Crystal and Molecular Structures of Tris(1-Methylimidazol-2-yl)Phosphine,Tris(4-Methylthiazol-2-yl)Phosphine and its Sulfide

Abstract  Two crystal structures of tris(azolyl)phosphines, PR₃ [R′ = 1-methylimidazol-2-yl (1) or R′′ = 4-methylthiazol-2-yl (2)], and the crystal structure of the sulfurisation product of 2, R′′₃PS (3), were determined. All compounds crystallise in polar space groups, 1 in the orthorhombic space group Pna2₁ with cell parameters a = 13.9779(15) ?, b = 9.2492(10) ? and c = 10.2439(11) ?; 2 in the trigonal space group, R3c, with a = 15.2383(10) ? and c = 10.5882(13) ? and 3 in the orthorhombic space group, Cmc2₁, with a = 13.466(3) ?, b = 9.308(2) ? and c = 12.207(3) ?. Graphical Abstract  This article presents two crystal structures of tris(azolyl)phosphines and one of a tris(thiazolyl)phosphine sulfide, a compound which show potential for wide application in coordination chemistry due to their multidentate nature.      

Bi-stability of SUDR+K model of epidemics and test kits applied to COVID-19

Nonlinear Dynamics - Motivated by the many diverse responses of different countries to the COVID-19 emergency, here we develop a toy model of the dependence of the epidemics spreading on the...     

Chiral ligand-exchange separation and resolution of extremely rigid glutamate analogs: 1-aminospiro[2.2]pentyl-1,4-dicarboxylic acids

Owing to their chelation ability, a series of fully constrained l-Glu analogs formed by the spiro-union of two cyclopropane rings (1-aminospiro[2.2]pentyl-1,4-dicarboxylic acids, ASPED A–D), was submitted to chiral ligand-exchange chromatographic (CLEC) analysis. As the initial step, two methodologically different chiral devices were evaluated. A chiral stationary phase (CSP) obtained by dynamic coating of C₁₈ chains with the S-trityl-(R)-cysteine ((R)-STC) was used first with this objective. The lack of separation of the enantiomers of ASPED C and D prompted us to utilize the chiral mobile phase (CMP) prepared from O-benzyl-(S)-serine ((S)-OBS). The latter afforded complete separation of the four pairs of enantiomers. For all the pairs, quantum mechanical investigations shed light on the main features responsible for the different enantiomer recognition mechanism with (S)-OBS. The validated analytical method was then fruitfully adopted for semi-preparative-scale isolation of the enantiomers of ASPED C.     

A model of the early mineralization process of mantle dentin

The aim of this study was to investigate the relationship between proteoglycans (PGs) and collagen fibrils at the early mineralization process of mantle dentin. Ten first molar dental germs of rats were removed and fixed in glutaraldehyde/formaldehyde in cacodylate buffer and post-fixed in osmium tetroxide. The samples were dehydrated and embedded in epoxy resin. Ultrathin sections were contrasted and analyzed in TEM before and after treatment with EDTA, chondroitinases AC and ABC. After EDTA treatment, a electrondense substance associated with collagen fibril was removed, and did not stain again. A high magnification of these areas showed globular structures with 15 nm diameter surrounding collagen fibrils. In advanced mineralization areas, collagen fibrils showed a banded pattern and at high magnification the fibrils presented a light 10 nm ring inside and a dark 10 nm ring outside. After chondroitinase treatment, the electrondense substance associated with collagen fibrils was removed, showing a banded pattern of clear and dark areas along them. From morphological data, the authors proposed a model of interaction between PGs and collagen fibrils, where glicosaminoglycans chains are inside the fibrils, while the protein core remains outside. That stereochemical arrangement would start the crystal nucleation.     

Large Deviations for a Stochastic Model of Heat Flow

We investigate a one-dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ₋ and τ₊. Kipnis et al. (J. Statist. Phys., 27:65–74 (1982).) proved that this model satisfies Fourier’s law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has a linear energy density profile , u ∈[−1,1]. We derive the large deviation function S(θ(u)) for the probability of finding, in the stationary state, a profile θ(u) different from . The function S(θ) has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general models and find the features common in these two and other models whose S(θ) is known.     

Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida [16]. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer [15] for the asymmetric exclusion process.     

Light modulation by a real stationary ultrasonic field

The temporal modulation of a light beam diffracted by a real stationary ultrasonic field in a liquid is studied. The stationary fields, experimentally obtained, are really ‘pseudo-stationary’, due to volume absorption and reflection losses.The modulation waveforms are analysed in a ‘thick-screen model’. The pseudo-stationary field has been considered as built up both by two antiparallel progressive beams of different amplitude, and by a stationary field plus a residual progressive beam. Different modulation formulae are obtained for beams either spatially superposed or placed at a finite distance.     

Verhalten von Vinylpolymeren in gemischten Einzelschichten

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