Numerical simulations of systems of PDEs by variational iteration method

In this Letter, a general framework of the variational iteration method (VIM) is presented for solving systems of linear and nonlinear partial differential equations (PDEs). In VIM, a correction functional is constructed by a general Lagrange's multiplier which can be identified via a variational theory. VIM yields an approximate solution in the form of a rapid convergent series. Comparison with the exact solutions shows that VIM is a powerful method for the solution of linear and nonlinear systems of PDEs.     

On near-wall effects in hard disk packing between two concentric cylinders

Monodisperse packing of disks in confined geometries is rarely addressed in the literature. We present some theoretical aspects of the microstructural properties of 2D static packing of disks between two concentric cylinders. In the core of the geometry, the packing is intact, while it is dilated in the vicinity of the walls as a result of the removal of overlapping disks. We have derived the formula for average packing density in concentric cylinders geometry with given ratio of the particle diameter to the gap between cylinders. It is verified and analyzed further by constructing ordered and disordered packs of monodisperse disks in computer. In this context, Voronoi tessellation is performed for the resulting packs to demonstrate the thickness of the static boundary layer where the packing is influenced by the presence of cylindrical walls.     

Optimization study of polyethylene glycol and solvent system for gas permeation membranes

Cellulose acetate (CA) membranes blended with Polyethylene glycol (PEG) in acetone–water solvent system were synthesized by using solution-casting method that resulted in the formation of flexible, white membranes. Different molecular weight (MW) grades of PEG (including MW 1000, 10,000 and 20,000?g/mol) were used. Cast membranes were tested for tensile strength and permeability at different loading of PEG MW 10,000 and 20,000?g/mol. Excellent flexible membranes were produced in acetone–water solvent system in the presence of PEG, which were otherwise brittle. Surface structure and morphology were analysed using scanning electron microscopy. The presence of different functional groups was confirmed using Fourier transform infra-red spectroscopy and the mechanical characteristics were studied by tensile testing. The introduction of PEG caused an increase in permeability of the membranes. The increase in permeability is due to the opening up of pores as the membrane becomes more flexible, when the plasticizer is added. The permeability continues to increase with the addition of PEG. Moreover, the resulting membranes are not only more flexible, but also have largely improved tensile strength as compared to the CA membranes without PEG. This improved tensile strength can also be attributed to the improved flexibility of the membrane. A trade-off is reached between tensile strength and permeability as increasing amount of PEG improves tensile strength but the resulting membrane becomes too permeable to be used for gas separation. Moreover, using PEG of higher MW resulted in porous membranes, even at low amounts of PEG. Therefore, we concluded that CA membrane with less amount of low-MW PEG (i.e. 5% PEG of MW 1000?g/mol) must be used to optimize both permeability and tensile strength of the membrane.     

Metastates in Disordered Mean-Field Models II: The Superstates

We continue to investigate the size dependence of disordered mean-field models with finite local spin space in more detail, illustrating the concept of superstates as recently proposed by Bovier and Gayrard. We discuss various notions of convergence for the behavior of the paths (t_[tN]()) _{t(0, 1]} in the thermodynamic limit N. Here _n () is the Gibbs measure in the finite volume {1,..., n} and is the disorder variable. In particular we prove refined convergence statements in our concrete examples, the Hopfield model with finitely many patterns (having continuous paths) and the Curie–Weiss random-field Ising model (having singular paths).     

Enhancing Built-in Electric Fields for Efficient Photocatalytic Hydrogen Evolution by Encapsulating C60 Fullerene into Zirconium-Based Metal-Organic Frameworks

High-efficiency photocatalysts based on metal-organic frameworks (MOFs) are often limited by poor charge separation and slow charge-transfer kinetics. Herein, a novel MOF photocatalyst is successfully constructed by encapsulating C₆₀ into a nano-sized zirconium-based MOF, NU-901. By virtue of host-guest interactions and uneven charge distribution, a substantial electrostatic potential difference is set-up in C₆₀@NU-901. The direct consequence is a robust built-in electric field, which tends to be 10.7 times higher in C₆₀@NU-901 than that found in NU-901. In the catalyst, photogenerated charge carriers are efficiently separated and transported to the surface. For example, photocatalytic hydrogen evolution reaches 22.3 mmol g⁻¹ h⁻¹ for C₆₀@NU-901, which is among the highest values for MOFs. Our concept of enhancing charge separation by harnessing host-guest interactions constitutes a promising strategy to design photocatalysts for efficient solar-to-chemical energy conversion.     

Heptagon-Containing Nanographene Embedded into [10]Cycloparaphenylene

We report the synthesis and characterization of a novel type of nanohoop, consisting of a cycloparaphenylene derivative incorporating a curved heptagon-containing π-extended polycyclic aromatic hydrocarbon (PAH) unit. We demonstrate that this new macrocycle behaves as a supramolecular receptor of curved π-systems such as fullerenes C₆₀ and C₇₀, with remarkably large binding constants (ca. 10⁷ M⁻¹), as estimated by fluorescence measurements. Nanosecond and femtosecond spectroscopic analysis show that these host-guest complexes are capable of quasi-instantaneous charge separation upon photoexcitation, due to the ultrafast charge transfer from the macrocycle to the complexed fullerene. These results demonstrate saddle-shaped PAHs with dibenzocycloheptatrienone motifs as structural components for new macrocycles displaying molecular receptor abilities and versatile photochemical responses with promising electron-donor properties in host-guest complexes.     

ATP-Independent and Cell-Free Biosynthesis of β-Hydroxy Acids Using Vinyl Esters as Smart Substrates

In vitro biosynthetic pathways that condense and reduce molecules through coenzyme A (CoASH) activation demand energy and redox power in the form of ATP and NAD(P)H, respectively. These coenzymes must be orthogonally recycled by ancillary reactions that consume chemicals, electricity, or light, impacting the atom economy and/or the energy consumption of the biosystem. In this work, we have exploited vinyl esters as dual acyl and electron donor substrates to synthesize β-hydroxy acids through a non-decarboxylating Claisen condensation, reduction and hydrolysis stepwise cascade, including a NADH recycling step, catalyzed by a total of 4 enzymes. Herein, the chemical energy to activate the acyl group with CoASH and the redox power for the reduction are embedded into the vinyl esters. Upon optimization, this self-sustaining cascade reached a titer of (S)-3-hydroxy butyrate of 24 mM without requiring ATP and simultaneously recycling CoASH and NADH. This work illustrates the potential of in vitro biocatalysis to transform simple molecules into multi-functional ones.     

Biomimetic Design of a Robustly Stabilized Folded State Enabling Seed-Initiated Supramolecular Polymerization under Microfluidic Mixing**

We have investigated the folding and assembly behavior of a cystine-based dimeric diamide bearing pyrene units and solubilizing alkyl chains. In low-polarity solvents, it forms a 14-membered ring through double intramolecular hydrogen bonds between two diamide units. The spectroscopic studies revealed that the folded state is thermodynamically unstable and eventually transforms into more energetically stable helical supramolecular polymers that show an enhanced chiral excitonic coupling between the transition dipoles of the pyrene units. Importantly, compared to an alanine-based monomeric diamide, the dimeric diamide exhibits a superior kinetic stability in the metastable folded state, as well as an increased thermodynamic stability in the aggregated state. Accordingly, the initiation of supramolecular polymerization can be regulated using a seeding method even under microfluidic mixing conditions. Furthermore, taking advantage of a self-sorting behavior observed in a mixture of l -cysteine- and d -cysteine-based dimeric diamides, a two-step supramolecular polymerization was achieved by stepwise addition of the corresponding seeds.     

The Story of the Little Blue Box: A Tribute to Siegfried Hünig

The tetracationic cyclophane, cyclobis(paraquat-p-phenylene), also known as the little blue box, constitutes a modular receptor that has facilitated the discovery of many host–guest complexes and mechanically interlocked molecules during the past 35 years. Its versatility in binding small π-donors in its tetracationic state, as well as forming trisradical tricationic complexes with viologen radical cations in its doubly reduced bisradical dicationic state, renders it valuable for the construction of various stimuli-responsive materials. Since the first reports in 1988, the little blue box has been featured in over 500 publications in the literature. All this research activity would not have been possible without the seminal contributions carried out by Siegfried Hünig, who not only pioneered the syntheses of viologen-containing cyclophanes, but also revealed their rich redox chemistry in addition to their ability to undergo intramolecular π-dimerization. This Review describes how his pioneering research led to the design and synthesis of the little blue box, and how this redox-active host evolved into the key component of molecular shuttles, switches, and machines.