Interplay among tetrahedrane, butterfly diradical, and planar rhombus structures in the chemistry of the binuclear iron carbonyl phosphinidene complexes Fe2(CO)6(PX)2

Density functional theory studies on a series of Fe2(CO)6(PX)2 derivatives show the tetrahedrane to be the most stable for the alkyl (X = Me, tBu), P-H (X = H), and chloro (X = Cl) derivatives. However, butterfly diradical and planar rhombus structures are found to be more stable than tetrahedranes for the amino (X = NH2, NMe2, and NiPr2) and aryloxy (R = 2,6-tBu2-4-Me-C6H2O) derivatives. For the chloro (X = Cl) and methoxy (X = OMe) derivatives energetically accessible bishomotetrahedrane Fe2(CO)6P2(mu-X)2 isomers are observed in which the X substituents on the phosphorus atoms interact with the iron atom to form two direct Fe-X bonds at the expense of two of the four Fe-P bonds. In addition, the global minimum for the hydroxy (X = OH) derivative is an unusual FeP-butterfly structure with a central Fe-P bond as well as two external Fe-P bonds, one external P-P bond, and one external Fe=Fe double bond. Comparison of calculated with experimental nu(CO) frequencies shows that low-temperature Nujol matrix photolysis of (iPr2NP)2COFe2(CO)6 leads to a planar rhombus rather than a tetrahedrane isomer of Fe2(CO)6(PNiPr2)2.     

When arsine makes the difference: chelating phosphino and bridging arsinoarylthiolato gallium complexes

The (organo)gallium compounds GaCl{(SC6H4-2-PPh2)-kappa2S,P}2 (1), Ga{(SC6H4-2-PPh2)-kappa2S,P}{(SC6H4-2-PPh2)-kappaS}2 (2), GaMe2{(SC6H4-2-PPh2)-kappa2S,P} (3), GatBu2{(SC6H4-2-PPh2)-kappa2S,P} (4), GatBu{(SC6H4-2-PPh2)-kappa2S,P}{(SC6H4-2-PPh2)-kappaS} (5), [GaMe2{(mu2-SC6H4-2-AsPh2)-kappaS}]2 (6), and GatBu{(SC6H4-2-AsPh2)-kappa2S,As}{(SC6H4-2-AsPh2)-kappaS} (7) were obtained from the reaction of 2-EPh2C6H4SH (E = P (PSH), As (AsSH)) with GaCl3 (1, 2) or GaR3 (R = Me, tBu; 3-7) in different molar ratios and under different reaction conditions. Compound 2 was also obtained from Li(PS) and GaCl3 (3.5:1). While a monomeric structure with a chelating phosphinoarylthiolato ligand is observed in GaMe2{(SC6H4-2-PPh2)-kappa2S,P} (3), a dimeric arsinoarylthiolato-bridged complex [GaMe2{(mu2-SC6H4-2-AsPh2)-kappaS}]2 (6) is obtained with the corresponding AsS- ligand. B3LYP/6-31G(d) calculations show that although the dimer is thermodynamically favored for both ligands, the formation of 3 is due to the combination of higher stability of the chelate compared with the monodentate phosphorus ligand and a higher barrier for the ring opening of the PS- than of the AsS- chelate.     

Minimal Translation Hypersurfaces in Euclidean Space

The graph of a function f defined in some open set of the Euclidean space of dimension (p + q) is said to be a translation graph if f may be expressed as the sum of two independent functions ? and ψ defined in open sets of the Euclidean spaces of dimension p and q, respectively. We obtain a useful expression for the mean curvature of the graph of f in terms of the Laplacian, the gradient of ? and ψ as well as of the mean curvatures of their graphs. We study translation graphs having zero mean curvature, that is, minimal translation graphs, by imposing natural conditions on ? and ψ, like harmonicity, minimality and eikonality (constant norm of the gradient), giving several examples as well as characterization results.     

Further Results for kth order Kantorovich Modification of Linking Baskakov Type Operators

In this paper we consider a non-trivial link between Baskakov type operators and their genuine Durrmeyer type modification as well as the kth order Kantorovich variant. Recursion formulas for the moments and the images of monomials are proved in order to derive asymptotic expansions. Furthermore we investigate convexity properties of the linking operators and the limiting behavior for certain function spaces.     

The phase transitions of the planar random-cluster and Potts models with $$q \ge 1$$ are sharp

We prove that random-cluster models with \(q \ge 1\) on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter \(p_c\) below which the model exhibits exponential decay and above which there exists a.s. an infinite cluster. The result may be extended to the Potts model via the Edwards–Sokal coupling. Our method is based on sharp threshold techniques and certain symmetries of the lattice; in particular it makes no use of self-duality. Part of the argument is not restricted to planar models and may be of some interest for the understanding of random-cluster and Potts models in higher dimensions. Due to its nature, this strategy could be useful in studying other planar models satisfying the FKG lattice condition and some additional differential inequalities.     

Voronovskaya Type Theorems in Weighted Spaces

In this article, we introduce a generalization of Gamma operators based on a function ρ having some properties and prove quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems via weighted modulus of continuity.     

Pyrolysis of polyphenylenes with PCL or/and PSt side chains

Thermal degradation characteristic of polyphenylenes is an important issue for developing a rational technology of polymer processing and applications. In this study, we discussed thermal degradation of polyphenylenes (PP) with poly(-caprolactone) (PCL) and/or PCL/polystyrene copolymers (PSt) prepared by combined controlled polymerization and cross-coupling processes via direct pyrolysis mass spectrometry. When PP-graft-PCL/PSt copolymers were considered, thermally less stabile PCL side chains decomposed in the first step. In the second stage of pyrolysis, the decomposition of the polystyrene chains has taken place. A slight increase in thermal stability of PCL chains for PP-graft-PCL/PSt copolymers was noted compared to copolymer PP-graft-PCL due to the interaction between PSt and PCL chains. This interaction was stronger when PSt chains were linked to the 2-position of the 1,4-phenylene ring.     

Synthesis and Characterization of α,ω‐Heterofunctional Poly(ethylene oxide) Macromonomers

A novel α,ω‐heterofunctional poly(ethylene oxide) (PEO) macromonomer possessing methacryloyl and thienyl end groups was prepared by ring‐opening polymerization of ethylene oxide initiated by potassium thienylethoxide and termination of the living PEO ends with methacryloyl chloride. Incorporation of methacryloyl and thienyl groups was confirmed by free‐radical and oxidative polymerization processes, respectively, and by means of ¹H NMR analysis.

     

A rheological model based on primary laboratory data of lubricants with polymers additives

The present work reports some experimental data consisting in traction behavior for lubricants with polymer additives. The rheological response of lubricants without polymer additives and with additives as a function of polymer concentration, pressure and temperature is discussed. Based on the laboratory data, the paper presents a quasi-empirical approach which predicts elastic shear modulus, limiting shear stress and characteristic shear stress of a lubricant with polymer additives.