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1.
Inorg Chem ; 60(10): 6930-6938, 2021 May 17.
Artículo en Inglés | MEDLINE | ID: mdl-33792308

RESUMEN

Heterogeneous catalysis based on air-stable lanthanide complexes is relatively rare, especially for electrochemical water oxidation and reduction. Therefore, it is highly desired to investigate the synergy caused by cocatalysts on the lanthanide complex family for heterogeneous catalysis because of their structural diversity, air/moisture insensitivity, and easy preparation under an air atmosphere. Two mononuclear and three dinuclear dysprosium complexes containing a series of Schiff-base ligands have been demonstrated as robust electrocatalysts for triggering heterogeneous water oxidation in alkaline solution, in which the complex [Dy2(hmb)2(OAc)4]·MeCN(3) was revealed to have the best activity toward heterogeneous water oxidation among all five complexes in the present study. The molecular activation of dysprosium complexes has also been investigated with a series of N-containing heterocyclic additives [i.e., 4-(dimethylamino)pyridine (DMAP), bis(triphenylphosphine)iminium chloride ([PPN]Cl), indole, and quinoline]. In particular, the corresponding overpotential was effectively enhanced by 211 mV (at a current density of 10 mA cm-2) with the assistance of DMAP. On the basis of electrochemical and ex situ/in situ spectroscopic investigations, the best catalyst, DMAP-complex 3 on a carbon paper electrode, was confirmed with well-maintained molecular identity during heterogeneous water oxidation free of forming any dysprosium oxide and/or undesired products.

2.
Inorg Chem ; 57(20): 12448-12451, 2018 Oct 15.
Artículo en Inglés | MEDLINE | ID: mdl-30260216

RESUMEN

The effect of the directions of the anisotropy axes on the energy barriers of single-molecule magnets (SMMs) was investigated. By introducing nitrophenolate (NP)-type coligands with different substitutions, the energy barrier was significantly changed. The structural and magnetic properties of three novel SMMs based on trinuclear {Dy3O5} phenoxo- and methoxyl-bridged triangular motifs were explored. All complexes share the formula [Dy3(Hhmb)4(µ3-OMe)2(OMe)(NP)][Dy3(Hhmb)4(µ3-OMe)2(NP)]·solvent·3Cl, where Hhmb = (2-hydroxy-3-methoxyphenyl)methylene(benzoicotino)hydrazine, secondary ligand NP = 2-nitrophenol (2-NP, complex 1), 2,4-dinitrophenol (2,4-DNP, complex 2), and 2,4,6-trinitrophenol (2,4,6-TNP, complex 3), and solvent = 2MeOH·2Et2O (1) and 4MeOH (2 and 3). Magnetic measurements for 1 and 2 revealed observable slow magnetic relaxation behavior with anisotropic energy barriers of 12.18 and 4.96 K, respectively, for SMMs and only the tail of the peaks in the out-of-phase susceptibility, χ″, was observed in complex 3. Comparing a series of NP coligands, we could easily study the correlation between the directions of the anisotropic axes and magnetic properties for this trinuclear SMM system.

3.
Inorg Chem ; 55(12): 6095-9, 2016 Jun 20.
Artículo en Inglés | MEDLINE | ID: mdl-27281290

RESUMEN

Inspired by the ferromagnetic coupling in the cubane model CaMn(IV)3O4 of the oxygen-evolving complex of photosystem II, 3d-4f mixed-metal DyMn3O4 clusters were prepared for investigation of the magnetic properties. For comparison, YMn(IV)3O4 and YMn(IV)2Mn(III)O4 clusters were investigated as well and showed ferromagnetic interactions, like the calcium analogue. DyMn(IV)3O4 displays single-molecule-magnet properties, while the one-electron-reduced species (DyMn(IV)2Mn(III)O4) does not, despite the presence of a Mn(III) center with higher spin and single-ion anisotropy.


Asunto(s)
Manganeso/química , Espectroscopía de Resonancia por Spin del Electrón , Oxidación-Reducción
4.
Langmuir ; 31(23): 6538-45, 2015 Jun 16.
Artículo en Inglés | MEDLINE | ID: mdl-26030343

RESUMEN

Palladium octahedra, truncated octahedra, cuboctahedra, truncated cubes, and nanocubes with sizes of tens of nanometers have been synthesized in an aqueous mixture of H2PdCl4 solution, cetyltrimethylammonium chloride (CTAC) surfactant, KBr solution, dilute KI solution, and ascorbic acid solution at 35 °C for 30 min. By tuning the amount of dilute KBr solution introduced, particle shape control can be achieved. Adjusting the volumes of the Pd precursor and KBr solutions added, smaller and larger Pd nanocrystals were obtained with excellent shape control. Extensive structural and optical characterization of these nanocrystals has been performed. Two absorption bands in the ultraviolet region can be discerned for these Pd nanocrystals. Concave Pd cubes can also be prepared. Pd cubes were found to grow at a faster rate than that for the formation of octahedra. The concentrations of KBr and KI in the solution are so low that spectral shifts were not detected upon their addition to the solution. The Pd nanocrystals can readily be used for various applications after simple removal of surfactant.

5.
Inorg Chem ; 54(1): 59-64, 2015 Jan 05.
Artículo en Inglés | MEDLINE | ID: mdl-25521310

RESUMEN

We report the syntheses and electrochemical properties of nine new clusters ([LLnMn(IV)3O4(OAc)3(DMF)n](+) (Ln = La(3+), Ce(3+), Nd(3+), Eu(3+), Gd(3+), Tb(3+), Dy(3+), Yb(3+), and Lu(3+), n = 2 or 3)) supported by a ligand (L(3-)) based on a 1,3,5-triarylbenzene motif appended with alkoxide and pyridine donors. All complexes were obtained by metal substitution of Ca(2+) with lanthanides upon treatment of previously reported LMn3CaO4(OAc)3(THF) with Ln(OTf)3. Structural characterization confirmed that the clusters contain the [LnMn3O4] cubane motif. The effect of the redox-inactive centers on the electronic properties of the Mn3O4 cores was investigated by cyclic voltammetry. A linear correlation between the redox potential of the cluster and the ionic radii or pKa of the lanthanide metal ion was observed. Chemical reduction of the LMn(IV)3GdO4(OAc)3(DMF)2 cluster with decamethylferrocene, resulted in the formation of LGdMn(IV)2Mn(III)O4(OAc)3(DMF)2, a rare example of mixed-valence [MMn3O4] cubane. The lanthanide-coordinated ligands can be substituted with other donors, including water, the biological substrate.


Asunto(s)
Derivados del Benceno/química , Elementos de la Serie de los Lantanoides/química , Compuestos Organometálicos/química , Oxígeno/química , Complejo de Proteína del Fotosistema II/química , Calcio/química , Técnicas Electroquímicas , Evolución Molecular , Compuestos Ferrosos/química , Manganeso/química , Compuestos Organometálicos/síntesis química , Oxidación-Reducción , Piridinas/química , Agua/química
6.
J Am Chem Soc ; 136(41): 14373-6, 2014 Oct 15.
Artículo en Inglés | MEDLINE | ID: mdl-25241826

RESUMEN

Synthetic model compounds have been targeted to benchmark and better understand the electronic structure, geometry, spectroscopy, and reactivity of the oxygen-evolving complex (OEC) of photosystem II, a low-symmetry Mn4CaOn cluster. Herein, low-symmetry Mn(IV)3GdO4 and Mn(IV)3CaO4 cubanes are synthesized in a rational, stepwise fashion through desymmetrization by ligand substitution, causing significant cubane distortions. As a result of increased electron richness and desymmetrization, a specific µ3-oxo moiety of the Mn3CaO4 unit becomes more basic allowing for selective protonation. Coordination of a fifth metal ion, Ag(+), to the same site gives a Mn3CaAgO4 cluster that models the topology of the OEC by displaying both a cubane motif and a "dangler" transition metal. The present synthetic strategy provides a rational roadmap for accessing more accurate models of the biological catalyst.


Asunto(s)
Calcio/química , Manganeso/química , Oxígeno/química , Complejo de Proteína del Fotosistema II/química , Calcio/metabolismo , Electrones , Ligandos , Manganeso/metabolismo , Modelos Moleculares , Estructura Molecular , Oxígeno/metabolismo , Complejo de Proteína del Fotosistema II/metabolismo
7.
Chemistry ; 20(18): 5327-37, 2014 Apr 25.
Artículo en Inglés | MEDLINE | ID: mdl-24664616

RESUMEN

The reaction of (µ-Cl)2Ni2(NHC)2 (NHC = 1,3-bis(2,6-diisopropylphenyl)-1,3-dihydro-2H-imidazol-2-ylidene (IPr) or 1,3-bis(2,6-diisopropylphenyl)imidazolidin-2-ylidene (SIPr)) with either one equivalent of sodium cyclopentadienyl (NaCp) or lithium indenyl (LiInd) results in the formation of diamagnetic NHC supported Ni(I) dimers of the form (µ-Cp)(µ-Cl)Ni2(NHC)2 (NHC = IPr (1 a) or SIPr (1 b); Cp = C5H5) or (µ-Ind)(µ-Cl)Ni2(NHC)2 (NHC = IPr (2 a) or SIPr (2 b); Ind = C7H9), which contain bridging Cp and indenyl ligands. The corresponding reaction between two equivalents of NaCp or LiInd and (µ-Cl)2Ni2(NHC)2 (NHC = IPr or SIPr) generates unusual 17 valence electron Ni(I) monomers of the form (η(5)-Cp)Ni(NHC) (NHC = IPr (3 a) or SIPr (3 b)) or (η(5)-Ind)Ni(NHC) (NHC = IPr (4 a) or SIPr (4 b)), which have nonlinear geometries. A combination of DFT calculations and NBO analysis suggests that the Ni(I) monomers are more strongly stabilized by the Cp ligand than by the indenyl ligand, which is consistent with experimental results. These calculations also show that the monomers have a lone unpaired-single-electron in their valence shell, which is the reason for the nonlinear structures. At room temperature the Cp bridged dimer (µ-Cp)(µ-Cl)Ni2(NHC)2 undergoes homolytic cleavage of the Ni-Ni bond and is in equilibrium with (η(5)-Cp)Ni(NHC) and (µ-Cl)2Ni2(NHC)2. There is no evidence that this equilibrium occurs for (µ-Ind)(µ-Cl)Ni2(NHC)2. DFT calculations suggest that a thermally accessible triplet state facilitates the homolytic dissociation of the Cp bridged dimers, whereas for bridging indenyl species this excited triplet state is significantly higher in energy. In stoichiometric reactions, the Ni(I) monomers (η(5)-Cp)Ni(NHC) or (η(5)-Ind)Ni(NHC) undergo both oxidative and reductive processes with mild reagents. Furthermore, they are rare examples of active Ni(I) precatalysts for the Suzuki-Miyaura reaction. Complexes 1 a, 2 b, 3 a, 4 a and 4 b have been characterized by X-ray crystallography.

8.
J Opt Soc Am A Opt Image Sci Vis ; 31(1): 16-20, 2014 Jan 01.
Artículo en Inglés | MEDLINE | ID: mdl-24561934

RESUMEN

Effective methods for speckle reduction are essential in improving the image quality of laser imaging applications. Accordingly, the present study proposes a novel technique for reducing the speckle contrast in laser imaging applications by means of the magneto-optic Kerr effect induced by a rotating magneto-optical (MO) disk. The performance of the proposed method is evaluated experimentally using a laboratory-built prototype model. The experimental results show that the rotating MO disk can reduce the speckle contrast of the captured image by 60% of the previous value. As a result, the proposed method yields an effective improvement in image quality. Overall, the proposed method provides a promising solution for improving the performance of a wide range of laser imaging applications.

9.
Comput Methods Programs Biomed ; 254: 108260, 2024 May 31.
Artículo en Inglés | MEDLINE | ID: mdl-38878357

RESUMEN

BACKGROUND AND OBJECTIVE: Proteome microarrays are one of the popular high-throughput screening methods for large-scale investigation of protein interactions in cells. These interactions can be measured on protein chips when coupled with fluorescence-labeled probes, helping indicate potential biomarkers or discover drugs. Several computational tools were developed to help analyze the protein chip results. However, existing tools fail to provide a user-friendly interface for biologists and present only one or two data analysis methods suitable for limited experimental designs, restricting the use cases. METHODS: In order to facilitate the biomarker examination using protein chips, we implemented a user-friendly and comprehensive web tool called BAPCP (Biomarker Analysis tool for Protein Chip Platforms) in this research to deal with diverse chip data distributions. RESULTS: BAPCP is well integrated with standard chip result files and includes 7 data normalization methods and 7 custom-designed quality control/differential analysis filters for biomarker extraction among experiment groups. Moreover, it can handle cost-efficient chip designs that repeat several blocks/samples within one single slide. Using experiments of the human coronavirus (HCoV) protein microarray and the E. coli proteome chip that helps study the immune response of Kawasaki disease as examples, we demonstrated that BAPCP can accelerate the time-consuming week-long manual biomarker identification process to merely 3 min. CONCLUSIONS: The developed BAPCP tool provides substantial analysis support for protein interaction studies and conforms to the necessity of expanding computer usage and exchanging information in bioscience and medicine. The web service of BAPCP is available at https://cosbi.ee.ncku.edu.tw/BAPCP/.

10.
J Am Chem Soc ; 134(12): 5598-609, 2012 Mar 28.
Artículo en Inglés | MEDLINE | ID: mdl-22428955

RESUMEN

Ammonia-borane (NH(3)BH(3), AB) has garnered interest as a hydrogen storage material due to its high weight percent hydrogen content and ease of H(2) release relative to metal hydrides. As a consequence of dehydrogenation, B-N-containing oligomeric/polymeric materials are formed. The ability to control this process and dictate the identity of the generated polymer opens up the possibility of the targeted synthesis of new materials. While precious metals have been used in this regard, the ability to construct such materials using earth-abundant metals such as Fe presents a more economical approach. Four Fe complexes containing amido and phosphine supporting ligands were synthesized, and their reactivity with AB was examined. Three-coordinate Fe(PCy(3))[N(SiMe(3))(2)](2) (1) and four-coordinate Fe(DEPE)[N(SiMe(3))(2)](2) (2) yield a mixture of (NH(2)BH(2))(n) and (NHBH)(n) products with up to 1.7 equiv of H(2) released per AB but cannot be recycled (DEPE = 1,2-bis(diethylphosphino)ethane). In contrast, Fe supported by a bidentate P-N ligand (4) can be used in a second cycle to afford a similar product mixture. Intriguingly, the symmetric analogue of 4 (Fe(N-N)(P-P), 3), only generates (NH(2)BH(2))(n) and does so in minutes at room temperature. This marked difference in reactivity may be the result of the chemistry of Fe(II) vs Fe(0).

11.
Langmuir ; 28(30): 11258-64, 2012 Jul 31.
Artículo en Inglés | MEDLINE | ID: mdl-22809109

RESUMEN

In this work, palladium tripod nanocrystals have been synthesized by mixing an aqueous solution of cetyltrimethylammonium bromide (CTAB) surfactant, Na(2)PdCl(4), copper acetate, and ascorbic acid at 30 °C for 3 h. Addition of a small amount of copper ion source is critical to the formation of these tripods with a pod length reaching 100 nm. The incorporation of Cu atoms into the Pd tripods has been verified. The entire Pd tripod is single-crystalline with their branches growing along the [111] and [200] directions. Formation of side branches can be observed in some tripods. Triangular nanoplates are initially formed and evolved into the tripod structure in 20-30 min of reaction. Further growth leads to elongation of the pods. The large Pd tripods can serve as active and recyclable catalysts for a broad range of Sonogashira coupling reactions in water using a variety of aromatic halides containing electron-donating and -withdrawing substituents.

12.
Comput Struct Biotechnol J ; 20: 1295-1305, 2022.
Artículo en Inglés | MEDLINE | ID: mdl-35356542

RESUMEN

Kawasaki disease (KD) is a form of acute systemic vasculitis that primarily affects children and has become the most common cause of acquired heart disease. While the etiopathogenesis of KD remains unknown, the diagnostic criteria of KD have been well established. Nevertheless, the diagnosis of KD is currently based on subjective clinical symptoms, and no molecular biomarker is yet available. We have previously performed and combined methylation array (Illumina HumanMethylation450 BeadChip) and transcriptome array (Affymetrix GeneChip Human Transcriptome Array 2.0) to identify genes that are differentially methylated/expressed in KD patients compared with control subjects. We have found that decreased methylation levels combined with elevated gene expression can indicate genes (e.g., toll-like receptors and CD177) involved in the disease mechanisms of KD. In this study, we constructed a database called KDmarkers to allow researchers to access these valuable potential KD biomarkers identified via methylation array and transcriptome array. KDmarkers provides three search modes. First, users can search genes differentially methylated and/or differentially expressed in KD patients compared with control subjects. Second, users can check the KD patient groups in which a given gene is differentially methylated and/or differentially expressed. Third, users can explore the DNA methylation levels and gene expression levels in all samples (KD patients and controls) for a particular gene of interest. We further demonstrated that the results in KDmarkers are strongly associated with KD immune responses. All analysis results can be downloaded for downstream experimental designs. KDmarkers is available online at https://cosbi.ee.ncku.edu.tw/KDmarkers/.

13.
J Am Chem Soc ; 133(40): 15814-7, 2011 Oct 12.
Artículo en Inglés | MEDLINE | ID: mdl-21899323

RESUMEN

Bis(imino)pyridine pincer ligands in conjunction with two isothiocyanate ligands have been used to prepare two mononuclear Co(II) complexes. Both complexes have a distorted square-pyramidal geometry with the Co(II) centers lying above the basal plane. This leads to significant spin-orbit coupling for the d(7) Co(II) ions and consequently to slow relaxation of the magnetization that is characteristic of Single-Molecule Magnet (SMM) behavior.

14.
J Am Chem Soc ; 133(23): 8830-3, 2011 Jun 15.
Artículo en Inglés | MEDLINE | ID: mdl-21563820

RESUMEN

The magnetic dilution method was employed in order to elucidate the origin of the slow relaxation of the magnetization in a Dy(2) single-molecule magnet (SMM). The doping effect was studied using SQUID and micro-SQUID measurements on a Dy(2) SMM diluted in a diamagnetic Y(2) matrix. The quantum tunneling of the magnetization that can occur was suppressed by applying optimum dc fields. The dominant single-ion relaxation was found to be entangled with the neighboring Dy(III) ion relaxation within the molecule, greatly influencing the quantum tunneling of the magnetization in this complex.

15.
J Am Chem Soc ; 133(48): 19286-9, 2011 Dec 07.
Artículo en Inglés | MEDLINE | ID: mdl-22032273

RESUMEN

A dysprosium(III) sandwich complex, [Dy(III)(COT″)(2)Li(THF)(DME)], was synthesized using 1,4-bis(trimethylsilyl)cyclooctatetraenyl dianion (COT″). The complex behaves as a single-ion magnet and demonstrates unusual multiple relaxation modes. The observed relaxation pathways strongly depend on the applied static dc fields.

16.
J Am Chem Soc ; 133(49): 19993-20000, 2011 Dec 14.
Artículo en Inglés | MEDLINE | ID: mdl-22091631

RESUMEN

By using octahedral gold nanocrystals with sizes of approximately 50 nm as the structure-directing cores for the overgrowth of Pd shells, Au-Pd core-shell heterostructures with systematic shape evolution can be directly synthesized. Core-shell octahedra, truncated octahedra, cuboctahedra, truncated cubes, and concave cubes were produced by progressively decreasing the amount of the gold nanocrystal solution introduced into the reaction mixture containing cetyltrimethylammonium bromide (CTAB), H(2)PdCl(4), and ascorbic acid. The core-shell structure and composition of these nanocrystals has been confirmed. Only the concave cubes are bounded by a variety of high-index facets. This may be a manifestation of the release of lattice strain with their thick shells at the corners. Formation of the [CTA](2)[PdBr(4)] complex species has been identified spectroscopically. Time-dependent UV-vis absorption spectra showed faster Pd source consumption rates in the growth of truncated cubes and concave cubes, while a much slower reduction rate was observed in the generation of octahedra. The concave cubes and octahedra were used as catalysts for a Suzuki coupling reaction. They can all serve as effective and recyclable catalysts, but the concave cubes gave higher product yields with a shorter reaction time attributed to their high-index surface facets. The concave cubes can also catalyze a wide range of Suzuki coupling reactions using aryl iodides and arylboronic acids with electron-donating and -withdrawing substituents.

17.
J Am Chem Soc ; 133(14): 5319-28, 2011 Apr 13.
Artículo en Inglés | MEDLINE | ID: mdl-21425794

RESUMEN

A family of five dinuclear lanthanide complexes has been synthesized with general formula [Ln(III)(2)(valdien)(2)(NO(3))(2)] where (H(2)valdien = N1,N3-bis(3-methoxysalicylidene)diethylenetriamine) and Ln(III) = Eu(III)1, Gd(III)2, Tb(III)3, Dy(III)4, and Ho(III)5. The magnetic investigations reveal that 4 exhibits single-molecule magnet (SMM) behavior with an anisotropic barrier U(eff) = 76 K. The step-like features in the hysteresis loops observed for 4 reveal an antiferromagnetic exchange coupling between the two dysprosium ions. Ab initio calculations confirm the weak antiferromagnetic interaction with an exchange constant J(Dy-Dy) = -0.21 cm(-1). The observed steps in the hysteresis loops correspond to a weakly coupled system similar to exchange-biased SMMs. The Dy(2) complex is an ideal candidate for the elucidation of slow relaxation of the magnetization mechanism seen in lanthanide systems.

18.
J Am Chem Soc ; 133(40): 15806-9, 2011 Oct 12.
Artículo en Inglés | MEDLINE | ID: mdl-21894963

RESUMEN

Two mononuclear high-spin Fe(II) complexes with trigonal planar ([Fe(II)(N(TMS)(2))(2)(PCy(3))] (1) and distorted tetrahedral ([Fe(II)(N(TMS)(2))(2)(depe)] (2) geometries are reported (TMS = SiMe(3), Cy = cyclohexyl, depe = 1,2-bis(diethylphosphino)ethane). The magnetic properties of 1 and 2 reveal the profound effect of out-of-state spin-orbit coupling (SOC) on slow magnetic relaxation. Complex 1 exhibits slow relaxation of the magnetization under an applied optimal dc field of 600 Oe due to the presence of low-lying electronic excited states that mix with the ground electronic state. This mixing re-introduces orbital angular momentum into the electronic ground state via SOC, and 1 thus behaves as a field-induced single-molecule magnet. In complex 2, the lowest-energy excited states have higher energy due to the ligand field of the distorted tetrahedral geometry. This higher energy gap minimizes out-of-state SOC mixing and zero-field splitting, thus precluding slow relaxation of the magnetization for 2.

19.
Inorg Chem ; 50(15): 7059-65, 2011 Aug 01.
Artículo en Inglés | MEDLINE | ID: mdl-21736368

RESUMEN

The syntheses, structures, and magnetic properties are reported for four new lanthanide clusters [Sm(4)(µ(3)-OH)(2)L(2)(acac)(6)]·4H(2)O (1), [Gd(4)(µ(3)-OH)(2)L(2)(acac)(6)]·4CH(3)CN (2), and [Ln(4)(µ(3)-OH)(2)L(2)(acac)(6)]·2H(2)L·2CH(3)CN (3, Ln = Tb; 4, Ln = Dy) supported by salen-type (H(2)L = N,N'-bis(salicylidene)-1,2-cyclohexanediamine) and ß-diketonate (acac = acetylacetonate) ligands. The four clusters were confirmed to be essentially isomorphous by infrared spectroscopy and single-crystal X-ray diffraction. Their crystal structures reveal that the salen-type ligand provides a suitable tetradentate coordination pocket (N(2)O(2)) to encapsulate lanthanide(III) ions. Moreover, the planar Ln(4) core is bridged by two µ(3)-hydroxide, four phenoxide, and two ketonate oxygen atoms. Magnetic properties of all four compounds have been investigated using dc and ac susceptibility measurements. For 4, the static and dynamic data indicate that the Dy(4) complex exhibits slow relaxation of the magnetization below 5 K associated with single-molecule magnet behavior.

20.
Dalton Trans ; 51(1): 69-73, 2021 Dec 20.
Artículo en Inglés | MEDLINE | ID: mdl-34897306

RESUMEN

The control of the self-assembly of lanthanide helical chain and their helical handedness have been investigated for the first time. Δ- and Λ-form lanthanide chain complexes were obtained by introducing thiazolidine ligands that were synthesised from L- and D-cysteine, respectively, and shared the same formula: [Ln2(L)3(H2O)5]∞·3H2O (Ln: Sm and Eu) (L: 2-(2-hydroxy-3,5-dinitrophenyl)thiazolidine-4-carboxylic acid). The crystallographic, circular dichroism, and luminescence properties of these novel lanthanide chain complexes were studied.

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