Infinite family of transmission irregular trees of even order

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph $G$. The transmission of a vertex $v$ is the sum of distances from $v$ to all the other vertices of $G$. If transmissions of all vertices are mutually distinct, then $G$ is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klav?ar (2018). The following problem was posed in Alizadeh and Klav?ar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.     

Divergent Synthesis of Oxa-Cyclic Nitrones through Gold(I)-Catalyzed 1,3-Azaprotio Transfer of Propargylic α-Ketocarboxylate Oximes: Experimental and DFT Studies

1,3-Azaprotio transfer of propargylic α-ketocarboxylate oximes, a new type of alkynyl oximes featuring an ester tether, has been explored by taking advantage of gold catalysis. The incorporation of an oxygen atom to the chain of alkynyl oximes led to the formation of two different oxa-cyclic nitrones. It was found that internal alkynyl oximes with an E-configuration deliver five-membered nitrones, whereas terminal alkynyl oximes with an E-configuration afford six-membered nitrones. DFT calculations on four possible pathways supported a stepwise formation of C−N and C−H bonds, in which a 1,3-acyloxy-migration competes with the 1,3-azaprotio-transfer, especially in the case of internal alkynyl oximes. The relative nucleophilic properties of oxygen in the carbonyl group and the nitrogen in the oxime, the electronic effects of alkynes, and the influence of the ring system have been investigated computationally.     

Development of Sulfonic-Acid-Functionalized Mesoporous Materials: Synthesis and Catalytic Applications

Sulfonic acid based mesostructures (SAMs) have been developed in recent years and have important catalytic applications. The primary applications of these materials are in various organic synthesis reactions, such as multicomponent reactions, carbon–carbon bond couplings, protection reactions, and Fries and Beckman rearrangements. This review aims to provide an overview of the recent developments in the field of SAMs with a particular emphasis on the reaction scope and advantages of heterogeneous solid acid catalysts.     

Molecular-Based Design of Microporous Carbon Nanosheets

Microporous carbons afford high surface areas, large pore volumes, and good conductivity, and are fascinating over a wide range of applications. Traditionally synthesized microporous carbon materials usually suffer from some limitations, such as poor accessibility and slow mass transport of molecules due to the micrometer-scale diffusion pathways and space confinement imposed by small pore sizes. Two-dimensional microporous carbon materials, denoted as microporous carbon nanosheets (MCNs), possess nanoscale thickness, which allows fast mass and heat transport along the z axis; thus overcoming the drawbacks of their bulk counterparts. Herein, recent breakthroughs in the synthetic strategies for MCNs are summarized. Three typical methods are discussed in detail with several examples: pyrolysis of organic precursors with 2D units, a templating method that uses wet chemistry, and the molten salt method. Among them, molecular-based assembly of MCNs in the liquid phase shows more controllable morphology, thickness, and pore size distribution. Finally, challenges in this research area are discussed to inspire future explorations.     

Self-Healable Polyelectrolytes with Mechanical Enhancement for Flexible and Durable Supercapacitors

The practical application of advanced personalized electronics is inseparable from flexible, durable, and even self-healable energy storage devices. However, the mechanical and self-healing performance of supercapacitors is still limited at present. Herein, highly transparent, stretchable, and self-healable poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPSA)/poly(vinyl alcohol) (PVA)/LiCl polyelectrolytes were facilely prepared by one-step radical polymerization. The cooperation of PAMPSA and PVA significantly increased the mechanical and self-healing capacity of the polyelectrolyte, which exhibited superior stretchability of 938 %, stress of 112.68 kPa, good electrical performance (ionic conductivity up to 20.6 mS cm⁻¹), and high healing efficiency of 92.68 % after 24 h. After assembly with polypyrrole-coated single-walled carbon nanotubes, the resulting as-prepared supercapacitor had excellent electrochemical properties with high areal capacitance of 297 mF cm⁻² at 0.5 mA cm⁻² and good rate capability (218 mF cm⁻² at 5 mA cm⁻²). Besides, after cutting in two the supercapacitor recovered 99.2 % of its original specific capacitance after healing for 24 h at room temperature. The results also showed negligible change in the interior contact resistance of the supercapacitor after ten cutting/healing cycles. The present work provides a possible solution for the development of smart and durable energy storage devices with low cost for next-generation intelligent electronics.     

Molecular dynamics of the intramolecular 1, 3-dipolar ene reaction of a nitrile oxide and an alkene: non-statistical behavior of a reaction involving a diradical intermediate*

ABSTRACT

Potential energy surfaces and molecular dynamics of the intramolecular 1, 3-dipolar cycloaddition and ene reaction of a nitrile oxide with an alkene were performed in the gas phase and in dichloromethane with density functional theory. One hundred trajectories were propagated in the gas phase and in dichloromethane, respectively. Twenty percent of the trajectories in the gas phase involve bicyclic intermediate and the mean time gap is 472fs. A dynamically stepwise reaction is observed. In dichloromethane, more reactive trajectories were obtained and the time gap is larger than that in the gas phase.     

Highly Proton-Conductive Zinc Metal-Organic Framework Based On Nickel(II) Porphyrinylphosphonate

The design of new solid-state proton-conducting materials is a great challenge for chemistry and materials science. Herein, a new anionic porphyrinylphosphonate-based MOF ( IPCE-1Ni ), which involves dimethylammonium (DMA) cations for charge compensation, is reported. As a result of its unique structure, IPCE-1Ni exhibits one of the highest value of the proton conductivity among reported proton-conducting MOF materials based on porphyrins (1.55×10⁻³ S cm⁻¹ at 75 °C and 80 % relative humidity).     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.