Lewis acid catalyzed reactions of donor-acceptor cyclopropanes with 1- and 2-pyrazolines: formation of substituted 2-pyrazolines and 1,2-diazabicyclo[3.3.0]octanes

The reaction of 2-substituted cyclopropane-1,1-dicarboxylates with 1- and 2-pyrazolines is efficiently catalyzed by scandium or ytterbium triflates to give N-substituted 2-pyrazolines or 1,2-diazabicyclo[3.3.0]octanes. The reactions of 2-pyrazolines give diazabicyclooctanes as the major products. In contrast, the reactions starting from 1-pyrazolines predominantly give N-substituted 2-pyrazolines, which become the major compounds obtained if an equimolar amount of GaCl₃ is used. A possible reaction mechanism is suggested.     

Impact of synthesis conditions on surface chemistry and structure of carbide-derived carbons

Carbide-derived carbons produced by chlorination of titanium carbide at 600, 800, or 1100 °C were subjected to a post-treatment at 600 °C in Ar, H₂, or NH₃ atmosphere. Experimental results suggest that the chlorination temperature influences the ordering of carbon in a manner that impacts specific surface area and porosity. Higher chlorination temperatures lead to higher total pore volume and increased ordering, but lower microporosity. The effect of post-treatments on surface chemistry is pronounced only for samples chlorinated at 600 °C; post-treatments in Ar are shown to be less effective for chlorine removal than those performed in H₂ or NH₃. Post-treatments in Ar result in a lower total pore volume compared to the ones in H₂ or NH₃ for the same chlorination temperature. Samples chlorinated at higher temperatures contained less oxygen functionalities than samples chlorinated at 600 °C, and showed correspondingly less desorption of H₂O, possibly due to diminished uptake of ambient water.     

Two-dimensional liquid chromatography with mixed mode stationary phases

Mixed mode stationary phases with ion-pairing reagent (acidic or basic) as integral part of hydrophobic chain offers unique selectivity, and hence, are ideal for multidimensional separations. The retention of hydrophobic components is a function of organic content, whereas that of charged species is a function of organic content, ionogenic modifier and its level in the mobile phase. Hence, by controlling the parameters influencing component retention (stationary phase and mobile phase), the selectivity of chemical components in the two-dimensional plane can be manipulated to improve the separation. A two-dimensional liquid chromatograph has been developed by coupling similar and dissimilar mixed mode stationary phases in the two dimensions. This technique has immense potential in resolving co-eluting components as the retention mechanism in the two-dimensions are complementary. However, with only part of the primary column eluent sampled into the secondary column, the technique is limited to qualitative analysis.     

Synthesis and molecular structure of [((CO)3RuBr2)2(μ-SePh)2Ru(CO)4] cluster with a Ru3Se2 chain core

Treatment of ruthenium carbonyl, [Ru₃(CO)₁₂] with phenylseleno tribromide PhSeBr₃ afforded a new triruthenium cluster, [(CO)₁₀Br₄Ru₃(μ-SePh)₂] (1). Its molecular structure was determined by single crystal XRD method (P2₁/c; a = 10.514(3) Å; b = 10.814(3) Å; c = 19.063(5) Å; β = 105.064(4)°; V = 2093.1(10) Å³) and shown to have two lateral Ru(CO)₃Br₂ units attached via two PhSe bridges to a Ru(CO)₄ center forming a chain-like Ru-Se-Ru-Se-Ru cluster core. This is in contrast with a recently reported reaction of PhTeBr₃ with [Ru₃(CO)₁₂] which formed a monomeric complex of ruthenium-dicarbonyl-dibromo fragment coordinating two PhTeBr ligands, [(CO)₂RuBr₂(PhTeBr)₂].     

Hydrodynamic formation of stable anisotropic structures in Couette flow of dilute suspensionFormation hydrodynamique pour structures anisotropiques stables dans un flux de Couette d'une suspension diluée

The problem of rotary motion of rigid axially symmetric elongated particles in the Couette flow of dilute suspension with anisotropic carrier fluid is solved. It is shown that the stable stationary solutions of the dynamical set of ordinary differential equations describing the particles rotary motion are possible in the case of forming the stationary anisotropy in the carrier fluid of the suspension. It allows us to detect the stationary orientation of suspended particles and formation of stable anisotropic liquid-crystalline structures in the considered suspension under the action of hydrodynamic forces. The study of rheological properties of such a structured suspension shows that it behaves as a viscoelastic quasi-Newtonian anisotropic liquid medium. To cite this article: E.Yu. Taran et al., C. R. Mecanique 332 (2004).     

Saint-Venant problem for solids with helical anisotropy

We discuss the solution of Saint-Venant’s problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension–torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters.     

The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper, we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the “near-flip” instability, we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.      

Asymptotic splitting in the three-dimensional problem of elasticity for non-homogeneous piezoelectric plates

A novel asymptotic approach to the theory of non-homogeneous anisotropic plates is suggested. For the problem of linear static deformations we consider solutions, which are slowly varying in the plane of the plate in comparison to the thickness direction. A small parameter is introduced in the general equations of the theory of elasticity. According to the procedure of asymptotic splitting, the principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms. Three-dimensional conditions of compatibility make the analysis more efficient and straightforward. We obtain the system of equations of classical Kirchhoff's plate theory, including the balance equations, compatibility conditions, elastic relations and kinematic relations between the displacements and strain measures. Subsequent analysis of the edge layer near the contour of the plate is required in order to satisfy the remaining boundary conditions of the three-dimensional problem. Matching of the asymptotic expansions of the solution in the edge layer and inside the domain provides four classical plate boundary conditions. Additional effects, like electromechanical coupling for piezoelectric plates, can easily be incorporated into the model due to the modular structure of the analysis. The results of the paper constitute a sound basis to the equations of the theory of classical plates with piezoelectric effects, and provide a trustworthy algorithm for computation of the stressed state in the three-dimensional problem. Numerical and analytical studies of a sample electromechanical problem demonstrate the asymptotic nature of the present theory.     

Weak variations of Lipschitz graphs and stability of phase boundaries

In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity.