Solving second-order differential equations with variable coefficients

A method is developed in which an analytical solution is obtained for certain classes of second-order differential equations with variable coefficients. By the use of transformations and by repeated iterated integration, a desired solution is obtained. This alternative method represents a different way to acquire a solution from classic power series techniques and other approaches. It is, at times, more involved than traditional methods.     

The not-so-peculiar case of calcium oxide: a weakness in atomic natural orbital basis sets for calcium

Atomic natural orbital (ANO) basis sets for calcium may produce surprisingly poor atomic and molecular properties and energetics. The weaknesses in these basis sets may be traced primarily to deficiencies within the sets of d functions which are incapable of effectively correlating the 3s and 3p electrons. Examples are given which show that addition of tight d functions to the ANO basis is required to achieve qualitatively correct energetics and structures for conventionally bonded calcium compounds.     

Tuning the Photo-electrochemical Performance of RuII-Sensitized Two-Dimensional MoS2

Covalently tethering photosensitizers to catalytically active 1T-MoS₂ surfaces holds great promise for the solar-driven hydrogen evolution reaction (HER). Herein, we report the preparation of two new Ru^II-complex-functionalized MoS₂ hybrids [Ru^II(bpy)₂(phen)]-MoS₂ and [Ru^II(bpy)₂(py)Cl]-MoS₂. The influence of covalent functionalization of chemically exfoliated 1T-MoS₂ with coordinating ligands and Ru^II complexes on the HER activity and photo-electrochemical performance of this dye-sensitized system was studied systematically. We find that the photo-electrochemical performance of this Ru^II-complex-sensitized MoS₂ system is highly dependent on the surface extent of photosensitizers and the catalytic activity of functionalized MoS₂. The latter was strongly affected by the number and the kind of functional groups. Our results underline the tunability of the photovoltage generation in this dye-sensitized MoS₂ system by manipulation of the surface functionalities, which provides a practical guidance for smart design of future dye-sensitized MoS₂ hydrogen production devices towards improved the photofuel conversion efficiency.     

CHARACTERIZATION OF AN ACRYLAMIDE MODIFIED ETHYL ACRYLATE LATEX BY CARBON-13 NMR SPECTROSCOPY

The structure of a 70/30 ethyl acrylate-acrylamide latex made in a semi-continuous process with surfactant has been investigated. The molar composition and relative concentration of the polymers in the serum phase, on the surface and in the particle were characterized by coupling a filtration procedure, serum replacement, with carbon-13 NMR spectroscopy. The development of polymer in the different phases could be monitored by taking samples at timed intervals during the polymerization. Post-treatment of the latex with sodium hydroxide selectively hydrolyzed the copolymerized ethyl acrylate in the serum and on the surface. By measurement of spin lattice relaxation times it was possible to estimate surface concentration of oligomeric polymer     

Preparation and Characterisation of a Bis-μ-Hydroxo-NiIII2 Complex

Hydroxide-bridged high-valent oxidants have been implicated as the active oxidants in methane monooxygenases and other oxidases that employ bimetallic clusters in their active site. To understand the properties of such species, bis-μ-hydroxo-Ni^II₂ complex ( 1 ) supported by a new dicarboxamidate ligand (N,N′-bis(2,6-dimethyl-phenyl)-2,2-dimethylmalonamide) was prepared. Complex 1 contained a diamond core made up of two Ni^II ions and two bridging hydroxide ligands. Titration of the 1 e⁻ oxidant (NH₄)₂[Ce^IV(NO₃)₆] with 1 at −45 °C showed the formation of the high-valent species 2 and 3 , containing Ni^IINi^III and Ni^III₂ diamond cores, respectively, maintaining the bis-μ-hydroxide core. Both complexes were characterised using electron paramagnetic resonance, X-ray absorption, and electronic absorption spectroscopies. Density functional theory computations supported the spectroscopic assignments. Oxidation reactivity studies showed that bis-μ-hydroxide-Ni^III₂ 3 was capable of oxidizing substrates at −45 °C at rates greater than that of the most reactive bis-μ-oxo-Ni^III complexes reported to date.     

Rational Design of a Uranyl Metal–Organic Framework for the Capture and Colorimetric Detection of Organic Dyes

A new uranyl containing metal–organic framework, RPL-1 : [(UO₂)₂(C₂₈H₁₈O₈)] ^. H₂O (RPL for Radiochemical Processing Laboratory), was prepared, structurally characterized, and the solid-state photoluminescence properties explored. Single crystal X-ray diffraction data reveals the structure of RPL - 1 consists of two crystallographically unique three dimensional, interpenetrating nets with a 4,3-connected tbo topology. Each net contains large pores with an average width of 22.8 Å and is formed from monomeric, hexagonal bipyramidal uranyl nodes that are linked via 1,2,4,5-tetrakis(4-carboxyphenyl)benzene (TCPB) ligands. The thermal and photophysical properties of RPL-1 were investigated using thermogravimetric analysis and absorbance, fluorescence, and lifetime spectroscopies. The material displays excellent thermal stability and temperature dependent uranyl and TCPB luminescence. The framework is stable in aqueous media and due to the large void space (constituting 76 % of the unit cell by volume) can sequester organic dyes, the uptake of which induces a visible change to the color of the material.     

Self-assembly mechanism of PEG-b-PCL and PEG-b-PBO-b-PCL amphiphilic copolymer micelles in aqueous solution from coarse grain modeling

We followed the self-assembly of high-molecular weight MePEG- b -PCL (poly(methyl ethylene glycol)-block-poly(ε-caprolactone)) diblock and MePEG- b -PBO- b -PCL (poly(methyl ethylene glycol)-block-poly(1,2-butylene oxide)-block-poly(ε-caprolactone)) into micelles using molecular dynamics simulation with a coarse grain (CG) force field based on quantum mechanics (CGq FF). The triblock polymer included a short poly(1,2-butylene oxide) (PBO) at the hydrophilic-hydrophobic interface of these systems. Keeping the hydrophilic length fixed (MePEG₄₅), we considered 250 chains in which the hydrophobic length changed from PCL₄₄ or PBO₆- b -PCL₄₃ to PCL₆₂ or PBO₉- b -PCL₆₁. The polymers were solvated in explicit water for 2 μs of simulations at 310.15 K. We found that the longer diblock system undergoes a morphological transition from an intermediate rod-like micelle to a prolate-sphere, while the micelle formed from the longer triblock system is a stable rod-like micelle. The two shorter diblock and triblock systems show similar self-assembly processes, both resulting in slightly prolate-spheres. The dynamics of the self-assembly is quantified in terms of chain radius of gyration, shape anisotropy, and hydration of the micelle cores. The final micelle structures are analyzed in terms of the local density components. We conclude that the CG model accurately describes the molecular mechanisms of self-assembly and the equilibrium micellar structures of hydrophilic and hydrophobic chains, including the quantity of solvent trapped inside the micellar core.