Two-parameter analysis of the scaling behavior at the onset of chaos: tricritical and pseudo-tricritical points

We discuss the so-called tricritical points at the border of the period-doubling transition to chaos and examine to what extent the associated universality applies to 2D dissipative maps. As a concrete example, the Ikeda map is studied together with its 1D analog. For the approximate 1D map, the tricritical points appear as the terminal points of Feigenbaum's critical curves in the parameter plane. For the 2D map the same type of critical behavior does not occur in a rigorous sense. It may be observed as a kind of intermediate asymptotics, however, when one considers a finite number of period doublings. We refer to the associated points in the parameter plane as pseudo-tricritical. For the Ikeda map, we present estimates of the number of period doublings, after which the departure from the tricritical universality becomes essential.     

1‐(2,4,6‐Tri­methyl­phenyl)‐1H‐1,2,3,4‐tetrazole

In the title compound, C₁₀H₁₂N₄, the tetrazole and phenyl rings are planar to within 0.001 (2) and 0.006 (2) Å, respectively. The two rings are not coplanar and have a dihedral angle of 69.07 (9)° between them. Each mol­ecule is connected with two adjacent ones by C—H?N bridges between atoms of tetrazole rings forming chains parallel with the y axis of the unit cell.     

catena‐Poly­[[tetrakis(2‐allyl­tetrazole‐κN4)‐tetra‐μ‐chloro‐tricopper(II)]‐di‐μ‐chloro]

In the crystal structure of the title compound, [Cu₃Cl₆(C₄H₆N₄)₄]_n, there are three Cu atoms, six Cl atoms and four 2‐allyl­tetrazole ligands in the asymmetric unit. The polyhedron of one Cu atom adopts a flattened octahedral geometry, with two 2‐allyl­tetrazole ligands in the axial positions [Cu—N4 = 1.990 (2) and 1.991 (2) Å] and four Cl atoms in the equatorial positions [Cu—Cl = 2.4331 (9)–2.5426 (9) Å]. The polyhedra of the other two Cu atoms have a square‐pyramidal geometry, with three basal sites occupied by Cl atoms [Cu—Cl = 2.2487 (9)–2.3163 (8) and 2.2569 (9)–2.3034 (9) Å] and one basal site occupied by a 2‐allyl­tetrazole ligand [Cu—N4 = 2.028 (2) and 2.013 (2) Å]. A Cl atom lies in the apical position of either pyramid [Cu—Cl = 2.8360 (10) and 2.8046 (9) Å]. The possibility of including the tetrazole N3 atoms in the coordination sphere of the two Cu atoms is discussed. Neighbouring copper polyhedra share their edges with Cl atoms to form one‐dimensional polymeric chains running along the a axis.     

Stereoselective synthesis of and atropisomerism in 4-pyridyl-3-(1-pyridinio)-3,4-trans-1,2,3,4-tetrahydropyridines and their transformation products

A series of 2-oxo-4-pyridyl-3-(1-pyridinio)-5-cyano-3,4-trans-1,2,3,4-tetrahydropyridine-6-6-olates were prepared by condensation of pyridinium ylides with α,β-unsaturated carbonyl compounds or more conveniently by a three-component condensation of pyridinium ylides, pyridine aldehydes, and ethyl cyanoacetate 3 and/or 6 . This analogues of the above tetrahydropyridines were prepared in a similar way starting from suitable substrates. Spectroscopic data revealed that the reaction leads to trans-isomers around the C³-C⁴ bond and is atroposelective. The conformation of and tautomerism in the tetrahydropyridines are discussed in the light of ¹H NMR data. The reaction of 5-cyano-3-(3-methyl-1-pyridinio)-2-oxo-4-(3-pyridyl)-1,2,3,4-tetrahydropyridine-6-thiolate 10c with phenacyl bromide was found to give 3-hydroxy-5-oxo-7-(3-pyridyl)-6-(3-methyl-1-pyridinio)-3-phenyl-8-cyano-6,7-trans-2,3,6,7-tetrahydrothiazol[3,2a]pyridine bromide, the crystal and molecular structure of which has been determined by X-ray crystallographic analysis.     

Synthesis of Substituted N‐Formylaminomethylenediphosphonates and Their Derivatives

The convenient methods for the synthesis of new trimethylsilyl esters of aminomethylenediphosphonic acids are elaborated. The new substituted N‐formylaminomethylenediphosphonates are obtained via the interaction of trimethylsilyl esters of methylenediphosphonic acids with a mixture of triethyl orthoformate and ethanol. Also boron trifluoride–diethyl etherate as an effective catalyst is used for the interaction of hydrochlorides of ethoxymethylene imines with diethyl trimethylsilyl phosphite. The corresponding aminomethylenediphosphonic acids are presented.     

Modulating Photochemical Properties to Enhance the Stability of Electronically Dimmable Eye Protection Devices†

The study evaluates compatibility of stabilizers with dye doped liquid crystal (LC) scaffolds that are used in electronically dimmable materials. The photodegradation of the materials was investigated and suitable stabilizers were evaluated to slow the degradation process. Various types of benzotriazole-based stabilizers were evaluated for stabilizing the liquid crystals. Based on spin trapping experiments, radicals generated upon UV exposure is likely responsible for the degradation of the system. The radical generation is competitively inhibited by the addition of stabilizers.     

Properties of polystyrene/poly(butyl acrylate) core/shell polymers modified with N‐methylol acrylamide

Polystyrene/poly(butyl acrylate) PS/PBA polymer dispersions with core/shell particles functionalized by N‐methylol acrylamide (N‐MA) were prepared through two‐step emulsion polymerization. The influence of N‐MA situated in shell and/or in core/shell of particles on the crosslinking reaction was studied to relate its mechanical properties and organic solvent resistance of films cast from basic and modified PS/PBA latexes. The changes in the phase arrangement of functionalized and unfunctionalized films after treatment with solvent and annealing were monitored. It was found that at the presence of N‐MA the crosslinking reaction occured already during the polymerization. Films from functionalized dispersions exhibit improved tensile strength and higher resistance against organic solvent.     

Synthesis of new functionalized aryl‐substituted methylphosphonic and methylenediphosphonic acids and their derivatives

The convenient syntheses of new aryl‐substituted hydroxymethylphosphonic and methylenediphosphonic acids from the aromatic aldehydes, their derivatives, and phosphorous acid esters in the presence of the effective catalysts (trimethylsilyl trifluoromethanesulfonate, zinc chloride, and cadmium iodide) were developed.     

Quantum chemical interpretation of the effects induced by tetramethylethylenediamine and dimethoxyethane in RLi non-polar monomer systems

The energetic and electronic parameters of various mono- and bidentate complexes of CH₃Li with N- and O-containing electron donors were calculated by the MNDO method. It was shown that N,N,N′,N′-tetramethylethylenediamine (TMD) forms a more stable bidentate complex with CH₃Li than 1,2-dimethoxyethane (DME). However, DME, in contrast to TMD, may form a bis-bidentate complex with CH₃Li in which the C Li bond is weakened to a higher degree than in complexes of CH₃Li with N-containing electron donors. Much lower steric hindrance of DME, as compared to that of TMD, makes an easy formation of bis- and tris-monodentate complexes of DME with CH₃Li possible; in these bis- and tris-monodentate complexes DME was simulated by (CH₃)₂O. Parameters of the C Li bond in the tris-monodentate complexes of (CH₃)₂O and tetrahydrofuran (THF) with CH₃Li are comparable to those of the bis-bidentate complex CH₃Li · 2 DME. These results are in qualitative agreement with experimental data, according to which THF and DME, in contrast to TMD, can favor the formation of separated ion pairs as active sites in anionic polymerization.