Kinetics and mechanisms of the unimolecular elimination of 2,2-diethoxypropane and 1,1-diethoxycyclohexane in the gas phase: experimental and theoretical study

The gas-phase thermal elimination of 2,2-diethoxypropane was found to give ethanol, acetone, and ethylene, while 1,1-diethoxycyclohexane yielded 1-ethoxycyclohexene and ethanol. The kinetics determinations were carried out, with the reaction vessels deactivated with allyl bromide, and the presence of the free radical suppressor cyclohexene and toluene. Temperature and pressure ranges were 240.1-358.3 °C and 38-102 Torr. The elimination reactions are homogeneous, unimolecular, and follow a first-order rate law. The rate coefficients are given by the following Arrhenius equations: for 2,2-diethoxypropane, log k(1) (s(-1)) = (13.04 ± 0.07) - (186.6 ± 0.8) kJ mol(-1) (2.303RT)(-1); for the intermediate 2-ethoxypropene, log k(1) (s(-1)) = (13.36 ± 0.33) - (188.8 ± 3.4) kJ mol(-1) (2.303RT)(-1); and for 1,1-diethoxycyclohexane, log k = (14.02 ± 0.11) - (176.6 ± 1.1) kJ mol(-1) (2.303RT)(-1). Theoretical calculations of these reactions using DFT methods B3LYP, MPW1PW91, and PBEPBE, with 6-31G(d,p) and 6-31++G(d,p) basis set, demonstrated that the elimination of 2,2-diethoxypropane and 1,1-diethoxycyclohexane proceeds through a concerted nonsynchronous four-membered cyclic transition state type of mechanism. The rate-determining factor in these reactions is the elongation of the C-O bond. The intermediate product of 2,2-diethoxypropane elimination, that is, 2-ethoxypropene, further decomposes through a concerted cyclic six-membered cyclic transition state mechanism.     

Endothelial cell adhesion on polyelectrolyte multilayer films functionalised with fibronectin and collagen

The seeding of endothelial cells on biomaterial surfaces has become a major challenge to achieve better haemocompatibility of these surfaces. Multilayers of polyelectrolytes formed by the layerby-layer method are promising in this respect. In this study, the interactions of endothelial cells with multilayered polyelectrolytes films were investigated. The build-ups were prepared by selfassembled alternatively adsorbed polyanions and polycations functionalised with fibronectin and collagen. Anionic poly(sodium 4-styrenesulfonate) and cationic poly(allylamine hydrochloride) polyelectrolytes were chosen as a model system. Elaborated surfaces were characterised by electrochemical impedance spectroscopy and cyclic voltammetry. The modified electrode showed good reversible electrochemical properties and high stability in an electrolyte solution. The film ohmic resistance was highest when the film was coated with fibronectin; the parameters so determined were correlated with atomic force microscopy images. Cell colorimetric assay (WST-1) and immunofluorescence were used to quantify the cell viability and evaluate the adhesion properties. When cultured on a surface where proteins were deposited, cells adhered and proliferated better with fibronectin than with collagen. In addition, a high surface free energy was favourable to adhesion and proliferation (48.8 mJ m⁻² for fibronectin and 39.7 mJ m⁻² for collagen, respectively). Endothelial cells seeded on functionalised-polyelectrolyte multilayer films showed a good morphology and adhesion necessary for the development of a new endothelium.     

Numerical analysis of a locking‐free mixed finite element method for a bending moment formulation of Reissner‐Mindlin plate model

This article deals with the approximation of the bending of a clamped plate, modeled by Reissner‐Mindlin equations. It is known that standard finite element methods applied to this model lead to wrong results when the thickness t is small. Here, we propose a mixed formulation based on the Hellinger‐Reissner principle which is written in terms of the bending moments, the shear stress, the rotations and the transverse displacement. To prove that the resulting variational formulation is well posed, we use the Babu?ka‐Brezzi theory with appropriate t ‐dependent norms. The problem is discretized by standard mixed finite elements without the need of any reduction operator. Error estimates are proved. These estimates have an optimal dependence on the mesh size h and a mild dependence on the plate thickness t. This allows us to conclude that the method is locking‐free. The proposed method yields direct approximation of the bending moments and the shear stress. A local postprocessing leading to H¹ ‐type approximations of transverse displacement and rotations is introduced. Moreover, we propose a hybridization procedure, which leads to solving a significantly smaller positive definite system. Finally, we report numerical experiments which allow us to assess the performance of the method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n ^th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation ${f(x) + f(2x) + \cdots + f(nx) = 0, x \in \mathbb{R}}$ . The continuity of the solutions depends on the sign of the real part of each zero.     

4‐Carboxypiperidinium 1‐carboxycyclobutane‐1‐carboxylate

The title salt, C₆H₁₂NO₂⁺·C₆H₇O₄⁻ or ISO⁺·CBDC⁻, is an ionic ensemble assisted by hydrogen bonds. The amino acid moiety (ISO or piperidine‐4‐carboxylic acid) has a protonated ring N atom (ISO⁺ or 4‐carboxypiperidinium), while the semi‐protonated acid (CBDC⁻ or 1‐carboxycyclobutane‐1‐carboxylate) has the negative charge residing on one carboxylate group, leaving the other as a neutral –COOH group. The –⁺NH₂– state of protonation allows the formation of a two‐dimensional crystal packing consisting of zigzag layers stacked along a separated by van der Waals distances. The layers extend in the bc plane connected by a complex network of N—H...O and O—H...O hydrogen bonds. Wave‐like ribbons, constructed from ISO⁺ and CBDC⁻ units and described by the graph‐set symbols C₃³(10) and R₃³(14), run alternately in opposite directions along c. Intercalated between the ribbons are ISO⁺ cations linked by hydrogen bonds, forming rings described by the graph‐set symbols R₆⁶(30) and R₄²(18). A detailed analysis of the structures of the individual components and the intricate hydrogen‐bond network of the crystal structure is given.     

Synthesis,Crystal Structure and Hydrogen-Bonding Patterns in (RS)-1-Carbamoyl Pyrrolidine-2-Carboxylic Acid

Abstract  

The title compound, N-carbamoyl-dl-proline, C₆H₁₀N₂O₃, crystallizes in the triclinic P-1 space group with unit cell parameters a = 7.610 (4) Å, b = 9.259 (5) Å, c = 11.749 (7) Å, α = 110.294 (11)°, β = 101.304 (13)°, γ = 91.391 (16)°, with two crystallographically independent molecules in the asymmetric unit. The ureido and carboxyl groups are equatorial and axial to the pyrrolidine rings, respectively. The pyrrolidine rings adopt envelope and twisted conformations in the residue A and B, respectively. The molecules are joined by N–H···O and O–H···O hydrogen bonds into cyclic structures with graph set R ₂²(8), forming infinite chains parallel to the cb plane with graph set C ₂²(14), that are further connected via N–H···O hydrogen bonds into a three-dimensional network.     

The Crystal Structure of 1-[2-(furan-2-yl)-6-methyl-1,2,3,4-tetrahydroquinolin-4-yl]Pyrrolidin-2-one

Abstract  

The title compound, C₁₈H₂₀N₂O₂, a potential pharmaceutical agent, crystallizes in the monoclinic P2₁/n space group with unit cell parameters a = 11.157 (7) ?, b = 8.776 (6) ?, c = 16.460 (11) ?, β = 103.08 (3)°. The tetrahydroquinoline ring system formed by the fusion of the benzene ring and the piperidine ring via two carbon atoms is coplanar, with the later adopting a sofa conformation. The pyrrolidine group in position 4 adopts an envelope conformation. Dimers related by inversion centers and linked by hydrogen bonds of the type N–H···O form cycles described by the graph set R₂²(16). Additionally, the dimers connect through weak hydrogen bonds of the type C–H···O with graph set C(10) to form chains extending along [001].     

Hydro­gen‐bonding patterns in cis‐4‐ammonio­cyclo­hexane­carboxyl­ate hemihydrate

In the title compound, C₇H₁₃NO₂·0.5H₂O, cis‐4‐amino­cyclo­hexane­carboxylic acid exists as a zwitterion and co‐crystallizes with water mol­ecules in a 2:1 amino acid–water ratio. The cyclo­hexane ring adopts a chair conformation, with the carboxyl­ate and ammonium groups in axial and equatorial positions, respectively. The basic motif in the crystal structure is a sandwich structure, formed by two amino acid units linked by head‐to‐tail hydrogen bonds. Hydro­gen bonds of the type N⁺—H⋯O—C—O⁻ link these motifs, forming helicoidally extended chains running along the c axis. The water molecule lies on a twofold axis and interacts with the chains by means of O—H⋯O hydrogen bonds.     

Capillarity driven instability of a soft solid

We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.