Perfect matchings extending on subcubes to Hamiltonian cycles of hypercubes

Recently, Fink [J. Fink, Perfect matchings extend to Hamilton cycles in hypercubes, J. Combin. Theory Ser. B 97 (2007) 1074-1076] affirmatively answered Kreweras’ conjecture asserting that every perfect matching of the hypercube extends to a Hamiltonian cycle. We strengthen this result in the following way. Given a partition of the hypercube into subcubes of nonzero dimensions, we show for every perfect matching of the hypercube that it extends on these subcubes to a Hamiltonian cycle if and only if it interconnects them.     

Electrodynamic coupling of electric dipole emitters to a fluctuating mode density within a nanocavity

We investigate the impact of rotational diffusion on the electrodynamic coupling of fluorescent dye molecules (oscillating electric dipoles) to a tunable planar metallic nanocavity. Fast rotational diffusion of the molecules leads to a rapidly fluctuating mode density of the electromagnetic field along the molecules' dipole axis, which significantly changes their coupling to the field as compared to the opposite limit of fixed dipole orientation. We derive a theoretical treatment of the problem and present experimental results for rhodamine 6G molecules in cavities filled with low and high viscosity liquids. The derived theory and presented experimental method is a powerful tool for determining absolute quantum yield values of fluorescence.     

Multimodal Analysis of Light-Driven Water Oxidation in Nanoporous Block Copolymer Membranes**

Heterogeneous light-driven catalysis is a cornerstone of sustainable energy conversion. Most catalytic studies focus on bulk analyses of the hydrogen and oxygen evolved, which impede the correlation of matrix heterogeneities, molecular features, and bulk reactivity. Here, we report studies of a heterogenized catalyst/photosensitizer system using a polyoxometalate water oxidation catalyst and a model, molecular photosensitizer that were co-immobilized within a nanoporous block copolymer membrane. Via operando scanning electrochemical microscopy (SECM), light-induced oxygen evolution was determined using sodium peroxodisulfate (Na₂S₂O₈) as sacrificial electron acceptor. Ex situ element analyses provided spatially resolved information on the local concentration and distribution of the molecular components. Infrared attenuated total reflection (IR-ATR) studies of the modified membranes showed no degradation of the water oxidation catalyst under the reported light-driven conditions.     

Understanding MOF Flexibility: An Analysis Focused on Pillared Layer MOFs as a Model System

Flexible porous frameworks are at the forefront of materials research. A unique feature is their ability to open and close their pores in an adaptive manner induced by chemical and physical stimuli. Such enzyme-like selective recognition offers a wide range of functions ranging from gas storage and separation to sensing, actuation, mechanical energy storage and catalysis. However, the factors affecting switchability are poorly understood. In particular, the role of building blocks, as well as secondary factors (crystal size, defects, cooperativity) and the role of host–guest interactions, profit from systematic investigations of an idealized model by advanced analytical techniques and simulations. The review describes an integrated approach targeting the deliberate design of pillared layer metal–organic frameworks as idealized model materials for the analysis of critical factors affecting framework dynamics and summarizes the resulting progress in their understanding and application.     

Efficient Transfection via an Unexpected Mechanism by Near Neutral Polypiperazines with Tailored Response to Endosomal pH

Cationic pH-responsive polymers promise to overcome critical challenges in cellular delivery. Ideally, the polymers become selectively charged along the endosomal pathway disturbing only the local membrane and avoiding unintended interactions or cytotoxic side effects at physiological conditions. Polypiperazines represent a novel, hydrophilic class of pH-responsive polymers whose response can be tuned within the relevant pH range (5–7.4). The authors discovered that the polypiperazines are effectively binding plasmid DNA (pDNA) and demonstrate high efficiency in transfection. By design of experiments (DoE), a wide parameter space (pDNA and polymer concentration) is screened to identify the range of effective concentrations for transfection. An isopropyl modified polypiperazine is highly efficient over a wide range of concentrations outperforming linear polyethylenimine (l-PEI, 25 kDa) in regions of low N*/P ratios. A quantitative polymerase chain reaction (qPCR) surprisingly revealed that the pDNA within the piperazine-based polyplexes can be amplified in contrast to polyplexes based on l-PEI. The pDNA must therefore be more accessible and bound differently than for other known transfection polymers. Considering the various opportunities to further optimize their structure, polypiperazines represent a promising platform for designing effective soluble polymeric vectors, which are charge-neutral at physiological conditions.