Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Role of FTFSI Anion Asymmetry on Physical Properties of AFTFSI (A=Li,Na and K) Based Electrolytes and Consequences on Supercapacitor Application

This study compares the physicochemical properties of six electrolytes comprising of three salts: LiFTFSI, NaFTFSI and KFTFSI in two solvent mixtures, the binary (3EC/7EMC) and the ternary (EC/PC/3DMC). The transport properties (conductivity, viscosity) as a function of temperature and concentration were modeled using the extended Jones-Dole-Kaminsky equation, the Arrhenius model, and the Eyring theory of transition state for activated complexes. Results are discussed in terms of ionicity, solvation shell, and cross-interactions between electrolyte components. The application of the six formulated electrolytes in symmetrical activated carbon (AC)//AC supercapacitors (SCs) was characterized by cyclic voltammetry (CV), galvanostatic cycling with potential limitation (GCPL), electrochemical impedance spectroscopy (EIS) and accelerated aging. Results revealed that the geometrical flexibility of the FTFSI anion allows it to access and diffuse easily in AC whereas its counter ions (Li⁺, Na⁺ or K⁺) can remain trapped in porosity. However, this drawback was partially resolved by mixing LiFTFSI and KFTFSI salts in the electrolyte.     

Effect of polymer and ion concentration on mechanical and drug release behavior of gellan hydrogels using factorial design

Developing optimized hydrogel products requires an in-depth understanding of the mechanisms that drive hydrogel tunability. Here, we performed a full 4 × 4 factorial design study investigating the impact of gellan, a naturally derived polysaccharide (1%, 2%, 3%, or 4% w/v) and CaCl₂ concentration (1, 3, 7, or 10 mM) on the viscoelastic, swelling, and drug release behavior of gellan hydrogels containing a model drug, vancomycin. These concentrations were chosen to specifically provide insight into gellan hydrogel behavior for formulations utilizing polymer and salt concentrations expanding beyond those commonly reported by previous studies exploring gellan. With increasing gellan and CaCl₂ concentration, the hydrogel storage moduli (0.1–100 kPa) followed a power-law relationship and on average these hydrogels had higher liquid absorption capability and greater total drug release over 6 days. We suggest that the effects of gellan and CaCl₂ concentration and their interactions on hydrogel properties can be explained by various phenomena that lead to increased swelling and increased resistance to network expansion.     

Rhodium-Catalyzed ortho-Bromination of O-Phenyl Carbamates Accelerated by a Secondary Amide-Pendant Cyclopentadienyl Ligand

It has been established that a newly developed cyclopentadienyl rhodium(III) [Cp^ARh^III] complex, bearing an acidic secondary amide moiety on the Cp ring, is able to catalyze the ortho-bromination of O-phenyl carbamates with N-bromosuccinimide (NBS) at room temperature. The presence of the acidic secondary amide moiety on the Cp^A ligand accelerates the bromination by the hydrogen bond between the acidic NH group of the Cp^A ligand and the carbonyl group of NBS.     

Photoredox/Cobalt Dual-Catalyzed Decarboxylative Elimination of Carboxylic Acids: Development and Mechanistic Insight

Recently, dual-catalytic strategies towards the decarboxylative elimination of carboxylic acids have gained attention. Our lab previously reported a photoredox/cobaloxime dual catalytic method that allows the synthesis of enamides and enecarbamates directly from N-acyl amino acids and avoids the use of any stoichiometric reagents. Further development, detailed herein, has improved upon this transformation's utility and further experimentation has provided new insights into the reaction mechanism. These new developments and insights are anticipated to aid in the expansion of photoredox/cobalt dual-catalytic systems.     

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.