Mobility of water molecules in Li+, Na+ and Cs+ ionic forms of Nafion membrane studied by NMR

Correlation times and diffusion coefficients of water molecules were measured for the first time by ¹H spin relaxation and pulsed field gradient NMR in Li⁺, Na⁺ and Cs⁺ ionic forms of Nafion 117 membrane. Hydration numbers of Li⁺, Na⁺ and Cs⁺ cations were calculated. It was shown that at high humidity macroscopic transfer is controlled by the local translational motion of water molecules.     

Functional Groups Assisted Tunable Dielectric Permittivity of Guest-Free Zn-Based Coordination Polymers for Gate Dielectrics

The dielectric properties of coordination polymers has been a topic of recent interest, but the role of different functional groups on the dielectric properties of these polymers has not yet been fully addressed. Herein, the effects of electron-donating (R=NH₂) and electron-withdrawing (R=NO₂) groups on the dielectric behavior of such materials were investigated for two thermally stable and guest-free Zn-based coordination polymers, [Zn(L₁)(L₂)]_n ( 1 ) and [Zn(L₁)(L₃)]_n ( 2 ) [L₁=2-(2-pyridyl) benzimidazole (Pbim), L₂=5-aminoisophthalate (Aip), and L₃=5-nitroisophthalate (Nip)]. The results of dielectric studies of 1 revealed that it possesses a high dielectric constant (κ=65.5 at 1 kHz), while compound 2 displayed an even higher dielectric constant (κ=110.3 at 1 kHz). The electron donating and withdrawing effects of the NH₂ and NO₂ substituents induce changes in the polarity of the polymers, which is due to the inductive effect from the aryl ring for both NO₂ and NH₂. Theoretical results from density functional theory (DFT) calculations, which also support the experimental findings, show that both compounds have a distinct electronic behavior with diverse wide bandgaps. The significance of the current work is to provide information about the structure-dielectric property relationships. So, this study promises to pave the way for further research on the effects of different functional groups on coordination polymers on their dielectric properties.     

High-fidelity Recognition of Organotrifluoroborate Anions (R−BF3−) as Designer Guest Molecules

The recognition of boron compounds is well developed as boronic acids but untapped as organotrifluoroborate anions (R−BF₃⁻). We are exploring the development of these and other designer anions as anion-recognition motifs by considering them as substituted versions of the parent inorganic ion. To this end, we demonstrate strong and reliable binding of organic trifluoroborates, R−BF₃⁻, by cyanostar macrocycles that are size-complementary to the inorganic BF₄⁻ progenitors. We find that recognition is modulated by the substituent's sterics and that the affinities are retained using the common K⁺ salts of R−BF₃⁻ anions.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

Yield enhancement of elliptical high harmonics driven by bicircular laser pulses

We theoretically investigate the yield enhancement of elliptical high harmonics in the interaction of molecules with bicircular laser pulses by solving the time-dependent Schrödinger equation. It is shown that by adjusting the relative intensity ratio of the two bicircular field components in specific ranges the yield of the molecular high harmonics for the plateau and cutoff regions can be respectively enhanced. To analyze this enhancement phenomenon, we calculate the weights of the electron classical trajectories. Additionally, we also study the ellipticity distribution of harmonics for different intensity ratios. We find that these enhanced harmonics are elliptically polarized, which we mainly attribute to the recombination dipole moment of the major weighted trajectories. These enhanced elliptical extreme ultraviolet and soft x-ray radiations may serve as essential tools for exploring the ultrafast dynamics in magnetic materials and chiral media.