Constructing the Cubus simus and the Dodecaedron simum via paper folding

The archimedean solids Cubus simus (snub cube) and Dodecaedron simum (snub dodecahedron) cannot be constructed by ruler and compass. We explain that for general reasons their vertices can be constructed via paper folding on the faces of a cube, respectively dodecahedron, and we present explicit folding constructions. The construction of the Cubus simus is particularly elegant. We also review and prove the construction rules of the other Archimedean solids.     

A fully discrete Galerkin method for Abel-type integral equations

In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in fractional-order Sobolev norms. The fully-discrete Galerkin method is defined by employing simple tensor-Gauss quadrature. We develop a corresponding perturbation analysis which allows to keep the number of quadrature points small. Numerical experiments have been performed which illustrate the sharpness of the theoretical estimates and the sensitivity of the solution with respect to some parameters in the equation.     

Order and Disorder in the Structures of Two Crystal Polymorphs of the Adduct Bis(Quinolinium-2-Carboxylate) DL-Malic Acid

Abstract  

The structures of two polymorphs of the anhydrous cocrystal adduct of bis(quinolinium-2-carboxylate) DL-malic acid, one triclinic the other monoclinic and disordered, have been determined at 200 K. Crystals of the triclinic polymorph 1 have space group P-1, with Z = 1 in a cell with dimensions a = 4.4854(4), b = 9.8914(7), c = 12.4670(8) ?, α = 79.671(5), β = 83.094(6), γ = 88.745(6)°. Crystals of the monoclinic polymorph 2 have space group P2₁/c, with Z = 2 in a cell with dimensions a = 13.3640(4), b = 4.4237(12), c = 18.4182(5) ?, β = 100.782(3)°. Both structures comprise centrosymmetric cyclic hydrogen-bonded quinolinic acid zwitterion dimers [graph set R₂²(10)] and 50% disordered malic acid molecules which lie across crystallographic inversion centres. However, the oxygen atoms of the malic acid carboxylic groups in 2 are 50% rotationally disordered whereas in 1 these are ordered. There are similar primary malic acid carboxyl O–H···O_{quinaldic acid} hydrogen-bonding chain interactions in each polymorph, extended into two-dimensional structures but in 1 this involves centrosymmetric cyclic head-to-head malic acid hydroxyl-carboxyl O–H···O interactions [graph set R₂²(10)] whereas in 2 the links are through single hydroxy-carboxyl hydrogen bonds.     

Trace analysis of environmental matrices by large-volume injection and liquid chromatography–mass spectrometry

The time-honored convention of concentrating aqueous samples by solid-phase extraction (SPE) is being challenged by the increasingly widespread use of large-volume injection (LVI) liquid chromatography–mass spectrometry (LC–MS) for the determination of traces of polar organic contaminants in environmental samples. Although different LVI approaches have been proposed over the last 40 years, the simplest and most popular way of performing LVI is known as single-column LVI (SC-LVI), in which a large-volume of an aqueous sample is directly injected into an analytical column. For the purposes of this critical review, LVI is defined as an injected sample volume that is ≥10% of the void volume of the analytical column. Compared with other techniques, SC-LVI is easier to set up, because it requires only small hardware modifications to existing autosamplers and, thus, it will be the main focus of this review. Although not new, SC-LVI is gaining acceptance and the approach is emerging as a technique that will render SPE nearly obsolete for many environmental applications. In this review, we discuss: the history and development of various forms of LVI; the critical factors that must be considered when creating and optimizing SC-LVI methods; and typical applications that demonstrate the range of environmental matrices to which LVI is applicable, for example drinking water, groundwater, and surface water including seawater and wastewater. Furthermore, we indicate direction and areas that must be addressed to fully delineate the limits of SC-LVI.     

The High‐Pressure Phase of MgB2C2

A high‐pressure modification of MgB₂C₂ was synthesized and structurally characterized. The compound crystallizes in the orthorhombic space group Pnnm, with the lattice parameters a = 7.19633(3) Å, b = 4.61791(13) Å and c = 2.77714(8) Å. The compound contains heterographene B–C nets, isoelectronic to graphite, just like the ambient pressure modification. The layers are intercalated by magnesium atoms, which are arranged in a chain‐like manner. According to Density Functional Theory (DFT) calculations, the high‐pressure form of MgB₂C₂ is a semiconductor with a band gap of 1.02 eV. The compound does not undergo a superconducting transition down to 2 K.     

Effects of chemical and physical parameters in the generation of microspheres by hydrodynamic flow focusing

Hydrodynamic flow focusing is a seminal, easy-to-use technology for micro- and nanodroplet generation. It is characterized by the co-axial focusing of two (or more) immiscible liquid streams forced through a small orifice. In this method, the outer continuous phase has a much higher flow velocity than the inner disperse phase. While passing through the orifice, the prevailing pressure drop and shear stress force the inner phase to break up into uniform droplets. Using a biodegradable poly(lactide-co-glycolide) (PLGA) polymer solution as the disperse phase, monodisperse and user-defined polymer micro- and nanospheres can be generated. Here we present a consecutive parameter study of hydrodynamic flow focusing to study the effect of chemical and physical parameters that effect the dispersity of the droplets generated in the 1-5 μm range. The parameter study shows the applicability and challenges of hydrodynamic flow focusing in the preparation of biodegradable microspheres. Applications for microspheres made with this method can be found in the medical, pharmaceutical and technical fields.     

Polymeric structures in the metal complexes of 5-sulfosalicylic acid: The rubidium(I), caesium(I) and lead(II) analogues

The complexes of 3-carboxy-4-hydroxybenzenesulfonic acid (5-sulfosalicylic acid, H₃SSA) with rubidium(I), caesium(I) and lead(II) have been synthesized and characterized using single-crystal X-ray methods at 130 K. The rubidium(I) complex 1, [Rb₃(H₂SSA)(HSSA)(H₂O)₄]_n, is an unstable hydrate variant of a previously described complex [Rb(H₂SSA)(H₂O)]_n, and comprises three independent and different seven-coordinate metal polyhedra interlinked through oxygen donors of the sulfonate, carboxylate and phenolate groups of the 5-sulfosalicylate ligands (one of which is dianionic, the other monoanionic), and one bridging water, giving a three-dimensional hydrogen-bonded framework polymer structure. The anhydrous caesium(I) complex 2 [Cs(H₂SSA)]_n, which has been previously described in a room-temperature determination, has a three-dimensional framework polymer structure based on an irregular Cs–O₉ repeating unit. Complex 3 with lead(II), [Pb(H₂SSA)₂(H₂O)]_n, forms helical step-polymer ribbon substructures having an irregular Pb–O₇ coordination centre comprising a single monodentate water and six sulfonate-O donors bridging three separate metals. The carboxylic acid and phenol substituent groups of the 5-sulfosalicylate ligand link the ribbons peripherally through hydrogen bonds, giving a three-dimensional layered framework polymer structure.