Using dynamic geometry to explore non-traditional theorems

The purpose of this article is to provide examples of ‘non-traditional’ theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The Appendix contains proof outlines for each theorem.     

1,2,5-Oxadiazolo[3,4-g]indoles via annelation of 6,7-dihydrobenzo[c][1,2,5]oxadiazol-4(5H)-one oxime with acetylene

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Design,Synthesis, and Application of a Water-soluble Photocage for Aqueous Cyclopentadiene-based Diels-Alder Photoclick Chemistry in Hydrogels

Spatiotemporally functionalized hydrogels have exciting applications in tissue engineering, but their preparation often relies on radical-based strategies that can be deleterious in biological settings. Herein, the computationally guided design, synthesis, and application of a water-soluble cyclopentadienone-norbornadiene (CPD-NBD) adduct is disclosed as a diene photocage for radical-free Diels-Alder photopatterning. We show that this scalable CPD-NBD derivative is readily incorporated into hydrogel formulations, providing gels that can be patterned with dienophiles upon 365 nm uncaging of cyclopentadiene. Patterning is first visualized through conjugation of cyanine dyes, then biological utility is highlighted by patterning peptides to direct cellular adhesion. Finally, the ease of use and versatility of this CPD-NBD derivative is demonstrated by direct incorporation into a commercial 3D printing resin to enable the photopatterning of structurally complex, printed hydrogels.     

12-Tungstophosphoric acid supported on inorganic oxides as heterogeneous and reusable catalysts for the selective preparation of alkoxymethyl ethers and their deprotections under different reaction conditions

A wide variety of primary and secondary alcohols were efficiently converted to their corresponding methoxymethyl (MOM) and ethoxymethyl (EOM) ethers in the presence of catalytic amounts of supported H₃PW₁₂O₄₀ on silica gel and zirconia at room temperature and under microwave irradiation at solvent-free conditions, whereas, phenols and tertiary alcohols remained intact under the same reaction conditions. Deprotection of these ethers to their parent alcohols was also achieved using these heterogeneous catalysts in ethanol, as a green solvent, under reflux conditions and microwave irradiation. Selective deprotection of primary and secondary MOM- and EOM-ethers in the presence of phenolic and tertiary ones, methyl and benzyl ethers, esters and trimethylsilyl ethers was achieved by these reagent systems. The present methodology offers several advantages such as short reaction times, high yields, simple procedure, heterogeneous reaction conditions, selectivity, non-toxicity and reusability of the catalysts.     

CO2 Overall Splitting by a Bifunctional Metal‐Free Electrocatalyst

Photo/electrochemical CO₂ splitting is impeded by the low cost‐effective catalysts for key reactions: CO₂ reduction (CDRR) and water oxidation. A porous silicon and nitrogen co‐doped carbon (SiNC) nanomaterial by a facile pyrolyzation was developed as a metal‐free bifunctional electrocatalyst. CO₂‐to‐CO and oxygen evolution (OER) partial current density under neutral conditions were enhanced by two orders of magnitude in the Tafel regime on SiNC relative to single‐doped comparisons beyond their specific area gap. The photovoltaic‐driven CO₂ splitting device with SiNC electrodes imitating photosynthesis yielded an overall solar‐to‐chemical efficiency of advanced 12.5 % (by multiplying energy efficiency of CO₂ splitting cell and photovoltaic device) at only 650 mV overpotential. Mechanism studies suggested the elastic electron structure of ?Si(O)?C?N? unit in SiNC as the highly active site for CDRR and OER simultaneously by lowering the free energy of CDRR and OER intermediates adsorption.     

Experimental study of extraction fraction and mass transfer coefficient in a microchannel using butyl acetate/acetic acid/water chemical system

The droplet flow regime in microchannels can increase the mass transfer and chemical reactions considerably. In this work, the mass transfer of immiscible fluids of water as the solvent and butyl acetate containing 5 vol% of acetic acid as the feed is experimentally studied in a vertical flow inside a microchannel with the inner diameter of 8 mm. Effect of total flow velocity, Re number and volumetric flux ratio of two phases (Q_aq/Q_or) on the extraction fraction of acetic acid, mass transfer coefficient and droplet size were investigated. Based on the experiments, increasing the flux ratio can shift the flow regime from the plug to the droplet. Compared to the plug flow, the extraction fraction increased by 2–3 times in the droplet regime, depending on the total velocity, while the average diameter of the droplets decreased. Moreover, with the increase in the total velocity, the extraction fraction is reduced by 22%. However, in the case of the plug flow, the extraction fraction does not change appreciably with the increase in the total flow velocity. The mass transfer coefficient was found to increase monotonously with increasing Re number and an enhancement of 133% was achieved in the droplet flow regime.     

Microwave-promoted one-pot conversion of alcohols to oximes using 1-methylimidazolium nitrate, [Hmim][NO3], as a green promoter and medium

A wide variety of oximes were prepared from different types of alcohols with hydroxylamine hydrochloride using 1-methylimidaziloum nitrate, [Hmim][NO₃], ionic liquid as a reaction medium and promoter under microwave irradiation. This protocol provides a one-pot oxime synthesis with high yields that is facile, eco-friendly and the ionic liquid can be recovered and reused.     

Liquid–gas–liquid technique for microextraction and preconcentration of short chain fatty acids from aqueous samples

In this study, an organic solvent‐free microextraction technique termed liquid–gas–liquid microextraction (LGLME) was applied for cleanup and preconcentration of volatile short chain fatty acids in beverages and dairy products. Various parameters affecting the extraction efficiency such as extraction time, stirring speed, sodium chloride content, concentration and volume of donor and acceptor phases, and extraction temperature were studied. Repeatability (RSD, 4.2–8.5%), correlation coefficients (0.998–0.999), LODs (10–20 μg/L) and enrichment factors (152–249) were also investigated. Recoveries were achieved in the range of 90–102% in different matrices. The presented method was applied for the analysis of target analytes in some samples such as grape juice, vinegar and dairy products.