A note on dual modules and the transpose

Archiv der Mathematik - It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For F a non-Archimedean local field,...     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.     

A new database and benchmark of the bond energies of noble-gas-containing molecules

We have developed a new database of structures and bond energies of 59 noble-gas-containing molecules. The structures were calculated by CCSD(T)/aug-cc-pVTZ methods and the bond energies were obtained using the CCSD(T)/complete basis set method. Many wavefunction-based and density functional theory methods have been benchmarked against the 59 accurate bond energies. Our results show that the MPW1B95, B2GP-PLYP, and DSD-BLYP functionals with the aug-cc-pVTZ basis set excel in predicting the bond energies of noble-gas molecules with mean unsigned errors (MUEs) of 2.0 to 2.1 kcal/mol. When combinations of Dunning's basis sets are used, the MPW1B95, B2GP-PLYP, DSD-BLYP, and BMK functionals give significantly lower MUEs of 1.6 to 1.9 kcal/mol. Doubly hybrid methods using B2GP-PLYP and DSD-BLYP functionals and MP2 calculation also provide satisfactory accuracy with MUEs of 1.4 to 1.5 kcal/mol. If the Ng bond energies and the total atomization energies of a group of 109 main-group molecules are considered at the same time, the MPW1B95/aug-cc-pVTZ single-level method (MUE = 2.7 kcal/mol) and the B2GP-PLYP and DSD-PLYP functionals with combinations of basis sets or using the doubly hybrid method (MUEs = 1.9-2.2 kcal/mol) give the overall best result.     

DNAzyme-Mediated Genetically Encoded Sensors for Ratiometric Imaging of Metal Ions in Living Cells

Genetically encoded fluorescent proteins (FPs) have been used for metal ion detection. However, their applications are restricted to a limited number of metal ions owing to the lack of available metal-binding proteins or peptides that can be fused to FPs and the difficulty in transforming the binding of metal ions into a change of fluorescent signal. We report herein the use of Mg²⁺-specific 10–23 or Zn²⁺-specific 8–17 RNA-cleaving DNAzymes to regulate the expression of FPs as a new class of ratiometric fluorescent sensors for metal ions. Specifically, we demonstrate the use of DNAzymes to suppress the expression of Clover2, a variant of the green FP (GFP), by cleaving the mRNA of Clover2, while the expression of Ruby2, a mutant of the red FP (RFP), is not affected. The Mg²⁺ or Zn²⁺ in HeLa cells can be detected using both confocal imaging and flow cytometry. Since a wide variety of metal-specific DNAzymes can be obtained, this method can likely be applied to imaging many other metal ions, expanding the range of the current genetically encoded fluorescent protein-based sensors.     

Copper-Catalyzed Enantioselective Allylic Alkylation with a γ-Butyrolactone-Derived Silyl Ketene Acetal

Herein, we report a Cu-catalyzed enantioselective allylic alkylation using a γ-butyrolactone-derived silyl ketene acetal. Critical to the development of this work was the identification of a novel mono-picolinamide ligand with the appropriate steric and electronic properties to afford the desired products in high yield (up to 96 %) and high ee (up to 95 %). Aryl, aliphatic, and unsubstituted allylic chlorides bearing a broad range of functionality are well-tolerated. Spectroscopic studies reveal that a Cu^I species is likely the active catalyst, and DFT calculations suggest ligand sterics play an important role in determining Cu coordination and thus catalyst geometry.     

Synthesis of High χ–Low N Diblock Copolymers by Polymerization-Induced Self-Assembly

Polymerization-induced self-assembly (PISA) enables the scalable synthesis of functional block copolymer nanoparticles with various morphologies. Herein we exploit this versatile technique to produce so-called “high χ–low N” diblock copolymers that undergo nanoscale phase separation in the solid state to produce sub-10 nm surface features. By varying the degree of polymerization of the stabilizer and core-forming blocks, PISA provides rapid access to a wide range of diblock copolymers, and enables fundamental thermodynamic parameters to be determined. In addition, the pre-organization of copolymer chains within sterically-stabilized nanoparticles that occurs during PISA leads to enhanced phase separation relative to that achieved using solution-cast molecularly-dissolved copolymer chains.     

Reverse Thinking of the Aggregation-Induced Emission Principle: Amplifying Molecular Motions to Boost Photothermal Efficiency of Nanofibers**

Using reverse thinking of the aggregation-induced emission (AIE) principle, we demonstrate an ingenious and universal protocol for amplifying molecular motions to boost photothermal efficiency of fibers. Core–shell nanofibers having the olive oil solution of AIE-active molecules as the core surrounded by PVDF-HFP shell were constructed by coaxial electrospinning. The molecularly dissolved state of AIE-active molecules allows them to freely rotate and/or vibrate in nanofibers upon photoexcitation and thus significantly elevates the proportion of non-radiative energy dissipation, affording impressive heat-generating efficiency. Photothermal evaluation shows that the core–shell nanofibers with excellent durability can reach up to 22.36 % of photothermal conversion efficiency, which is 26-fold as the non-core–shell counterpart. Such a core–shell fiber can be used for photothermal textiles and solar steam generation induced by natural sunlight with green and carbon-zero emission.     

Optoelectronic Properties of Carbon-Bound Boron Difluoride Hydrazone Dimers

The creation of dimeric boron difluoride complexes of chelating N-donor ligands is a proven strategy for the enhancement of the optoelectronic properties of fluorescent dyes. We report dimers based on the boron difluoride hydrazone (BODIHY) framework, which offer unique and sometimes unexpected substituent-dependent absorption, emission, and electrochemical properties. BODIHY dimers have low-energy absorption bands (λ_max=421 to 479 nm, ϵ=17 200 to 39 900 m ⁻¹ cm⁻¹) that are red-shifted relative to monomeric analogues. THF solutions of these dimers exhibit aggregation-induced emission upon addition of water, with emission enhancement factors ranging from 5 to 18. Thin films of BODIHY dimers are weakly emissive as a result of the inner-filter effect, attributed to intermolecular π-type interactions. BODIHY dimers are redox-active and display two one-electron oxidation and two one-electron reduction waves that strongly depend on the N-aryl substituents. These properties are rationalized using density-functional theory calculations and X-ray crystallography experiments.     

Platinum Oxide Nanoparticles for Electrochemical Hydrogen Evolution: Influence of Platinum Valence State

Electrochemical hydrogen generation is a rising prospect for future renewable energy storage and conversion. Platinum remains a leading choice of catalyst, but because of its high cost and low natural abundance, it is critical to optimize its use. In the present study, platinum oxide nanoparticles of approximately 2 nm in diameter are deposited on carbon nitride (C3N4) nanosheets by thermal refluxing of C3N4 and PtCl₂ or PtCl₄ in water. These nanoparticles exhibit apparent electrocatalytic activity toward the hydrogen evolution reaction (HER) in acid. Interestingly, the HER activity increases with increasing Pt⁴⁺ concentration in the nanoparticles, and the optimized catalyst even outperforms commercial Pt/C, exhibiting an overpotential of only −7.7 mV to reach the current density of 10 mA cm⁻² and a Tafel slope of −26.3 mV dec⁻¹. The results from this study suggest that the future design of platinum oxide catalysts should strive to maximize the Pt⁴⁺ sites and minimize the formation of the less active Pt²⁺ species.     

Benchtop NMR analysis of piperazine-based drugs hyperpolarised by SABRE

Piperazine-based drugs, such as N-benzylpiperazine (BZP), became attractive in the 2000s due to possessing effects similar to amphetamines. Herein, BZP, in addition to its pyridyl analogues, 2-, 3-, and 4-pyridylmethylpiperidine (2-PMP, 3-PMP, and 4-PMP respectively) was subjected to the hyperpolarisation technique Signal Amplification By Reversible Exchange (SABRE) in order to demonstrate the use of this technique to detect these piperazine-based drugs. Although BZP was not hyperpolarised via SABRE, 2-PMP, 3-PMP, and 4-PMP were, with the ortho- and meta-pyridyl protons of 4-PMP showing the largest enhancement of 313-fold and 267-fold, respectively, in a 1.4-T detection field, following polarisation transfer at Earth's magnetic field. In addition to the freebase, 4-PMP.3HCl was also appraised by SABRE and was found not to polarise, however, the addition of increasing equivalents of triethylamine (TEA) produced the freebase, with a maximum enhancement observed upon the addition of 3 equivalents of TEA. Further addition of TEA led to a reduction in the observed enhancement. SABRE was also employed to polarise 4-PMP.3HCl (~20% w/w) in a simulated tablet to demonstrate the forensic application of the technique (138-fold enhancement for the ortho-pyridyl protons). The amount of 4-PMP.3HCl present in the simulated tablet was quantified via NMR using D₂O as a solvent and compared well to complimentary gas chromatography–mass spectrometry data. Exchanging D₂O for CD₃OD as the solvent utilised for analysis resulted in a significantly lower amount of 4-PMP.3HCl being determined, thus highlighting safeguarding issues linked to drug abuse in relation to determining the amount of active pharmaceutical ingredient present.