The size of sums of sets,II

We prove inequalities which give lower bounds for the Lebesgue measures of setsE +K whereK is a certain kind of Cantor set. For example, ifC is the Cantor middle-thirds subset of the circle groupT, then $$m(E)^{1 - log2/log3} \leqq m(E + C)$$ for every BorelE ?T.     

Phase transfer of metal cations by induced dynamic carrier agents: biphasic extraction based on dynamic covalent chemistry

In contrast to the classical method where a single molecule is designed to extract metal cations under specific conditions, dynamic covalent chemistry provides an approach based on the implementation of an adaptive dynamic covalent library for inducing the generation of the extractant species. This approach has been applied to the liquid–liquid extraction of copper(ii) nitrate based on a dynamic library of acylhydrazones constituents that self-build and distribute through the interface of a biphasic system. The addition of copper(ii) cations to this library triggers a modification of its composition and the up-regulation of the ligand molecules driven by coordination to the metal cations. Among these, one species has proven to be sufficiently lipophilic to play the role of carrier agent and its formation by component exchange enables the partial extraction of the copper(ii). The study of different pathways to generate the dynamic covalent library demonstrates the complete reversibility and the adaptability of the system. The detailed analytical investigation of the system provides a means to assess the mechanism of the dynamic extraction process.

Phase transfer of Cu(ii) cations is achieved by component exchange in a dynamic covalent library of acylhydrazone ligands. B1/B2 component exchange leads to the generation of a lipophilic carrier agent that extracts Cu(ii) into chloroform.     

Rational incorporation of defects within metal–organic frameworks generates highly active electrocatalytic sites

The allure of metal–organic frameworks (MOFs) in heterogeneous electrocatalysis is that catalytically active sites may be designed a priori with an unparalleled degree of control. An emerging strategy to generate coordinatively-unsaturated active sites is through the use of organic linkers that lack a functional group that would usually bind with the metal nodes. To execute this strategy, we synthesize a model MOF, Ni-MOF-74 and incorporate a fraction of 2-hydroxyterephthalic acid in place of 2,5-dihydroxyterephthalic acid. The defective MOF, Ni-MOF-74D, is evaluated vs. the nominally defect-free Ni-MOF-74 with a host of ex situ and in situ spectroscopic and electroanalytical techniques, using the oxidation of hydroxymethylfurtural (HMF) as a model reaction. The data indicates that Ni-MOF-74D features a set of 4-coordinate Ni–O₄ sites that exhibit unique vibrational signatures, redox potentials, binding motifs to HMF, and consequently superior electrocatalytic activity relative to the original Ni-MOF-74 MOF, being able to convert HMF to the desired 2,5-furandicarboxylic acid at 95% yield and 80% faradaic efficiency. Furthermore, having such rationally well-defined catalytic sites coupled with in situ Raman and infrared spectroelectrochemical measurements enabled the deduction of the reaction mechanism in which co-adsorbed *OH functions as a proton acceptor in the alcohol oxidation step and carries implications for catalyst design for heterogeneous electrosynthetic reactions en route to the electrification of the chemical industry.

The allure of metal–organic frameworks (MOFs) in heterogeneous electrocatalysis is that catalytically active sites may be designed a priori with an unparalleled degree of control.     

Site-to-site peptide transport on a molecular platform using a small-molecule robotic arm

Peptides attached to a cysteine hydrazide ‘transporter module’ are transported selectively in either direction between two chemically similar sites on a molecular platform, enabled by the discovery of new operating methods for a molecular transporter that functions through ratcheting. Substrate repositioning is achieved using a small-molecule robotic arm controlled by a protonation-mediated rotary switch and attachment/release dynamic covalent chemistry. A polar solvent mixtures were found to favour Z to E isomerization of the doubly-protonated switch, transporting cargo in one direction (arbitrarily defined as ‘forward’) in up to 85% yield, while polar solvent mixtures were unexpectedly found to favour E to Z isomerization enabling transport in the reverse (‘backward’) direction in >98% yield. Transport of the substrates proceeded in a matter of hours (compared to 6 days even for simple cargoes with the original system) without the peptides at any time dissociating from the machine nor exchanging with others in the bulk. Under the new operating conditions, key intermediates of the switch are sufficiently stabilized within the macrocycle formed between switch, arm, substrate and platform that they can be identified and structurally characterized by ¹H NMR. The size of the peptide cargo has no significant effect on the rate or efficiency of transport in either direction. The new operating conditions allow detailed physical organic chemistry of the ratcheted transport mechanism to be uncovered, improve efficiency, and enable the transport of more complex cargoes than was previously possible.

Peptides are transported in either direction between chemically similar sites on a molecular platform, substrate repositioning is achieved using a cysteine hydrazide transporter module and a small-molecule robotic arm controlled by a rotary switch.     

A supramolecular microfluidic optical chemosensor

A supramolecular microfluidic optical chemosensor (muFOC) has been fabricated. A serpentine channel has been patterned with a sol-gel film that incorporates a cyclodextrin supramolecule modified with a Tb(3+) macrocycle. Bright emission from the Tb(3+) ion is observed upon exposure of the (mu)FOC to biphenyl in aqueous solution. The signal transduction mechanism was elucidated by undertaking steady-state and time-resolved spectroscopic measurements directly on the optical chemosensor patterned within the microfluidic network. The presence of biphenyl in the cyclodextrin receptor site triggers Tb(3+) emission by an absorption-energy transfer-emission process. These results demonstrate that the intricate signal transduction mechanisms of supramolecular optical chemosensors are successfully preserved in microfluidic environments.     

1,2-Epoxycarotinoide. 3. Mitteilung. Isolierun von 1,2-Epoxy-1,2-dihydrolycopin aus Tomaten

1,2-Epoxycarotenoids: Isolation of 1,2-Epoxy-1,2-dihydrolycopene from Tomatoes The optically active, 1,2-epoxy-1,2-dihydrolycopene was isolated from tomatoes. Its constitution was established by comparison with the racemic synthetic compound.     

The “Facilitated Transition” hypothesis as an explanation for the gemdialkyl effect

A new technique of searching the conformational space of transition states was used to explore the cause of the rate acceleration in the gem-dialkyl effect in intramolecular cyclization reactions. Several previous hypotheses were discarded and a new hypothesis was advanced based on this new data. This hypothesis, the “Facilitated Transition” hypothesis, states that increased steric hindrance reduces the overall activation energy by facilitating rotation through the transition state. The older “Reactive Rotamer” hypothesis was eliminated by generating all conformations of the starting materials using the and computer programs and demonstrating that no relationship is found between rate increase and a change in the concentration of “reactive rotamers”.     

A rapid radiochemical procedure for indium

A rapid radiochcmical procedure was developed for the separation of indium radionuclides from a mixed fission-product solution. An alcoholic pyridine solution is added to a uranium solution containing indium and tin carriers. The resulting tin precipitate is separated from the indium-containing solution by filtering through a cellulose membrane filter. The decontamination factor for tin is 2·10³. Other fission products are only partially removed. The chemical yield of indium is about 44%, and the time required for the separation is about 10 sec. After the tin-separated indium has decayed, the tin daughters of indium are removed from all the other fission products at a specified time and measured, so that the amount of indium present at the time of the tin precipitation is determined.