Dimetallic complexes of a structurally versatile pyridazine-containing Schiff-base macrocyclic ligand with pendant pyridine arms

The new [2 + 2] Schiff-base macrocyclic ligand L2, containing pyridazine head units and pyridine pendant arms, was synthesised as [Ba(II)2L2(ClO4)4(OH2)] 1 from the barium(II) ion templated condensation reaction of 3,6-diformylpyridazine and N1-(2-aminoethyl)-N1-(methylene-2-pyridyl)-ethane-1,2-diamine. Subsequent transmetallation reactions of 1 with copper(II), iron(II) and manganese(II) perchlorates led to the formation of [Cu(II)2L2](ClO4)4.2MeCN 2, [Fe(II)2L2(MeCN)2](ClO4)4 3 and two manganese complexes, 4 and 5, with the same formula, [Mn(II)2L2(MeCN)(OH2)](ClO4)4, but slightly different crystal structures, respectively. Single-crystal X-ray structural analyses reveal the variety of structures which can be supported by L2 in order to meet the coordination environment preferences of the incorporated metal ions. The barium(II) ions in 1 have an irregular ten-coordinate geometry whereas the copper(II) ions in 2 have a square pyramidal geometry and the iron(II) ions in 3 have an octahedral geometry, while in 4 and 5 every manganese(II) ion is seven-coordinate and the environment can be best described as distorted pentagonal bipyramidal. In 1, 4 and 5 the pyridazine moieties bridge the metal centres [Ba(1)...Ba(2) 4.9557(3)A 1; Mn(1)...Mn(2) 4.520(1)A 4; Mn(1)[dot dot dot]Mn(2) 4.3707(8)A 5] but this is not observed in the copper(II) and iron(II) complexes, 2 and 3, in which the metal ions are well separated [Cu(1)...Cu(2) 5.9378(6)A 2; Fe(1)...Fe(2) 5.7407(12)A 3]. In the cyclic voltammogram of [Cu2(II)L2](ClO4)4.2MeCN 2 in MeCN vs. Ag/AgCl two separate reversible one-electron transfer steps are observed [E(1/2)=0.04 V, DeltaE= 0.12 V and E(1/2)= 0.20 V, DeltaE=0.12 V; K(c)=510; in this system E(1/2)(Fc+/Fc)=0.42 V and DeltaE(Fc+/Fc)=0.08 V]. The other complexes cannot be reversibly reduced/oxidised.     

Dimetallic complexes of acyclic pyridine-armed ligands derived from 3,6-diformylpyridazine

A bis(pyridine-armed) acyclic Schiff base ligand L1 has been synthesised from 3,6-diformylpyridazine and two equivalents of 2-(2-aminoethyl)pyridine. Reduction of this ligand using NaBH(4) resulted in the formation of the amine analogue L2. Complexes of the form [M(2)L1(mu-X)]Y(2)ClO(4)[where: M = Cu(II), X = OH(-) and Y = ClO(4)(-) 1, Cl(-) 2, Br(-) 3 or I(-) 4; M = Co(II), X = OH(-) and Y = ClO(4)(-) 5; M = Ni(II), X = SCN(-) 6 or X = N(3)(-) 7 and Y = ClO(4)(-)], and [Cu(2)L2(mu-OH)](ClO(4))(3) 8 were prepared and characterised. The complexes 1 and 5-7 have been characterised by single-crystal X-ray diffraction. The acyclic L1 ligand provides three nitrogen donor atoms per metal centre, including a pyridazine bridge between the metal centres, and the anion X also bridges the two metal centres. As required, coordinating solvent molecules or additional anions make up the remainder of the coordination sphere. The two copper centres of 1 are very strongly antiferromagnetically coupled (2J=-1146 cm(-1))via the pyridazine and hydroxide ion bridges, whereas the competing antiferromagnetic pyridazine bridging pathway and ferromagnetic 1,1-bridging azide pathway resulted in the observation of weak antiferromagnetic exchange in the dinickel(II) complex 7 (2J=-14 cm(-1)). Electrochemical examination of L1, L2 and complexes 1 and 5-8 revealed multiple redox processes. These have been tentatively assigned to a mixture of metal centred and ligand centred redox processes on the basis of cyclic voltammetry and coulometry results and comparisons with literature examples.     

Control of molecular architecture by the degree of deprotonation: self-assembled di- and tetranuclear copper(II) complexes of N,N'-bis(2-pyridylmethyl)pyrazine-2,3-dicarboxamide

In the absence of added base, a deep navy-blue dimeric copper complex [CuII(H2L)(MeCN)]2(BF4)4 (1) of the non-deprotonated bis-terdentate diamide ligand H2L self-assembles whereas in the presence of base a grass-green [2 x 2] grid complex [CuII(HL)]4(BF4)4 (2) of the monodeprotonated ligand HL-, a rare example of a discrete grid of pyrazine-bridged metal ions, is formed.     

Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

Fresnel incoherent correlation hologram—— a review （Invited Paper）

Holographic imaging offers a reliable and fast method to capture the complete three-dimensional （3D） information of the scene from a single perspective. We review our recently proposed single-channel optical system for generating digital Fresnel holograms of 3D real-existing objects illuminated by incoherent light. In this motionless holographic technique, light is reflected, or emitted from a 3D object, propagates through a spatial light modulator （SLM）, and is recorded by a digital camera. The SLM is used as a beamsplitter of the single-channel incoherent interferometer, such that each spherical beam originated from each object point is split into two spherical beams with two different curve radii. Incoherent sum of the entire interferences between all the couples of spherical beams creates the Fresnel hologram of the observed 3D object. When this hologram is reconstructed in the computer, the 3D properties of the object are revealed.