APPROACHING ALGEBRA THROUGH SEQUENCE PROBLEMS: EXPLORING CHILDREN'S STRATEGIES

We describe the first phase of a project concerned with the foundations of algebra. Data consists of the responses of 11 year-olds to selected questions from national tests. We focus on one question, which concerns a sequence of shapes and classify successful methods and incorrect solutions. The most common method of successful solution involves some form of table of numbers. Other methods include drawing and use of a relationship. Examination of incorrect answers suggests four common errors. The idea of a'best method' proves problematic, as both the apparently sophisticated and reliable methods sometimes produced incorrect solutions.     

Microwave-assisted in situ deprotection and ω-methoxylation of TMS-protected aryl alkynes

Using microwave technology, rapid ω-methoxylation of aryl alkynes is possible.     

N,N'-Carbonyldiimidazole-mediated functionalization of superparamagnetic nanoparticles as vaccine carrier

Particulates with specific sizes and characteristics can induce potent immune responses by promoting antigen uptake of appropriate immuno-stimulatory cell types. Magnetite (Fe(3)O(4)) nanoparticles have shown many potential bioapplications due to their biocompatibility and special characteristics. Here, superparamagnetic Fe(3)O(4) nanoparticles (SPIONs) with high magnetization value (70emug(-1)) were stabilized with trisodium citrate and successfully conjugated with a model antigen (ovalbumin, OVA) via N,N'-carbonyldiimidazole (CDI) mediated reaction, to achieve a maximum conjugation capacity at approximately 13 microgmicrom(-2). It was shown that different mechanisms governed the interactions between the OVA molecules and magnetite nanoparticles at different pH conditions. We evaluated as-synthesized SPION against commercially available magnetite nanoparticles. The cytotoxicity of these nanoparticles was investigated using mammalian cells. The reported CDI-mediated reaction can be considered as a potential approach in conjugating biomolecules onto magnetite or other biodegradable nanoparticles for vaccine delivery.     

The nature of in-plane skeleton Raman modes of P3HT and their correlation to the degree of molecular order in P3HT:PCBM blend thin films

The nature of main in-plane skeleton Raman modes (C=C and C-C stretch) of poly(3-hexylthiophene) (P3HT) in pristine and its blend thin films with [6,6]-phenyl-C(61)-butyric acid methyl ester (PCBM) is studied by resonant and nonresonant Raman spectroscopy and Raman simulations. Under resonant conditions, the ordered phase of P3HT with respect to its disordered phase is identified by (a) a large shift in the C=C mode peak position to lower wavenumber (~21 cm(-1) shift), (b) a narrower fwhm of the C=C mode (~9 cm(-1) narrower), (c) a larger intensity of the C-C mode relative to the C=C mode (~56% larger), and (d) a very small Raman dispersion (~5 cm(-1)) of the C=C mode. The behavior of the C=C and C-C modes of the ordered and disordered phases of P3HT can be explained in terms of different molecular conformations. The C=C mode of P3HT in P3HT:PCBM blend films can be reproduced by simple superposition of the two peaks observed in different phases of P3HT (ordered and disordered). We quantify the molecular order of P3HT after blending with PCBM and the subsequent thermal annealing to be 42 ± 5% and 94 ± 5% in terms of the fraction of ordered P3HT phase, respectively. The increased molecular order of P3HT in blends upon annealing correlates well with enhanced device performance (J(SC), -4.79 to -8.72 mA/cm(2) and PCE, 1.07% to 3.39%). We demonstrate that Raman spectroscopy (particularly under resonant conditions) is a simple and powerful technique to study molecular order of conjugated polymers and their blend films.     

Highly enantioselective Mannich reactions with α-aryl silyl ketene acetals and imines

Mannich reactions with chiral silicon Lewis acid activated acylhydrazones and α-aryl silyl ketene acetals and α-aryl,α-alkyl silyl ketene imines proceed efficiently and with good to excellent levels of both diastereoselectivity and enantioselectivity. The reactions provide access to α-aryl,β-hydrazido esters and α-aryl,α-alkyl,β-hydrazido nitriles, which are valuable analogs of β-amino acids.     

A new synthesis of pyrrolidines by way of an enantioselective Mannich/diastereoselective hydroamination reaction sequence

A new two-step synthesis of highly substituted pyrrolidines has been developed. Chiral silane Lewis acid promoted enantioselective Mannich reactions of silyl ketene imines with acylhydrazones may be used to access bishomoallylic benzoic hydrazides that in turn may be cyclized to pyrrolidines by way of the thermal hydroamination reaction reported recently by Beauchemin. Importantly, excellent diastereoselectivity may be realized in the hydroamination reactions.     

Hybrid nanoparticle design based on cationized gelatin and the polyanions dextran sulfate and chondroitin sulfate for ocular gene therapy

We describe the development of hybrid nanoparticles composed of cationized gelatin and the polyanions CS and DS for gene therapy in the ocular surface. The physicochemical properties of the nanoparticles that impact their bioperformance, such as average size and zeta potential, can be conveniently modulated by changing the ratio of polymers and the crosslinker. These systems associate plasmid DNA and are able to protect it from DNase I degradation. We corroborate that the introduction of CS or DS in the formulation decreases the in vitro toxicity of the nanoparticles to human corneal cells without compromising the transfection efficiency. These nanoparticles are potential candidates for the development of safer and more effective nanomedicines for ocular therapy.     

Eu(3+)-mediated polymerization of benzenetetracarboxylic acid studied by spectroscopy, temperature-dependent calorimetry, and density functional theory

Thermodynamic parameters for the complexation of Eu(3+) with pyromellitic acid (1,2,4,5-benzenetetracarboxylic acid, BTC) as a model system for polymerizable metal-complexing humic acids were determined using temperature-dependent time-resolved laser-induced fluorescence spectroscopy (TRLFS) and isothermal titration calorimetry (ITC). At low metal and ligand concentrations (<50 μM Eu(3+), <1 mM BTC), a 1:1 monomeric Eu-BTC complex was identified in the range of 25-60 °C. At elevated concentrations (>500 μM Eu(3+) and BTC) a temperature-dependent polymerization was observed, where BTC monomers are linked via coordinating shared Eu(3+) ions. The two methods lead to comparable thermodynamic data (ΔH = 18.5 ± 1.5/16.5 ± 0.1 kJ mol(-1); ΔS = 152 ± 5/130 ± 5 J mol(-1) K(-1); TRLFS/ITC) in the absence of polymerization. With the onset of polymerization, TRLFS reveals the water coordination number of the lanthanide, whereas calorimetry is superior in determining the thermodynamic data in this regime. Evaluating the heat uptake kinetics, the monomer and polymer formation steps could be separated by "time-resolved" ITC, revealing almost identical binding enthalpies for the sequential reactions. Structural features of the complexes were studied by Fourier-transform infrared (FTIR) spectroscopy in combination with density functional theory (DFT) calculations showing predominantly chelating coordination with two carboxylate groups in the monomeric complex and monodentate binding of a single carboxylate group in the polymeric complex of the polycarboxylate with Eu(3+). The data show that pyromellitic acid is a suitable model for the study of metal-mediated polymerization as a crucial factor in determining the effect of humic acids on the mobility of heavy metals in the environment.