Erratum to: Determination of metal ion content of beverages and estimation of target hazard quotients: a comparative study

This is a correction to the following paper: Hague T, Petroczi A, Andrews PR, Barker J, Naughton DP: Determination of metal ion content of beverages and estimation of target hazard quotients: a comparative study. Chem Central J 2008, 2:13.     

Oxidation of divalent tin in aqueous solutions of SnF2 and 3D transition metals allowed to crystallize slowly in air

Chlorides, nitrates and sulfates of M (M=Mn, Fe, Co, Ni and Zn) were dissolved in aqueous solutions of SnF₂ at M/Sn molar ratios of 0.5 to 3. No HF was used. The solutions were allowed to evaporate in air. Very small amounts of hexagonally shaped crystals of unknown materials were obtained for M=Mn, Co, Ni and Zn. Fe did not yield this phase. X-ray powder diffraction gives identical patterns for the four materials, which are therefore most likely isostructural, and showed that the products are not MSn₂F₆·6H₂O or MSnF₆·6H₂O. Tin-119 Mössbauer spectroscopy gives a single line at negative isomer shift, characteristic of [Sn(IV)F₆]^2– ions.     

Counting arithmetical structures on paths and cycles

Let $G$ be a finite, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(diag\left(\mathbf{d}\right)?A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices $(diag\left(\mathbf{d}\right)?A)$). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients $\left(\genfrac{}{}{0ex}{}{2n?1}{n?1}\right)$, and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.     

Integer programming models and linearizations for the traveling car renter problem

The traveling car renter problem (CaRS) is an extension of the classical traveling salesman problem (TSP) where different cars are available for use during the salesman’s tour. In this study we present three integer programming formulations for CaRS, of which two have quadratic objective functions and the other has quadratic constraints. The first model with a quadratic objective function is grounded on the TSP interpreted as a special case of the quadratic assignment problem in which the assignment variables refer to visitation orders. The second model with a quadratic objective function is based on the Gavish and Grave’s formulation for the TSP. The model with quadratic constraints is based on the Dantzig–Fulkerson–Johnson’s formulation for the TSP. The formulations are linearized and implemented in two solvers. An experiment with 50 instances is reported.     

Molecular dynamics simulation of La2O3-Na2O-SiO2 glasses. II. The clustering of La cations

Clustering of high-field strength rare-earth ions in silicate glasses has been experimentally observed for a wide range of concentrations. Clustering has also been observed by molecular dynamics (MD) computer simulations over a range 1-10 mol% in soda silicate glasses. Although there have been numerous experimental studies, atomic-level details of the mechanisms that lead to clustering remain unclear. Coupling experiment with MD simulations is essential to uncovering the factors that lead to clustering. In this work, MD computer simulations are used to verify that clustering found in previous MD simulations is not an artifact of the simulation method. This work also provides clues as to the mechanism of atomic-level clustering.     

Velocity map imaging and theoretical study of the Coulomb explosion of CH3I under intense femtosecond IR pulses

The Coulomb explosion of CH(3)I in an intense (10-100 TW cm(-2)), ultrashort (50 fs) and nonresonant (804 nm) laser field has been studied experimentally and justified theoretically. Ion images have been recorded using the velocity map imaging (VMI) technique for different singly and multiply charged ion fragments, CH(3)(p+) (p = 1) and I(q+) (q ≤ 3), arising from different Coulomb explosion channels. The fragment kinetic energy distributions obtained from the measured images for these ion fragments show significantly lower energies than those expected considering only Coulomb repulsion forces. The experimental results have been rationalized in terms of one-dimensional wave packet calculations on ab initio potential energy curves of the different multiply charged species. The calculations reveal the existence of a potential energy barrier due to a bound minimum in the potential energy curve of the CH(3)I(2+) species and a strong stabilization with respect to the pure Coulombic repulsion for the higher charged CH(3)I(n+) (n = 3, 4) species.     

Characterization of Fe3O4 Nanoparticles for Applications in Catalytic Activity in the Adsorption/Degradation of Methylene Blue and Esterification

The aim of this study is to evaluate the applicability of the catalytic activity (CA) of the Fe₃O₄ magnetic system in the adsorption/degradation of methylene blue and esterification. The thermal decomposition method allowed the preparation of Fe₃O₄ nanoparticles. The crystallites of the Fe₃O₄ structural phase present an acicular form confirmed by X-ray diffraction. Transmission electron microscopy results identified the acicular shape and agglomeration of the nanoparticles. Mössbauer spectroscopy showed that the spectrum is composed of five components at room temperature, a hyperfine magnetic field distribution (HMFD), two sextets, a doublet, and a singlet. The presence of the HMFD means that a particle size distribution is present. Fluorescence spectroscopy studied the CA of the nanoparticles with methylene blue and found adsorption/degradation properties of the dye. The catalytic activity of the nanoparticles was evaluated in the esterification reaction by comparing the results in the presence and absence of catalyst for the reaction with isobutanol and octanol, where it is observed that the selectivity for the products MIBP and MNOP is favored in the first three hours of reaction.     

Water‐soluble,thermoresponsive, hyperbranched copolymers based on PEG‐methacrylates: Synthesis,characterization, and LCST behavior

A series of water‐soluble thermoresponsive hyperbranched copoly(oligoethylene glycol)s were synthesized by copolymerization of di(ethylene glycol) methacrylate (DEG‐MA) and oligo(ethylene glycol) methacrylate (OEG‐MA, M_w = 475 g/mol), with ethylene glycol dimethacrylate (EGD‐MA) used as the crosslinker, via reversible addition fragmentation chain transfer polymerization. Polymers were characterized by size exclusion chromatography and nuclear magnetic resonance analyses. According to the monomer composition, that is, the ratio of OEG‐MA: DEG‐MA: EGD‐MA, the lower critical solution temperature (LCST) could be tuned from 25 °C to 90 °C. The thermoresponsive properties of these hyperbranched copolymers were studied carefully and compared with their linear analogs. It was found that molecular architecture influences thermoresponsive behavior, with a decrease of around 5–10 °C in the LCST of the hyperbranched polymers compared with the LCST of linear chains. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2783–2792, 2010     

Structure, dynamics, and electronic properties of lithium disilicate melt and glass

Ab initio molecular dynamics simulations within the framework of density functional theory have been performed to study the structural, dynamic, and electronic properties of lithium disilicate melt and the glass derived from quenching the melt. It is found that lithium ions have a much higher diffusion coefficient and show different diffusion mechanisms than the network forming silicon and oxygen ions in the melt. The simulated lithium disilicate glass structure has 100% four coordinated silicon, close to theoretical nonbridging oxygen to bridging oxygen ratio (2:3), and Q(n) distributions of 20.8%, 58.4%, and 20.8% for n=2,3,4, respectively. In the melt there are considerable amounts (10%-15%) of silicon coordination defects; however, the average silicon coordination number remains about 4, similar to that in the glass. The lithium ion coordination number increases from 3.7 in the glass to 4.4 in the melt mainly due to the increase of bridging oxygen in the first coordination shell. The bond length and bond angle distributions, vibrational density of states, and static structure factors of the simulated glass were determined where the latter was found to be in good agreement with experimental measurement. Atomic charges were obtained based on Bader and Hirshfeld population analyses [Atoms in Molecule: A Quantum Theory (Oxford University Press, Oxford, 1990); Theor. Chim. Acta 44, 129 (1977)]. The average Bader charges found in lithium disilicate glass were -1.729, 3.419, and 0.915 for oxygen, silicon, and lithium, respectively. The corresponding Hirshfeld charges were -0.307, 0.550, and 0.229. The electronic densities of states of the melt and glass were calculated and compared with those of crystalline lithium disilicate.     

Molecular dynamics simulation of La2O3-Na2O-SiO2 glasses. III. The driving forces of clustering

Molecular dynamics simulations have been carried out to determine the mean force and the potential of mean force of two La ions in a soda silicate glass. The reaction coordinate starts from a well separated state where the network accommodates the high-field strength cations and then brings them together to form an La-O-La linkage that can lead to the formation of free O anions. It is found that clustering of La ions is favored, at least for dimer states. Similar calculations for the ion pairs of La-La, Na-Na and La-Na in pure silica reveal that the local molecular environments of La and Na ions are quite distinct.