First integrals for Finsler metrics with vanishing $$\chi $$ -curvature

Annals of Global Analysis and Geometry - We prove that in a Finsler manifold with vanishing $$\chi $$ -curvature (in particular with constant flag curvature) some non-Riemannian geometric...     

Structural and magnetic investigations of the mixed-valence Fe(II,III) two-dimensional layer complex, [Fe2(II) Fe2(III)(HCOO)10(C6H7N)6]n.

The structure of the complex, [Fe2(II)Fe2(III)(HCOO)10(C6H7N6)n, (1) exhibits a neutral two-dimensional layer network of alternating iron(II) and iron(III) ions, bridged equatorially by formate groups. All iron atoms are octahedrally coordinated, with iron(III) coordinating axially to one gamma-picoline and one formate group, while the iron(II) centers interact axially with two gamma-picoline groups, above and below the layer plane. The complex crystallizes in the triclinic space group P1 at all studied temperatures [at 120 K, the cell dimensions are: a = 10.228(1), b = 12.071(1), c = 12.072(1) A, alpha = 89.801(2), beta = 71.149(2), gamma = 73.371(2) degrees]. An intralayer antiferromagnetic exchange interaction of J = -2.8 cm(-1) between iron(II) and iron(III) was observed in the magnetic studies. Decreasing the temperature to close to 20 K causes a magnetic-ordering phenomenon to occur and a low-temperature phase with a long-range antiferromagnetic spin orientation appears. The magnetic phase transition was confirmed by M?ssbauer spectroscopic studies at temperatures above and below the critical temperature. Structural information of 1 from synchrotron X-ray diffraction data collected at room temperature and 16 K suggests that the antiferromagnetic ordering is caused by an enhanced pi-pi interaction between chi-picoline groups from adjacent layers.     

New ferrocene-containing structures: Poly(silyl ester)s

Two new polymeric structures containing ferrocene units along the chains, namely poly(silyl ester)s, have been synthesized and characterized: a geminal poly(silyl ester) (g-PSE) and one having a disiloxane spacer between the silyl ester groups (s-PSE). The condensation polymerization of AA/BB monomer systems in solution was used in both cases as preparation method involving a silicon-containing diol, (diphenylsilane diol or 1,3-bis(hydroxy)-tetramethyldisiloxane), and 1,1′-di(chlorocarbonyl)ferrocene. The polymers were investigated by differential pulse voltammetry in order to evaluate the redox behavior. Due to the presence of the silyl ester groups in the chain, these polymers are hydrolytically degradable.     

Studies of chromium cages and wheels

Studies of two distinct classes of chromium(III) cage complexes are discussed. The first are compact oxo- and carboxylate cages, made by heating precursors to high temperature under a flow of nitrogen. One of these cages, [Cr₁₂O₉(OH)₃(O₂CCMe₃)₁₅], has an S = 6 spin ground state which proves a very interesting subject for study by EPR and MCD spectroscopy. Use of other carboxylates leads to other octa- and dodeca-nuclear complexes. The second class of compounds are homo- and hetero-metallic wheels and chains bridged by fluoride and carboxylates. These include the first heterometallic anti-ferromagnetically coupled ring systems and are being widely studied in areas as diverse as magnetic cooling and quantum information processing. The mechanism by which these unusual cyclic and acyclic structures form is discussed.     

Phenylmercury(II) derivatives of tetraorganodichalcogenoimidodiphosphorus acids. Crystal and molecular structure of [PhHg{(OPR2)(SPPh2)N}]2 (R=Me, Ph)

The reactions between PhHgCl or PhHgAc and M[(XPR₂)(YPR′₂)N] (M=Na, K; X, Y=O, S; R, R′=Me, Ph, OEt), in 1:1 molar ratio, have been investigated. PhHg[(XPR₂)(YPR′₂)N] derivatives were isolated as microcrystalline powders and were characterised using IR and NMR (¹H, ¹³C and ³¹P) spectroscopy and mass spectrometry. The molecular structure of PhHg[(OPR₂)(SPPh₂)N] [R=Me (1), Ph (2)] was investigated by X-ray diffraction. In the monomeric unit, PhHg[(OPR₂)(SPPh₂)N], the mercury atom forms the primary bonds with the carbon of the phenyl group and the sulfur atom of the phosphorus ligand [Hg(1)-S(1) 2.405(1) Å for 1, 2.398(2) Å for 2]. These primary bonds are significantly deviated from the expected linear arrangement [C(1)-Hg(1)-S(1) 166.4(2)° for 1, 165.0(2)° for 2]. Both compounds exhibit dimeric associations in the crystal through S,O-bridging organophosphorus ligands [Hg(1)-O(1) 2.556(4) Å for 1, 2.588(4) Å for 2], thus resulting in a distorted T-shaped arrangement of the CHgSO coordination core.. The formation of a 12-membered Hg₂O₂S₂P₄N₂ ring with different conformation in 1 and 2, respectively, results in different additional chalcogen atoms being in the proximity of the metal atom. Weak transannular Hg?O [2.753(4) Å] are also established in 1, leading to a tricyclic ladder structure with a planar central Hg₂O₂ ring.     

Host-guest chemistry of the chromium-wheel complex [Cr8F8(tBuCO2)16]: prediction of inclusion capabilities by using an electrostatic potential distribution determined by modeling synchrotron X-ray structure factors at 16 K

The structure and detailed electron density distribution (EDD) of the large octanuclear chromium-wheel host complex [Cr8F8(tBuCO2)16] (1) has been determined from synchrotron X-ray structure factors collected at 16(5) K. The complex has a central cavity with a minimum entry distance between carbon atoms of the pivalate methyl groups (pivalic acid = tBuCO2H) of 4.027(4) A on one side of the molecule and 7.273(4) A on the other. The screened side of the molecule can be "opened" by rotation of methyl groups to create a strained host structure, which is compensated for by improved host-guest and host-solvent interaction. The EDD of the 272-atom complex (1144 e-) was determined by multipole modeling based on the experimental structure factors. 3d orbital populations on the Cr atoms and topological analysis of the EDD show that the covalent part of the metal-ligand interactions consists mainly of sigma donation from the ligands, but that overall the interactions are predominantly electrostatic. The electrostatic potential (EP) has been calculated from the experimental EDD. Knowledge of the geometry of the naked complex 1 as well as the EP in the central cavity of this molecule allows us to deduce which characteristic properties guest molecules must have to be accepted into the void. To probe these predictions, a series of complexes of 1 with different guest inclusions were synthesized (2 = 1 + N,N'-dimethylformamide (DMF), 3 = 1 + N,N'-dimethylacetamide (DMA), 4 = 1 + DMA + DMF, 5 = 1 + 2CH3CN), and their structures were examined by using X-ray diffraction data measured at 120(1) K. Results of these studies indicate that in the crystalline state, the optimal guest molecule should be linear and possess a permanent dipole. Attempts to crystallize the host complex with cations incorporated into the cavity were fruitless, although electrospray ionization mass spectrometry showed that a [1 + potassium]+ entity pre-exists in solution and can be transferred intact into the gas phase.     

New organomercury(II) compounds containing intramolecular N → Hg interactions: crystal and molecular structure of [2-(Me2NCH2)C6H4]HgCl and [2-(Me2NCH2)C6H4]Hg[S(S)PPh2]

[2-(Me₂NCH₂)C₆H₄]HgCl (1) was prepared by reacting HgCl₂ with [2-(Me₂NCH₂)C₆H₄]Li in diethyl ether. The reactions of 1 with the sodium or ammonium salt of the appropriate thiophosphinato ligand, in 1:1 molar ratio, afford the isolation of [2-(Me₂NCH₂)C₆H₄]Hg[S(S)PR₂] [R=Me (2), Et (3), Ph (4)], [2-(Me₂NCH₂)C₆H₄]Hg[S(O)PPh₂] (5) and [2-(Me₂NCH₂)C₆H₄]Hg[S(S)P(OⁱPr)₂] (6). The compounds were investigated by IR and multinuclear NMR (¹H, ¹³C and ³¹P) spectroscopy. The molecular structures of 1 and 4 were determined by single-crystal X-ray diffraction. Due to the strong intramolecular coordination of the N atom of the pendant CH₂NMe₂ arm [Hg(1)-N(1) 2.764(6) and 2.725(4) Å in 1 and 4, respectively] both compounds exhibit a T-shaped (C,N)HgX core in the molecular unit, with almost linear arrangement of the covalent bonds [C(1)-Hg(1)-Cl(1) 176.93(18)° in 1, and C(1)-Hg(1)-S(1) 169.54(16)° in 4]. The crystals of 1 contain discrete monomeric molecules, while the crystals of 4 contain dimer associations built through asymmetric bridging dithiophosphinato ligands [Hg(1)-S(1) 2.3911(16) Å, Hg(1)?S(2a) 3.102(2) Å], thus resulting in an overall pseudo-trigonal bipyramidal (or seesaw) (C,N)HgS₂ core, with the nitrogen atom and the weekly bonded sulfur atom in equatorial positions [N(1)-Hg(1)?S(2a) 82.01(10)°].     

Physical properties (thermal,thermomechanical, magnetic,and adhesive) of some smart orthodontic wires

Thermal, thermomechanical, and caloric properties of commercial orthodontic wires (produced by Natural Orthodontics Corp., USA) with cylindrical and rectangular geometry were studied. Depending on the applied forces, there were identified the range of elasticity, the elasticity–viscoelasticity coexistence domain and the domain in which a maximum force of 18 N is applied, for the orthodontic wires. When increasing the thickness of orthodontic wires, deformation decreases. The Controlled Force Module, in the tension mode, was used for the determination of the orthodontic wires elongation at application of the stretching forces from 0 to 13 N, at 35 °C, maintaining each static force value for 3 min. The increase in the cross-sectional area of the orthodontic wires disfavors the process of elongation of the sample, at the same applied static force. Using the Multi-Frequency–Strain–Stress modulus, in the tension mode, DMA cyclic heating–cooling measurements were performed. The measured physical quantities for orthodontic wires were Storage Modulus, Loss Modulus, Tanδ and Stiffness, at heating and cooling. Thus, the characteristic temperatures of the phase transitions (A_s, A_f, M_s, M_f), of all the studied orthodontic wires were identified. Also, the values of the elasticity modulus (Young’s Modulus) of the orthodontic wires were calculated at 35 °C. With the DSC Q200 device, using temperature-modulated differential scanning calorimetry method, a multi-step temperature variation program, was applied to a rectangular wire, in three stages (cooling–heating–cooling). Through the interpretation of heat fluxes (reversible, irreversible and total), the phase transitions in the formation of martensite, austenite, but also of the rombohedral phase (R-phase), were identified. Formations of austenite and martensite were also evidenced by the classical DSC method, but the classical DSC method also enabled the R-phase identification. The adherence of some food dyes on the orthodontic wires, as well as the modification of the surface roughness of the orthodontic wire after the deposition of the food dye, was also studied. By magnetic measurements, it was established that the orthodontic wires had paramagnetic properties at room temperature, and nitinol was a mixture of 49.2% austenite and 50.8% martensite.