On the Structure of ∞-Harmonic Maps

Let H ∈ C ²(? ^N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E _∞(u, Ω) = ‖H(Du)‖ _{L ^∞(Ω)} defined on maps u: Ω ? ? ⁿ  → ? ^N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ? ^N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.     

On‐Surface Reactive Planarization of Pt(II) Complexes

A series of Pt(II) complexes with tetradentate luminophores has been designed, synthesized, and deposited on coinage metal surfaces with the aim to produce highly planar self‐assembled monolayers. Low‐temperature scanning tunneling microscopy (STM) and density functional theory (DFT) calculations reveal a significant initial nonplanarity for all complexes. A subsequent metal‐catalyzed separation of the nonplanar moiety at the bridging unit via the scission of a C?N bond is observed, leaving behind a largely planar core complex. The activation barrier of this bond scission process is found to depend strongly on the chemical nature of both bridging group and coordination plane, and to increase from Cu(111) through Ag(111) to Au(111).     

Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators

We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator ? Δ ? V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N ? 2)²/4|x|^?2 or the critical borderline potential V(x) =  (1/4)dist(x, ?Ω)^?2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.     

Iodine-transfer polymerization and CuAAC “click” chemistry: A versatile approach toward poly(vinylidene fluoride)-based amphiphilic triblock terpolymers

This study presents the synthesis and properties of linear PVDF-based amphiphilic triblock terpolymers with PS and PEO, [PVDF-b-PS-b-PEO], by adopting a procedure that involves: (a) iodine-transfer polymerization (ITP) of VDF with 1-iodoperfluorohexane (C₆F₁₃I) serving as chain-transfer agent (CTA) to afford C₆F₁₃-PVDF-I, (b) ITP of styrene with the C₆F₁₃-PVDF-I macromolecular-CTA to obtain C₆F₁₃-PVDF-b-PS-I diblock copolymer, (c) end-group exchange from iodo- to azido-group by nucleophilic substitution reaction with NaN_3, and (d) copper-catalyzed azide-alkyne cycloaddition (CuAAC) with alkyne-terminated PEO to achieve C₆F₁₃-PVDF-b-PS-b-PEO triblock terpolymers. The ¹H and ¹⁹F NMR spectroscopy confirmed the presence of all blocks, while gel permeation chromatography traces showed the living nature of ITP technique. The self-assembly of these terpolymers was investigated in films (atomic force microscopy and DSC), as well as in aqueous and organic solvents (DLS). The analysis of crystalline phases based on the FTIR spectroscopy indicated the conversion of PVDF α-phase into α + β-phases and β + γ-phases upon the incorporation of PS and PEO blocks, respectively. The synthesized amphiphilic copolymers were evaluated (fluorescence spectroscopy) as carriers of small hydrophobic molecules in water. © 2019 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 163–171     

Electrochemical studies on novel films consisting of phosphorus-doped multi-walled carbon nanotubes

Ionics - Films consisting of phosphorus-doped multi-walled carbon nanotubes (further denoted as P-MWCNTs) were fabricated by means of chemical vapor deposition technique with decomposition of...     

A new tricrystalline triblock terpolymer by combining polyhomologation and ring‐opening polymerization. synthesis and thermal properties

New tricrystalline triblock terpolymers, polyethylene‐block‐poly(ε‐caprolactone)‐block‐poly(L‐lactide) (PE‐b‐PCL‐b‐PLLA), were synthesized by ROP of ε‐caprolactone (CL) and L‐lactide (LLA) from linear ω‐hydroxyl polyethylene (PE‐OH) macroinitiators. The linear PE‐OH macroinitiators were prepared by C1 polymerization of methylsulfoxonium methylide (polyhomologation). Tin(II) 2‐ethylhexanoate was used as the catalyst for the sequential ROP of CL and LLA in one‐pot polymerization at 85 °C in toluene (PE‐OH macroinitiators are soluble in toluene at 80 °C). ¹H NMR spectra confirmed the formation of PE‐b‐PCL‐b‐PLLA triblock terpolymers through the appearance of the characteristic proton peaks of each block. GPC traces showed the increase in the number average molecular weight from PE‐OH macroinitiator to PE‐b‐PCL, and PE‐b‐PCL‐b‐PLLA corroborating the successful synthesis. The existence of three crystalline blocks was proved by DSC and XRD spectroscopy. © 2019 The Authors. Journal of Polymer Science Part A: Polymer Chemistry published by Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2450–2456     

A portable sensor for the rapid detection of naphthalene acetic acid in fruits and vegetables using stabilized in air lipid films with incorporated auxin-binding protein 1 receptor

The present technique describes the development of a simple sensitive spot optical test and the construction of a portable biosensor for the rapid one-shot detection of naphthalene acetic acid (NAA) using stabilized lipid films supported on a methacrylate polymer on a glass fiber filter with incorporated auxin-binding protein 1 receptor. The lipid films without the receptor provided fluorescence under a UV lamp. The use of the receptor in these films quenched this fluorescence and the colour became similar to that of the filters without the lipid films. A drop of aqueous solution of naphthalene acetic acid provided a “switching on” of the fluorescence which allows the rapid detection of this stimulant at the levels of 10⁻⁹ M concentrations. It was also possible to have quantitative data based on a calibration graph. The effect of potent interferences included a wide range of compounds. The results showed no interferences from these compounds in concentration levels usually found in real samples. The method was applied for the determination of NAA in fruits and vegetables and the reproducibility of the method was checked in about 50 samples. A quantitative method for the detection of NAA in crops that can be complimentary to HPLC methods is provided in the present paper. These lipid films can be used as portable biosensors for the rapid one-shot detection of NAA in fruits and vegetables by non-skilled personnel in the field.     

Salicylaldoxime in manganese(III) carboxylate chemistry: Synthesis, structural characterization and physical studies of hexanuclear and polymeric complexes

The use of salicylaldehyde oxime (H₂salox) in manganese(III) carboxylate chemistry has yielded new members of the family of hexanuclear compounds presenting the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core, complexes [Mn^III₆(μ₃-O)₂(O₂CPh)₂(salox)₆(L₁)₂(L₂)₂] (L₁ = py, L₂ = H₂O (1); L₁ = Me₂CO, L₂ = H₂O (2); L₁ = L₂ = MeOH (3)). Addition of NaOMe to the acetonitrile reaction mixture, afforded the 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(MeCN)]_n (4), whereas addition of NaClO₄ to the acetone reaction mixture afforded an analogous 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(Me₂CO)]_n (5). The structures of 1–3 present the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core and can be described as two [Mn₃(μ₃-O)]⁷⁺ triangular subunits linked by two μ₂-oximato oxygen atoms of the salox²⁻ ligands, which show the less common μ₃-κ²O:κO′:κN coordination mode. The benzoato ligands are coordinated through the usual syn,syn-μ₂-κO:κO′ mode. The 1D polymeric structures of 4 and 5 consist of alternating [Mn₃(μ₃-O)]⁷⁺ subunits and Na⁺ atoms linked through two μ₃-κ²O:κO′:κN and one μ₄-κ²O:κ²O′:κN salox²⁻ ligands as well as one syn,anti-μ₂-κO:κO′ benzoato ligand. DC and AC magnetic susceptibility studies on 1 revealed the stabilization of an S = 4 ground state, and indications of single-molecule magnetism behavior, whereas the DC experimental data from polycrystalline sample of 5 are indicative of antiferromagnetic interactions within the [Mn₃] subunit. Solid state ¹H NMR data of 1 were used to probe the spin-lattice relaxation of the system.