ,Catalysis ,0104 chemical sciences ,Nanomaterials ,chemistry.chemical_compound ,Colloid and Surface Chemistry ,Nanocages ,chemistry ,Coordination cage ,Metal-organic framework - Abstract
Designing supramolecular architectures with uncommon geometries embedded with functional building units is of immense importance in contemporary research. In this report, we present a new water-soluble Pd12L6 supramolecular coordination nanocage (1) that was synthesized via self-assembly of a tetradentate donor (L) with ditopic acceptor cis-[(en)Pd(NO3)2] [en = ethylenediamine]. Self-assembly of a tetratopic donor with a cis-blocked 90° acceptor commonly produces tri/tetra- or hexagonal barrel-type structures. However, the resulting cage 1 has an uncommon geometry consisting of two triangular cupolas conjoined through an irregular common hexagonal base. Incorporation of the benzothiadiazole unit in the structure helped in the photogeneration of reactive oxygen species (ROS) in water. Many nanomaterials have shown to have the ability to mimic the catalytic activity of natural enzymes (nanozymes). Majority of such nanozymes are water insoluble metal/metal-oxide nanoparticles or extended metal organic frameworks (MOFs)/metal-carbon composites, etc. The present water-soluble Pd12 nanocage 1 has shown excellent oxidase-like activity upon irradiation with white light. The enzymatic activity of 1 is photoregulated which offers other obvious advantages, such as external control of enzymatic activity and noninvasiveness. The oxidase-like activity and exogenous ROS generation have been further exploited in photocatalytic antibacterial activity against methicillin-resistant Staphylococcus aureus (MRSA) bacterial strain.
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- 2020
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7. Self-Assembled PtII8 Metallosupramolecular Tubular Cage as Dual Warhead Antibacterial Agent in Water
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Mrinmoy De, Ennio Zangrando, Jagabandhu Sahoo, Soumalya Bhattacharyya, Partha Sarathi Mukherjee, and M. Venkateswarulu
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010405 organic chemistry ,Singlet oxygen ,Ligand ,Supramolecular chemistry ,010402 general chemistry ,01 natural sciences ,Combinatorial chemistry ,Fluorescence ,0104 chemical sciences ,Inorganic Chemistry ,chemistry.chemical_compound ,Membrane ,chemistry ,Photosensitizer ,Physical and Theoretical Chemistry ,Antibacterial activity ,Antibacterial agent - Abstract
Development of photosensitizer-based self-assembled metallosupramolecular architectures with important applications is an emerging trend in supramolecular chemistry. In this study, we report a new benzothiadiazole-based tetra-pyridyl ligand (L), which upon self-assembly with a cis-block 90° Pt(II) acceptor generated an unprecedented tetrafacial Pt(II)8 photoactive tubular molecular cage (PMB1). This cage could bring an extraordinary photosensitizer, benzothiadiazole, into water which is otherwise insoluble. PMB1 is fluorescent and shows photogeneration of singlet oxygen in an aqueous medium. These features make PMB1 a potent antimicrobial agent in water in both the presence and absence of light. In comparison to its building blocks and water-soluble alkylated charged ligand ([LMe4][4NO3]), the cage shows much enhanced photoinduced antibacterial activity against methicillin-resistant Staphylococcus aureus (MRSA) as a representative of Gram-positive bacteria and Pseudomonas aeruginosa (PA) as a representative of Gram-negative bacteria. PMB1 is successful at inactivating the bacterial growth via both photoactivation of molecular oxygen and membrane depolarization mechanisms, thus proving to be a dual warhead. Inactivation of bacteria in water using such a supramolecular architecture is noteworthy and can shed light on the generation of new antimicrobial supramolecular systems.
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- 2020
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8. Emissive Platinum(II) Macrocycles as Tunable Cascade Energy Transfer Scaffolds
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Koushik Acharyya, Soumalya Bhattacharyya, Shuai Lu, Yan Sun, Partha Sarathi Mukherjee, and Peter J. Stang
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Energy Transfer ,Water ,General Medicine ,General Chemistry ,Photosynthesis ,Hydrophobic and Hydrophilic Interactions ,Catalysis ,Platinum - Abstract
Developing artificial light-harvesting scaffolds with a cascade energy transfer process is significant for better understanding of photosynthesis. Here, we report [3+3] self-assembled Pt
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- 2022
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9. Silver(I)-Carbene Bond-Directed Rigidification-Induced Emissive Metallacage for Picric Acid Detection
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Prioti Choudhury Purba, Mangili Venkateswaralu, Soumalya Bhattacharyya, and Partha Sarathi Mukherjee
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Inorganic Chemistry ,Physical and Theoretical Chemistry - Abstract
A new triphenylamine-based tetraimidazolium salt
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- 2021
10. A Computationally Efficient Rayleigh–Ritz Model for Heterogeneous Oceanic Waveguides Using Fourier Series of Sound Speed Profile
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C. P. Vendhan, Soumalya Bhattacharyya, and A. D. Chowdhury
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Rayleigh–Ritz method ,Physics ,Acoustics and Ultrasonics ,Normal mode ,Wave propagation ,Applied Mathematics ,Acoustics ,Acoustic propagation ,Finite difference ,Sound speed profile ,Fourier series ,Finite element method ,Computer Science Applications - Abstract
The normal mode method is widely used in ocean acoustic propagation. Usually, finite difference and finite element methods are used in its solution. Recently, a method has been proposed for heterogeneous layered waveguides where the depth eigenproblem is solved using the classical Rayleigh–Ritz approximation. The method has high accuracy for low to high frequency problems. However, the matrices that appear in the eigenvalue problem for radial wavenumbers require numerical integration of the matrix elements since the sound speed and density profiles are numerically defined. In this paper, a technique is proposed to reduce the computational cost of the Rayleigh–Ritz method by expanding the sound speed profile in a Fourier series using nonlinear least square fit so that the integrals of the matrix elements can be computed in closed form. This technique is tested in a variety of problems and found to be sufficiently accurate in obtaining the radial wavenumbers as well as the transmission loss in a waveguide. The computational savings obtained by this approach is remarkable, the improvements being one or two orders of magnitude.
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- 2021
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11. Coordination-Assisted Reversible Photoswitching of Spiropyran-Based Platinum Macrocycles
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Sumit Kumar Panja, Soumalya Bhattacharyya, Peter J. Stang, Manik Lal Saha, Manoranjan Maity, Aniket Chowdhury, and Partha Sarathi Mukherjee
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Spiropyran ,Molecular switch ,Chemical substance ,Photoswitch ,010405 organic chemistry ,Supramolecular chemistry ,chemistry.chemical_element ,Nanotechnology ,010402 general chemistry ,01 natural sciences ,0104 chemical sciences ,Inorganic Chemistry ,Photochromism ,chemistry.chemical_compound ,chemistry ,Physical and Theoretical Chemistry ,Science, technology and society ,Platinum - Abstract
Control over the stimuli-responsive behavior of smart molecular systems can influence their capability to execute complex functionalities. Herein, we report the development of a suite of spiropyran-based multi-stimuli-responsive self-assembled platinum(II) macrocycles (5-7), rendering coordination-assisted enhanced photochromism relative to the corresponding ligands. 5 showed shrinking and swelling during photoreversal, while 6 and 7 are fast and fatigue-free supramolecular photoswitches. 6 turns out to be a better fatigue-resistant photoswitch and can retain an intact photoswitching ability of up to 20 reversible cycles. The switching behavior of the macrocycles can also be precisely controlled by tuning the pH of the medium. Our present strategy for the construction of rapid stimuli-responsive supramolecular architectures via coordination-driven self-assembly represents an efficient route for the development of smart molecular switches.
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- 2020
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12. Self-Assembled Fluorescent Pt(II) Metallacycles as Artificial Light-Harvesting Systems
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Soumalya Bhattacharyya, Shuai Lu, Peter J. Stang, Hajar Sepehrpour, Koushik Acharyya, Bingbing Shi, Xiaopeng Li, Partha Sarathi Mukherjee, Shubhadip Chakraborty, University of Utah, Indian Institute of Science, Institut de Physique de Rennes (IPR), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), Zhengzhou University, University of South Florida [Tampa] (USF), Science and Engineering Research Board, SERBFoundation for the National Institutes of Health, FNIH R01 CA215157CSIR - Indian Institute of Chemical Biology, CSIR-IICB, and Université de Rennes (UR)-Centre National de la Recherche Scientifique (CNRS)
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Models, Molecular ,Absorption spectroscopy ,010402 general chemistry ,Photochemistry ,Triphenylamine ,7. Clean energy ,01 natural sciences ,Biochemistry ,Article ,Catalysis ,Self assembled ,chemistry.chemical_compound ,Colloid and Surface Chemistry ,Organometallic Compounds ,Emission spectrum ,Photosynthesis ,Eosin Y ,Fluorescent Dyes ,Platinum ,[PHYS]Physics [physics] ,Ligand ,Spectrum Analysis ,General Chemistry ,Fluorescence ,Emission intensity ,0104 chemical sciences ,chemistry - Abstract
International audience; Light-harvesting is one of the key steps in photosynthesis, but developing artificial light-harvesting systems (LHSs) with high energy transfer efficiencies has been a challenging task. Here we report fluorescent hexagonal Pt(II) metallacycles as a new platform to fabricate artificial LHSs. The metallacycles (4 and 5) are easily accessible by coordination-driven self-assembly of a triphenylamine-based ditopic ligand 1 with di-platinum acceptors 2 and 3, respectively. They possess good fluorescence properties both in solution and in the solid state. Notably, the metallacycles show aggregation-induced emission enhancement (AIEE) characteristics in a DMSO-H2O solvent system. In the presence of the fluorescent dye Eosin Y (ESY), the emission intensities of the metallacycles decrease but the emission intensity of ESY increases. The absorption spectrum of ESY and the emission spectra of the metallacycles show a considerable overlap, suggesting the possibility of energy transfer from the metallacycles to ESY, with an energy transfer efficiency as high as 65% in the 4a+ESY system. © 2019 American Chemical Society.
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- 2019
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13. Self-Assembled Pt
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Soumalya, Bhattacharyya, Mangili, Venkateswarulu, Jagabandhu, Sahoo, Ennio, Zangrando, Mrinmoy, De, and Partha Sarathi, Mukherjee
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Methicillin-Resistant Staphylococcus aureus ,Singlet Oxygen ,Solubility ,Coordination Complexes ,Pseudomonas aeruginosa ,Water ,Anti-Bacterial Agents ,Platinum - Abstract
Development of photosensitizer-based self-assembled metallosupramolecular architectures with important applications is an emerging trend in supramolecular chemistry. In this study, we report a new benzothiadiazole-based tetra-pyridyl ligand (
- Published
- 2020
14. Multifunctional Self-Assembled Macrocycles with Enhanced Emission and Reversible Photochromic Behavior
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Rupak Saha, Soumalya Bhattacharyya, Partha Sarathi Mukherjee, and Aniket Chowdhury
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Spiropyran ,010405 organic chemistry ,010402 general chemistry ,Photochemistry ,01 natural sciences ,Fluorescence spectroscopy ,0104 chemical sciences ,Self assembled ,Inorganic Chemistry ,chemistry.chemical_compound ,Photochromism ,chemistry ,Physical and Theoretical Chemistry ,Bifunctional - Abstract
A series of self-assembled functional Pt(II) molecular hexagons (M1-M3) is reported. Hexagons M1 and M2 were designed employing aggregation induced emissive and photochromic building blocks, respectively, while macrocycle M3 is a bifunctional, containing both the kinds of building units. Hexagons M1 and M3 were found to inherit the enhanced emission with aggregate formation which was explored using UV-vis and fluorescence spectroscopy. The enhanced emission of macrocycle M3 compared to that of its building units was driven both by metal-ligand coordination and formation of nanoaggregates as evident from SEM, DLS and TEM analyses. Two of the macrocycles (M2 and M3) were also found to be photochromic due to the presence of spiropyran in the molecular backbone. Due to the virtue of protonation-deprotonation equilibrium of the spiropyran, these macrocycles (M2 and M3) showed reversible acidochromic behavior. Macrocycle M3 represents the first example of a self-assembled Pt(II) architecture which is multifunctional with aggregation-induced emission (AIE), photochromic, and acidochromic properties. This new generation macrocycle (M3) also showed coordination-driven enhanced emission and light-induced color change behavior compared to the starting building blocks. Our present approach of incorporating multiple functions into a single self-assembled structure with enhanced functionality compared to the starting building blocks via coordination self-assembly is noteworthy and has huge potential for the development of multifunctional materials.
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- 2019
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15. A Rayleigh-Ritz Model for the Depth Eigenproblem of Heterogeneous Pekeris Waveguides
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C. P. Vendhan, Anandita Chowdhury, Saba Mudaliar, and Soumalya Bhattacharyya
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Physics ,Rayleigh–Ritz method ,Acoustics and Ultrasonics ,0103 physical sciences ,Mathematical analysis ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,02 engineering and technology ,010301 acoustics ,01 natural sciences ,Music - Published
- 2018
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16. Linkage induced enhancement of fluorescence in metal-carbene bond directed metallacycles and metallacages
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Prioti Choudhury Purba, Partha Sarathi Mukherjee, Soumalya Bhattacharyya, Prodip Howlader, Sujay Mukhopadhyay, and Manoranjan Maity
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Linkage (mechanical) ,010402 general chemistry ,01 natural sciences ,Catalysis ,law.invention ,Metal ,chemistry.chemical_compound ,Transmetalation ,law ,Materials Chemistry ,Aggregation-induced emission ,Pyrrole ,010405 organic chemistry ,Metals and Alloys ,General Chemistry ,Metallacycle ,Fluorescence ,0104 chemical sciences ,Surfaces, Coatings and Films ,Electronic, Optical and Magnetic Materials ,Crystallography ,chemistry ,visual_art ,Ceramics and Composites ,visual_art.visual_art_medium ,Carbene - Abstract
Two new 1,4-dihydropyrrolo[3,2-b]pyrrole based aggregation induced emission (AIE)-inactive di- and tetra-imidazolium salts were employed with Ag(I) for the synthesis of a Ag–carbene bond directed metallacycle (1) and metallacage (2), respectively. Transmetalation of these complexes allowed their facile conversion to their respective Au(I)-metallacycle (3) and metallacage (4). The final assemblies exhibit linkage induced enhancement of fluorescence (LIEF). The free ligands are almost non-fluorescent (ΦF = 3.2, 3.4) in comparison to their metal–carbene counterparts (ΦF up to 32.0). Thus, without using any AIEgen, obtaining high emission efficiencies in complexes AgI–CNHC (1, 2) via linkage is a nice approach towards turn-on fluorescence.
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- 2019
17. Unusual Behavior of Donor-Acceptor Stenhouse Adducts in Confined Space of a Water-Soluble Pd
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Rupak, Saha, Anthonisamy, Devaraj, Soumalya, Bhattacharyya, Soumik, Das, Ennio, Zangrando, and Partha Sarathi, Mukherjee
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Donor-acceptor Stenhouse adducts (DASA) are new-generation photochromic compounds discovered recently. DASA exist normally in open form (blue/violet) and readily convert to cyclic (light yellow/colorless) zwitterionic form reversibly in the presence of green light in toluene/dioxane. In aqueous medium, the open form is not stable and converts to the cyclic zwitterionic form irreversibly. We report here a new self-assembled Pd
- Published
- 2019
18. Unusual Behavior of Donor-Acceptor Stenhouse Adducts in Confined Space of a Water-Soluble PdII8 Molecular Vessel
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Soumalya Bhattacharyya, Soumik Das, Ennio Zangrando, Anthonisamy Devaraj, Rupak Saha, Partha Sarathi Mukherjee, Saha, R., Devaraj, A., Bhattacharyya, S., Das, S., Zangrando, E., and Mukherjee, P. S.
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Stenhouse adducts ,crystal structure ,Chemistry ,photochromic compound ,octanuclear complex ,General Chemistry ,010402 general chemistry ,01 natural sciences ,Biochemistry ,Catalysis ,0104 chemical sciences ,Adduct ,Photochromism ,Colloid and Surface Chemistry ,Water soluble ,Polymer chemistry ,Open form ,Donor acceptor ,Confined space - Abstract
Donor–acceptor Stenhouse adducts (DASA) are new-generation photochromic compounds discovered recently. DASA exist normally in open form (blue/violet) and readily convert to cyclic (light yellow/colorless) zwitterionic form reversibly in the presence of green light in toluene/dioxane. In aqueous medium, the open form is not stable and converts to the cyclic zwitterionic form irreversibly. We report here a new self-assembled Pd8 molecular vessel (MV) that can stabilize and store the open form of DASA even in aqueous medium. Reaction of the 90° acceptor cis-(tmeda)Pd(NO3)2 (M) [tmeda = N,N,N′,N′-tetramethylethane-1,2-diamine] with a symmetric tetraimidazole donor (L, 3,3′,5,5′-tetra(1H-imidazol-1-yl)-1,1′-biphenyl) in a 2:1 molar ratio yielded a water-soluble [8+4] self-assembled M8L4 molecular barrel (MV). This barrel (MV) is found to be a potential molecular vessel to store and stabilize the open forms of DASA in aqueous medium over the more stable zwitterionic cyclic form, while in the absence of the barrel the same DASA exist in cyclic zwitterionic form in aqueous medium. The hydrophobic interaction between the cavity and the open form of DASA molecules benefits reaching an out-of-equilibrium or reverse equilibrium state in aqueous medium. The presence of excess MV could even drive the conversion of the stable cyclic form to the open form in aqueous medium. The host–guest complex is stable upon irradiating with green light. To the best of our knowledge, this is the first successful attempt to stabilize the open form of DASA molecules in aqueous medium and the first report on the fate of DASA in a confined space discrete molecular architecture. Furthermore, the molecular vessel has been utilized for catalytic Michael addition reactions of a series of nitrostyrene derivatives with 1,3-indandione in aqueous medium.
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- 2019
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19. Borate-based ligands with soft heterocycles and their ruthenium complexes
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Sundargopal Ghosh, Venkatachalam Ramkumar, Rosmita Borthakur, Dipak Kumar Roy, and Soumalya Bhattacharyya
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Atoms ,Cyclic voltammetry ,Ruthenium complexes ,Synthetic precursors ,Inorganic chemistry ,chemistry.chemical_element ,Ligands ,Mass spectrometry ,Biochemistry ,Medicinal chemistry ,Ruthenium ,Linkage isomerism ,Isomers ,Inorganic Chemistry ,Metal ,Stereochemistry ,Materials Chemistry ,Physical and Theoretical Chemistry ,Boron ,Nuclear magnetic resonance spectroscopy ,Borate ,Ligand ,Ruthenium compounds ,Organic Chemistry ,Sulfur ,Chlorine compounds ,chemistry ,Crystallographic analysis ,Scorpionate ,visual_art ,visual_art.visual_art_medium ,Coordination reactions ,Oxidation potentials ,2-mercaptobenzothiazole - Abstract
In a quest for effective synthetic precursors for the preparation of B-agostic complexes of ruthenium, we have shown that the reaction of [Cp?RuCl2]2 (Cp? = ?5-C5Me5) with [NaBt] or [NaBo] (Bt = dihydrobis(2-mercaptobenzthiazolyl)borate, Bo = dihydrobis(2-mercaptobenzoxazolyl)borate) led to the formation of B-agostic complexes [Cp?RuBH2L2], 1a,b (1a: L = 2-mercaptobenzthiazol, 1b: L = 2-mercaptobenzoxazol) and [Cp?RuBH3L], 2a,b (2a: L = 2-mercaptobenzthiazol, 2b: L = 2-mercaptobenzoxazol) in good yields. In parallel to the formation of 1a,b and 2a,b, this method also allowed the formation of ruthenium hydrotrisborate complexes [Cp?RuBYL3], 3a-c (3a: L = 2-mercaptobenzthiazol, Y = H, 3b: L = 2-mercaptobenzoxazol, Y = H, 3c: L = 2-mercaptobenzoxazol, Y = Cl). The key feature of complexes 3a-c is the coordination of one of the 2-mercaptobenzothiazole ligand that connects to the metal and the boron centre through a common sulfur atom. Upon heating, compounds 3a,b change into their corresponding S?N linkage isomers, in which the boron atom is bonded to three nitrogen atoms. The cyclic voltammetric studies on compounds 3a-c and 4a,b suggest that a deviation in coordination of the ligand change the oxidation potential of the metal centre. All the new compounds have been characterized in solution by 1H, 11B and 13C NMR spectroscopy, mass spectrometry and the structural types of 3a-c and 4b were unequivocally established by crystallographic analysis. � 2015 Elsevier B.V. All rights reserved.
- Published
- 2015
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20. Eigenproblem for an ocean acoustic waveguide with random depth dependent sound speed
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A. Datta Chowdhury, C. P. Vendhan, Soumalya Bhattacharyya, and Saba Mudaliar
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business.industry ,Mathematical analysis ,Perturbation (astronomy) ,Near and far field ,Finite element method ,symbols.namesake ,Optics ,Speed of sound ,Taylor series ,symbols ,Wavenumber ,Waveguide (acoustics) ,business ,Random variable ,Mathematics - Abstract
A recently developed deterministic FE model for range and depth dependent acoustic waveguides (Vendhan et al, J. Acoust. Am., 126, 3319–3326, 2010) may be extended to a medium with random properties. Such a model would require the eigensolution for a depth dependent waveguide at the far field of the FE domain. The aim of the present paper is to study the depth eigenproblem with random sound speed, which may be written as d2Z/dz2 + (1/k1 z )Z = 0 (1) where z denotes the depth coordinate, Z(z) the depth function and k z the depth wavenumber given by k2 z = (ω2/c2(z)-k1 r ) (2) In Eq.2, r k denotes the radial wavenumber of a cylindrically symmetric waveguide and c(z) the sound speed which is assumed to be random variable in the form c(z) = c (z) (1+a) where a denotes a small random fluctuation of the sound speed with c(z)as the mean value. The depth eigenmodes of a deterministic isovelocity waveguide are adopted to set up a Rayleigh-Ritz approximation for the depth eigenproblem (see Eq.1) in the form [K]{ψ} = λ [M]{ψ} (3) Choosing a perturbation approach (Nakagiri and Hisada, Proc. Intl. Conf. on FEM, 206–211, 1982; Ghanem and Spanos, Stochastic Finite Elements: A Spectral Approach, Springer Verlag, 1991) an approximate solution may be written in the form of a Taylor series as [M] = [M] + α [M 1 ] + α2/2[M 2 ] (4a)λ = λ + αλ 1 + (α2/2)λ 2 (4b){ψ} = {ψ} + α{ψ 1 } + α2/2{ψ 2 } (4c) where an over bar denotes deterministic quantity.
- Published
- 2014
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