On a family of elliptic curves of rank at least 2

Let C_m:y² = x³ ? m²x + p²q² be a family of elliptic curves over ?, where m is a positive integer and p, q are distinct odd primes. We study the torsion part and the rank of C_m(?). More specifically, we prove that the torsion subgroup of C_m(?) is trivial and the ?-rank of this family is at least 2, whenever m ? 0 (mod 3), m ? 0 (mod 4) and m ≡ 2 (mod 64) with neither p nor q dividing m.

     

Correction to: Macrocycles in dual role: ancillary ligands in metal complexes and organocatalysts for the ring‑opening polymerization of lactide

Journal of Inclusion Phenomena and Macrocyclic Chemistry - A correction to this paper has been published: https://doi.org/10.1007/s10847-021-01060-y     

Efficient monooleoyl glycerol synthesis employing hybrid ultrasonic-infrared-wave promoted reactor: Concurrent catalytic and noncatalytic esterification kinetics

For the first time, intensification of monooleoyl glycerol (MOG) synthesis has been investigated in an ultrasonic-infrared-wave (USIRW) promoted batch reactor. Esterification of octadecanoic acid (ODA) with glycerol (Gl) has been conducted [using Amberlyst 36 wet catalyst] in three different reactors, namely traditional batch reactor (TBR), infrared wave promoted batch reactor (IRWPBR), and USIRW-promoted batch reactor (USIRWPBR) to assess the relative efficacy. The energy-efficient USIRWPBR remarkably intensifies the ODA-Gl esterification as manifested through superior ODA conversion (92.5 ± 1.25%) compared to that achieved in IRWPBR (79.8 ± 1.2%) and TBR (36.39 ± 1.25%). The most favorable reaction condition for optimum ODA conversion and maximum MOG yield was identified through statistical optimization over a selected parametric range, namely 3-5 Gl/ODA mole ratio, 0.004-0.006 g/mL Amberlyst 36 catalyst concentration, 300-700 rpm impeller speed, and 333-353 K reaction temperature. The present study also reports the formulation and validation of an innovative reaction kinetics, that is, concurrent noncatalytic and heterogeneously catalyzed (CNCHC) reaction mechanism in addition to the conventional heterogeneous kinetic models (LH and Eley-Rideal mechanisms). Under combined USIRW, the CNCHC esterification mechanism could best describe ODA-Gl esterification (R² = 0.98) compared to LH (R² = 0.97) and Eley-Rideal (R² = 0.88) mechanisms. The optimal product (MOG) was characterized by differential scanning calorimetry and thermogravimetric analysis to assess its crystallization property and thermal stability for possible application as plasticizer/fuel additives.     

Optimizing the monomer structure of polyhedral oligomeric silsesquioxane for ion transport in hybrid organic–inorganic block copolymers

Poly(ethylene oxide)-b-polyhedral oligomeric silsesquioxane (PEO–POSS) mixed with lithium bis(trifluoromethanesulfonyl)imide salt is a nanostructured hybrid organic–inorganic block copolymer electrolyte that may enable lithium metal batteries. The synthesis and characteristics of three PEO–POSS block copolymer electrolytes which only differ by their POSS silica cage substituents (ethyl, isobutyl, and isooctyl) is reported. Changing the POSS monomer structure results in differences in both thermodynamics and ion transport. All three neat polymers exhibit lamellar morphologies. Adding salt results in the formation of a disordered window which closes and gives way to lamellae at higher salt concentrations. The width of disordered window decreases with increasing length of the POSS alkyl chain substituent from ethyl to isobutyl and is absent in the isooctyl sample. Rheological measurements demonstrate good mechanical rigidity when compared with similar all-organic block copolymers. While salt diffusion coefficient and current ratio are unaffected by substituent length, ionic conductivity increases as the length of the alkyl chain substituent decreases: the ethyl substituent is optimal for ion transport. This is surprising because conventional wisdom suggests that ion transport occurs primarily in the PEO-rich domains, that is, ion transport should be unaffected by substituent length after accounting for the minor change in conducting phase volume fraction. © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 363–371     

Two-Dimensional Layered Metallic VSe2/SWCNTs/rGO Based Ternary Hybrid Materials for High Performance Energy Storage Applications

In this work, the ternary hybrid structure VSe₂/SWCNTs/rGO is reported for supercapacitor applications. The ternary composite exhibits a high specific capacitance of 450 F g⁻¹ in a symmetric cell configuration, with maximum energy density of 131.4 Wh kg⁻¹ and power density of 27.49 kW kg⁻¹. The ternary hybrid also shows a cyclic stability of 91 % after 5000 cycles. Extensive density functional theory (DFT) simulations on the structure as well as on the electronic properties of the binary hybrid structure VSe₂/SWCNTs and the ternary hybrid structure VSe₂/SWCNTs/rGO have been carried out. Due to a synergic effect, there are enhanced density of states near the Fermi level and higher quantum capacitance for the hybrid ternary structure compared to VSe₂/SWCNTs, leading to higher energy and power density for VSe₂/SWCNTs/rGO, supporting our experimental observation. Computed diffusion energy barrier of electrolyte ions (K⁺) predicts that ions move faster in the ternary structure, providing higher charge storage performance.     

An Ultra-Microporous Metal–Organic Framework with Exceptional Xe Capacity

Molecular confinement plays a significant effect on trapped gas and solvent molecules. A fundamental understanding of gas adsorption within the porous confinement provides information necessary to design a material with improved selectivity. In this regard, metal–organic framework (MOF) adsorbents are ideal candidate materials to study confinement effects for weakly interacting gas molecules, such as noble gases. Among the noble gases, xenon (Xe) has practical applications in the medical, automotive and aerospace industries. In this Communication, we report an ultra-microporous nickel-isonicotinate MOF with exceptional Xe uptake and selectivity compared to all benchmark MOF and porous organic cage materials. The selectivity arises because of the near perfect fit of the atomic Xe inside the porous confinement. Notably, at low partial pressure, the Ni–MOF interacts very strongly with Xe compared to the closely related Krypton gas (Kr) and more polarizable CO₂. Further ¹²⁹Xe NMR suggests a broad isotropic chemical shift due to the reduced motion as a result of confinement.     

Chalcogen Stabilized bis-Hydridoborate Complexes of Cobalt: Analogues of Tetracyclo[4.3.0.02,4.03,5]nonane

Treatment of Li[BH₃ER] (E=Se or Te, R=Ph; E=S, R=CH₂Ph) with [Cp*CoCl]₂ led to the formation of hydridoborate complexes, [{CoCp*Ph}{Cp*Co}{μ-EPh}{μ-κ²-E,H-EBH₃}], 1a and 1 b ( 1 a : E=Se; 1 b : E=Te) and a bis-hydridoborate species [Cp*Co{μ-κ²-Se,H-SeBH₃}]₂, 2 . All the complexes, 1 a , 1 b and 2 are stabilized by β-agostic type interaction in which 1 b represents a novel bimetallic borate complex with a rare B−Te bond. QTAIM analysis furnished direct proof for the existence of a shared and dative B-chalcogen and Co-chalcogen interactions, respectively. In parallel to the formation of the hydridoborate complexes, the reactions also yielded tetracyclic species, [Cp*Co{κ³-E,H,H-E(BH₂)₂-C₅Me₅H₃}], 3 a and 3 b ( 3 a : E=Se and 3 b : E=S), wherein the bridgehead boron atoms are surrounded by one chalcogen, one cobalt and two carbon atoms of a cyclopentane ring. Molecules 3 a and 3 b are best described as the structural mimic of tetracyclo[4.3.0.0^2,4.0^3,5]nonane having identical structure and similar valence electron counts.     

Alcohols as Fluoroalkyl Synthons: Ni-catalyzed Dehydrogenative Approach to Access Polyfluoroalkyl Bis-indoles

An acceptorless dehydrogenative strategy for the synthesis of polyfluoroalkylated bis-indoles is described by employing an earth-abundant nickel-based catalytic system under air. The notable feature of the present transformation is the use of bench stable and easily affordable polyfluorinated alcohols without any pre-functionalization for the introduction of precious polyfluoroalkyl groups. The developed straightforward protocol accomplished biologically relevant fluoroalkyl bis-indoles in a sustainable fashion. Extensive DFT study predicts the unique role of indole molecules which stabilizes the transition states during the dehydrogenation process of polyfluorinated alcohols, presumably through non-covalent π⋅⋅⋅π and H-bonding interactions.     

C−C Bond Formation of Benzyl Alcohols and Alkynes Using a Catalytic Amount of KOtBu: Unusual Regioselectivity through a Radical Mechanism

We report a C?C bond‐forming reaction between benzyl alcohols and alkynes in the presence of a catalytic amount of KO^tBu to form α‐alkylated ketones in which the C=O group is located on the side derived from the alcohol. The reaction proceeds under thermal conditions (125 °C) and produces no waste, making the reaction highly atom efficient, environmentally benign, and sustainable. Based on our mechanistic investigations, we propose that the reaction proceeds through radical pathways.