Existence of time periodic solutions for a class of non-resonant discrete wave equations

The final publication is available at Springer via http://dx.doi.org/10.1186/s13662-015-0457-zIn this paper, a class of discrete wave equations with Dirichlet boundary conditions are obtained by using the center-difference method. For any positive integers m and T, when the existence of time mT-periodic solutions is considered, a strongly indefinite discrete system needs to be established. By using a variant generalized weak linking theorem, a non-resonant superlinear (or superquadratic) result is obtained and the Ambrosetti-Rabinowitz condition is improved. Such a method cannot be used for the corresponding continuous wave equations or the continuous Hamiltonian systems; however, it is valid for some general discrete Hamiltonian systems

Pyrene-Fused s-Indacene

One antiaromatic polycyclic hydrocarbon (PH) with and without solubilizing tert-butyl substituents, namely s-indaceno[2,1-a:6,5-a′]dipyrene (IDPs), has been synthesized by a four-step protocol. The IDPs represent the longitudinal, peri-extension of the indeno[1,2-b]fluorene skeleton towards a planar 40 π-electron system. Their structures were unambiguously confirmed by X-ray crystallographic analysis. The optoelectronic properties were studied by UV/vis absorption spectroscopy and cyclic voltammetry. These studies revealed that peri-fusion renders the IDP derivatives with a narrow optical energy gap of 1.8 eV. The maximum absorption of IDPs is shifted by 160 nm compared to the parent indenofluorene. Two quasi-reversible oxidation as well as reduction steps indicate an excellent redox behavior attributed to the antiaromatic core. Formation of the radical cation and the dication was monitored by UV/vis absorption spectroscopy during titration experiments. Notably, the fusion of s-indacene with two pyrene moieties lead to IDPs with absorption maxima approaching the near infrared (NIR) regime

Sulfur-doped Nanographenes Containing Multiple Subhelicenes

In this work, we describe the synthesis and characterization of three novel sulfur-doped nanographenes (NGs) (1–3) containing multiple subhelicenes, including carbo[4]helicenes, thieno[4]helicenes, carbo[5]helicenes, and thieno[5]helicenes. Density functional theory calculations reveal that the helicene substructures in 1–3 possess dihedral angles from 15° to 34°. The optical energy gaps of 1–3 are estimated to be 2.67, 2.45, and 2.30 eV, respectively. These three sulfur-doped NGs show enlarged energy gaps compared to those of their pristine carbon analogues

High-frequency vacuum electron devices

Vacuum electron devices at frequencies of millimeter waves and terahertz play highly important roles in the modern high-data rate and broadband communication system, high-resolution detection and imaging, medical diagnostics, magnetically confined nuclear fusion, etc. For the fast motion velocity of electrons in the vacuum medium, they have the advantages of high power and high efficiency, as well as compactness, compared with other present radiation sources, such as solid-state devices

Synthesis and Self-Assembly Behavior of Double Ullazine-Based Polycyclic Aromatic Hydrocarbons

Polycyclic aromatic azomethine ylides (PAMY, 1) are versatile building blocks for the bottom-up synthesis of nitrogen-containing polycyclic aromatic hydrocarbons (N-PAHs). Although the chemistry of PAMY was already established few years ago, the cycloaddition of a double PAMY building block has not been reported so far. In this work, we demonstrate the first cycloaddition of a PAMY-dimer (6), which opens the access to three different alkyl ester-substituted N-PAHs with a laterally extended double ullazine scaffold (DU-1, DU-2 and DU-3). Interestingly, the cyclic voltammetry of DU-1-3 exhibited three reversible oxidation waves, which confirmed the electron-rich nature of the double ullazine scaffold. Furthermore, in-situ spectroelectrochemistry study of ethylhexyl ester-substituted DU-3 revealed the formation of different cationic species with new absorption bands up to 1689 nm. Additionally, the influence of the attached substituents on the film formation and supramolecular organization in the thin films were investigated by polarized optical microscopy and grazing incidence wide-angle X-ray scattering

Tailoring Magnetic Features in Zigzag-Edged Nanographenes by Controlled Diels–Alder Reactions

Nanographenes (NGs) with tunable electronic and magnetic properties have attracted enormous attention in the realm of carbon-based nanoelectronics. In particular, NGs with biradical character at the ground state are promising building units for molecular spintronics. However, most of the biradicaloids are susceptible to oxidation under ambient conditions and photolytic degradation, which hamper their further applications. Herein, we demonstrated the feasibility of tuning the magnetic properties of zigzag-edged NGs in order to enhance their stability via the controlled Diels–Alder reactions of peri-tetracene (4-PA). The unstable 4-PA (y0=0.72; half-life, t1/2=3 h) was transformed into the unprecedented benzo-peri-tetracenes (BPTs) by a one-side Diels–Alder reaction, which featured a biradical character at the ground state (y0=0.60) and exhibited remarkable stability under ambient conditions for several months. In addition, the fully zigzag-edged circumanthracenes (CAs) were achieved by two-fold or stepwise Diels–Alder reactions of 4-PA, in which the magnetic properties could be controlled by employing the corresponding dienophiles. Our work reported herein opens avenues for the synthesis of novel zigzag-edged NGs with tailor-made magnetic properties. © 2020 Wiley-VCH Verlag GmbH & Co. KGaA, Weinhei

Helical Nanographenes Containing an Azulene Unit : Synthesis, Crystal Structures, and Properties

Three unprecedented helical nanographenes (1, 2, and 3) containing an azulene unit are synthesized. The resultant helical structures are unambiguously confirmed by X-ray crystallographic analysis. The embedded azulene unit in 2 possesses a record-high twisting degree (16.1°) as a result of the contiguous steric repulsion at the helical inner rim. Structural analysis in combination with theoretical calculations reveals that these helical nanographenes manifest a global aromatic structure, while the inner azulene unit exhibits weak antiaromatic character. Furthermore, UV/Vis-spectral measurements reveal that superhelicenes 2 and 3 possess narrow energy gaps (2: 1.88 eV; 3: 2.03 eV), as corroborated by cyclic voltammetry and supported by density functional theory (DFT) calculations. The stable oxidized and reduced states of 2 and 3 are characterized by in-situ EPR/Vis–NIR spectroelectrochemistry. Our study provides a novel synthetic strategy for helical nanographenes containing azulene units as well as their associated structures and physical properties. © 2019 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA