On a variant of Giuga numbers

In this paper, we characterize the odd positive integers n satisfying the congruence∑n -1 j=1 j n-1/2 ≡ 0 (mod n). We show that the set of such positive integers has an asymptotic density which turns out to be slightly larger than 3/8.     

Quantification of the surface diffusion of tripodal binding motifs on graphene using scanning electrochemical microscopy

The surface diffusion of a cobalt bis-terpyridine, Co(tpy)(2)-containing tripodal compound (1·2PF(6)), designed to noncovalently adsorb to graphene through three pyrene moieties, has been studied by scanning electrochemical microscopy (SECM) on single-layer graphene (SLG). An initial boundary approach was designed in which picoliter droplets (radii ~15-50 μm) of the tripodal compound were deposited on an SLG electrode, yielding microspots in which a monolayer of the tripodal molecules is initially confined. The time evolution of the electrochemical activity of these spots was detected at the aqueous phosphate buffer/SLG interface by SECM, in both generation/collection (G/C) and feedback modes. The tripodal compound microspots exhibit differential reactivity with respect to the underlying graphene substrate in two different electrochemical processes. For example, during the oxygen reduction reaction, adsorbed 1·2PF(6) tripodal molecules generate more H(2)O(2) than the bare graphene surface. This product was detected with spatial and temporal resolution using the SECM tip. The tripodal compound also mediates the oxidation of a Fe(II) species, generated at the SECM tip, under conditions in which SLG shows slow interfacial charge transfer. In each case, SECM images, obtained at increasing times, show a gradual decrease in the electrochemical response due to radial diffusion of the adsorbed molecules outward from the microspots onto the unfunctionalized areas of the SLG surface. This response was fit to a simple surface diffusion model, which yielded excellent agreement between the two experiments for the effective diffusion coefficients: D(eff) = 1.6 (±0.9) × 10(-9) cm(2)/s and D(eff) = 1.5 (±0.6) × 10(-9) cm(2)/s for G/C and feedback modes, respectively. Control experiments ruled out alternative explanations for the observed behavior, such as deactivation of the Co(II/III) species or of the SLG, and verified that the molecules do not diffuse when confined to obstructed areas. The noncovalent nature of the surface functionalization, together with the surface reactivity and mobility of these molecules, provides a means to couple the superior electronic properties of graphene to compounds with enhanced electrochemical performance, a key step toward developing dynamic electrode surfaces for sensing, electrocatalysis, and electronic applications.     

Syntheses and Crystal Structures of Two New One-dimensional Double Hydrogen-bonding-chain Complexes [Ni(bipy)_2Cl]·ClO_4 and [Zn(bipy)_2Cl]·BF_4

Two new transition metal complexes, [Ni(bipy)2Cl]·ClO4 (bipy = 2,2'-bipyridine) 1 and [Zn(bipy)2Cl]·BF4 2, have been synthesized and characterized by single-crystal X-ray diffraction analysis. Both 1 and 2 crystallize in monoclinic space group P21/n with Z = 4. For 1, a = 10.776(1), b = 12.067(1), c = 16.146(2) , β = 93.021(2)o, V = 2031.9(4) 3, Mr = 505.98, Dc = 1.654 g/cm3, μ = 1.255 mm–1, F(000) = 1032, the final R = 0.0406 and wR = 0.1002 for 3983 observed reflections with I > 2σ(I). For 2, a = 10.758(4), b = 12.058(4), c = 16.135(5) , β = 104.57(1)o, V = 2025.7(12) 3, Mr = 500.00, Dc = 1.639 g/cm3, μ = 1.396 mm–1, F(000) = 1008, the final R = 0.0470 and wR = 0.1237 for 3759 observed reflections with I > 2σ(I). The crystal structures of 1 and 2 are isostructural with very similar supramolecular structures. A one-dimen-sional zigzag double hydrogen-bonding-chain is generated by the intermolecular M-bipy ···anion···bipy- M hydrogen bonding interactions between the chelating ligands of bipy and anion.     

Modelling the optical response of gold nanoparticles

This tutorial review presents an overview of theoretical methods for predicting and understanding the optical response of gold nanoparticles. A critical comparison is provided, assisting the reader in making a rational choice for each particular problem, while analytical models provide insights into the effects of retardation in large particles and non-locality in small particles. Far- and near-field spectra are discussed, and the relevance of the latter in surface-enhanced Raman spectroscopy and electron energy-loss spectroscopy is emphasized.     

Synthesis and Structure of a Manganese(Ⅱ) Complex: [Mn_2·(dinitrobenzoic acid)_4·(1,10-phen)_2]_n

The title compound, [Mn2·(dinitrobenzoic acid)4·(1,10-phen)2]n, has a linear chain struc- ture containing binuclear [Mn2·(dinitrobenzoic acid)4(1,10-phen)2] repeat units. It crystallizes in the tricli- nic system, space group P1 with a = 7.9261(8), b = 12.1329(15), c = 14.847(2) , α = 103.845(5), β = 101.424(5), γ = 92.618(4)o, Mr = 657.37, V = 1352.3(2)3, Z = 2, Dc = 1.614 g/cm3, F(000) = 666, μ = 0.567 mm-1, the final R = 0.0407 and wR = 0.1015 for 4081 observed reflections with I > 2σ(I). The Mn atom is six-coordinated by two N and four O atoms, forming a slightly distorted octahedral geometry. All Mn–O and Mn–N bond distances range from 2.093(2) to 2.310(2) . Two adjacent octahedral units are bridged together by two pairs of bi-monodentate carboxyl groups of different dinitrobenzoic acids to form an eight-membered ring with chair-typed configuration, thus generating a one-dimensional chain along the a axis.     

Hydrothermal Synthesis,Crystal Structure and Electrochemical Properties of the Copper(II) Complex [Cu_4O_4(phen)_4(ClC_6H_4COO)_2(H_2O)_2]·(H_2O)_3

1 INTRODUCTION As we all know, copper is a necessary trace element for human body. For example, a large number of bi- nuclear or multi-nuclear transition metallic complex- es exist in active centers of some metalloprotein[1]. In the 1960’s, Bertand and Bock et al[2] reported the first tetra-nuclear copper complex with Cu4O3 unit. In 1996, a cyclo-tetranucleate complex bridged by pyridine was synthesized by Zhang Hua etc[3]. In 1999, Tan Xiangshi and coworkers[4] presented a cubic tet…     

Synthesis,Crystal Structure and Electrochemical Properties of a Cadmium（Ⅱ） Complex with α-Furoic Acid and 1,10-Phenanthroline

A new cadmium complex [Cd（phen）3]·（ClO4）2·（α-FRA）-（H2O）3 was prepared by self-assembly of α-furoic acid, 1,10-phenanthroline （phen）, and cadmium perchlorate. It crystallizes in the monoclinic system, space group P21/n, with a = 1.28130（15）, b = 2.5957（3）, c = 1.35449（16） nm, β = 109.395（2）°, V = 4.2492（9） nm^3, Dc = 1.491 g/cm^3, Z = 4, F（000） = 1926, GOOF = 1.023, the final R = 0.0729 and wR = 0.2086. The crystal structure analysis indicates that the cadmium ion is coordinated with six nitrogen atoms from six 1,10-phenanthroline molecules, giving a distorted octahedral coordination geometry. The cyclic voltametric behavior of the complex was also investigated.     

New magnetic copper(II) coordination polymers with the polynitrile ligand (C[C(CN)2]3)2- and N-donor co-ligands

Reactions between CuCl2 and K2tcpd (tcpd2- = [C10N6]2- = (C[C(CN)2]3)2-) in the presence of neutral co-ligands (bpym = 2,2'-bipyrimidine, and tn = 1,3-diaminopropane) in aqueous solution yield the new compounds [Cu2(bpym)(tcpd)2(H2O)4] x 2H2O (1), [Cu(tn)(tcpd)] (2), and [Cu(tn)2(tcpd)] x H2O (3), which are characterized by X-ray crystallography and magnetic measurements. Compound 1 displays a one-dimensional structure in which the bpym ligand, acting with a bis-chelating coordination mode, leads to [Cu2(bpym)]4+ dinuclear units which are connected by two mu2-tcpd2- bridging ligands. Compound 2 consists of a three-dimensional structure generated by [Cu(tn)]2+ units connected by a mu4-tcpd2- ligand. The structure of 3 is made up of centrosymmetric planar [Cu(tn)]2+ units connected by a mu2-tcpd2- ligand leading to infinite zigzag chains. In compounds 1 and 3, the bridging coordination mode of the tcpd2- unit involves only two nitrogen atoms of one C(CN)2 wing, while in 2, this ligand acts via four nitrogen atoms of two C(CN)2 wings. Despite this difference, the structural features of the tcpd2- units in 1-3 are essentially similar. Magnetic measurements for compound 1 exhibit a maximum in the chi(m) vs T plot (at approximately 150 K) which is characteristic of strong antiferromagnetic exchange interactions between the Cu(II) metal ions dominated by the magnetic exchange through the bis-chelating bpym. The fit of the magnetic data to a dimer model gives J and g values of -90.0 cm(-1) and 2.12, respectively. For compounds 2 and 3 the thermal variations of the magnetic susceptibility show weak antiferromagnetic interactions between the Cu(II) metal ions that can be well reproduced with an antiferromagnetic regular S = 1/2 chain model that gives J values of -0.07(2) and -0.18(1) cm(-1) with g values of 2.12(1) and 2.13(1) for compounds 2 and 3, respectively (the Hamiltonian is written in all the cases as H = -2JS(a)S(b)).     

Liquid chromatography-UV diode-array detection method for multi-residue determination of macrolide antibiotics in sheep's milk

A rapid, simple and sensitive liquid chromatography-UV diode-array detection method was developed for the simultaneous determination of seven macrolides (erythromycin, oleandomycin, roxithromycin, josamycin, spiramycin, tylosin and ivermectin) in sheep's milk. The column, mobile phase, temperature and flow rate were optimised to provide the best resolution of these analytes. The extraction of the antibiotic residues involves the treatment of protein-free samples with a combination of concentrated sodium hydroxide and ethyl acetate. Necessary defatting is achieved by alkaline hydrolysis. The recovery of each antibiotic was between 55% and 77%, with relative standard deviations ranging from 1% to 6.5%. The limit of quantification was 72.4 microg/kg for ivermectin, 48.3 microg/kg for roxithromycin, and 24.1 microg/kg for erythromycin, oleandomycin, spiramycin, josamycin and tylosin. The procedure was successfully used in the multi-residue determination of these macrolides at levels below the maximum concentrations legally allowed in milk samples.