Synthesis of Functionalized Tetrahydropyridines by SnCl4-Mediated [4+2] Cycloaddition between Donor–Acceptor Cyclobutanes and Nitriles

Cycloadditions of strained carbocycles promoted by Lewis acids are powerful methods to construct heterocyclic frameworks. In fact, the formal [3+2] cycloadditions of donor–acceptor (DA) cyclopropanes with nitriles has seen particular success in synthesis. In this work, we report on the first [4+2] cycloaddition of nitriles with DA cyclobutanes by Lewis acid activation. Tetrahydropyridine derivatives were obtained in up to 91 % yield from various aryl-activated cyclobutane diesters and aliphatic or aromatic nitriles.     

Lateral Metallation and Redistribution Reactions of Sodium Ferrates Containing Bulky 2,6-Diisopropyl-N-(trimethylsilyl)anilide Ligands

Alkali-metal ferrates containing amide groups have emerged as regioselective bases capable of promoting Fe−H exchanges of aromatic substrates. Advancing this area of heterobimetallic chemistry, a new series of sodium ferrates is introduced incorporating the bulky arylsilyl amido ligand N(SiMe₃)(Dipp) (Dipp=2,6-iPr₂-C₆H₃). Influenced by the large steric demands imposed by this amide, transamination of [NaFe(HMDS)₃] (HMDS=N(SiMe₃)₂) with an excess of HN(SiMe₃)(Dipp) led to the isolation of heteroleptic [Na(HMDS)₂Fe{N(SiMe₃)Dipp}]_∞ ( 1 ) resulting from the exchange of just one HMDS group. An alternative co-complexation approach, combining the homometallic metal amides [NaN(SiMe₃)Dipp] and [Fe{N(SiMe₃)Dipp}₂] induces lateral metallation of one Me arm from the SiMe₃ group in the iron amide furnishing tetrameric [NaFe{N(SiCH₂Me₂)Dipp}{N(SiMe₃)Dipp}]₄ ( 2 ). Reactivity studies support that this deprotonation is driven by the steric incompatibility of the single metal amides rather than the basic capability of the sodium reagent. Displaying synergistic reactivity, heteroleptic sodium ferrate 1 can selectively promote ferration of pentafluorobenzene using one of its HMDS arms to give heterotrileptic [Na{N(SiMe₃)Dipp}(HMDS)Fe(C₆F₅)]_∞ ( 4 ). Attempts to deprotonate less activated pyridine led to the isolation of NaHMDS and heteroleptic Fe(II) amide [(py)Fe{N(SiMe₃)Dipp}(HMDS)] ( 5 ), resulting from an alternative redistribution process which is favoured by the Lewis donor ability of this substrate.     

The influence of distal substitution on the base-induced isomerization of long-chain terminal alkynes

When compared to a long-straight chain terminal alkyne, a long chain terminal alkyne with a distal isopropyl unit (isobranched) isomerizes about two times faster when treated with strong base under identical conditions, and appears to follow pseudo first order kinetics. In both cases, equilibration to a 95–97:5–3 mixture of terminal:internal alkyne accompanies isomerization. The difference in rate may be due to an unusual folding of both long-chain alkynes, bringing the distal substituent close to the carbon-carbon-triple bond moiety. The distal isopropyl moiety may provide unanticipated steric hindrance that disrupts such folding, making the propargylic proton more available for reaction with base.     

Gradient single-crystal plasticity with free energy dependent on dislocation densities

This study develops a small-deformation theory of strain-gradient plasticity for single crystals. The theory is based on: (i) a kinematical notion of a continuous distribution of edge and screw dislocations; (ii) a system of microscopic stresses consistent with a system of microscopic force balances, one balance for each slip system; (iii) a mechanical version of the second law that includes, via the microscopic stresses, work performed during viscoplastic flow; and (iv) a constitutive theory that allows:

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the free energy to depend on densities of edge and screw dislocations and hence on gradients of (plastic) slip;

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the microscopic stresses to depend on slip-rate gradients.

The microscopic force balances when augmented by constitutive relations for the microscopic stresses results in a system of nonlocal flow rules in the form of second-order partial differential equations for the slips. When the free energy depends on the dislocation densities the microscopic stresses are partially energetic, and this, in turn, leads to backstresses in the flow rules; on the other hand, a dependence of these stresses on slip-rate gradients leads to a strengthening. The flow rules, being nonlocal, require microscopic boundary conditions; as an aid to numerical solutions a weak (virtual power) formulation of the flow rule is derived.     

A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin

This study develops a gradient theory of small-deformation viscoplasticity based on: a system of microforces consistent with its peculiar balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that accounts for the Burgers vector through a free energy dependent on , with H^p the plastic part of the elastic-plastic decomposition of the displacement gradient. The microforce balance and the constitutive equations, restricted by the second law, are shown to be together equivalent to a nonlocal flow rule in the form of a coupled pair of second-order partial differential equations. The first of these is an equation for the plastic strain-rate in which the stress T plays a basic role; the second, which is independent of T, is an equation for the plastic spin. A consequence of this second equation is that the plastic spin vanishes identically when the free energy is independent of, but not generally otherwise. A formal discussion based on experience with other gradient theories suggests that sufficiently far from boundaries solutions should not differ appreciably from classical solutions, but close to microscopically hard boundaries, boundary layers characterized by a large Burgers vector and large plastic spin should form.Because of the nonlocal nature of the flow rule, the classical macroscopic boundary conditions need be supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a variational formulation of the flow rule is derived.Finally, we sketch a generalization of the theory that allows for isotropic hardening resulting from dissipative constitutive dependences on .     

A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations

This study develops a small-deformation theory of strain-gradient plasticity for isotropic materials in the absence of plastic rotation. The theory is based on a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows:

•

the microstresses to depend on , the gradient of the plastic strain-rate, and

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the free energy ψ to depend on the Burgers tensor .

The microforce balance when augmented by constitutive relations for the microstresses results in a nonlocal flow rule in the form of a tensorial second-order partial differential equation for the plastic strain. The microstresses are strictly dissipative when ψ is independent of the Burgers tensor, but when ψ depends on G the gradient microstress is partially energetic, and this, in turn, leads to a back stress and (hence) to Bauschinger-effects in the flow rule. It is further shown that dependencies of the microstresses on lead to strengthening and weakening effects in the flow rule.Typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with flow, and, as an aid to numerical solutions, a weak (virtual power) formulation of the nonlocal flow rule is derived.     

Thermomechanics of the interface between a body and its environment

We formulate integral statements of force balance, energy balance, and entropy imbalance for an interface between a body and its environment. These statements account for interfacial energy, entropy, and stress but neglect the inertia of the interface. Our final results consist of boundary conditions describing thermomechanical interactions between the body and its environment. In their most general forms, these results are partial differential equations that account for dissipation and encompass as special cases Navier’s slip law, Newton’s law of cooling, and Kirchhoff’s law of radiation. When dissipation is neglected, our results reduce to the well-known zero-slip, free-surface, zero-shear, prescribed temperature, and flux-free conditions. Dedicated to James K. Knowles: teacher, colleague, friend     

A localized hybrid method of stress analysis: A combination of moiré interferometry and FEM

A method of combining moiré interferometry and the finite-element method to effect localized stress analysis is presented. The displacement data from local regions of interest in the optical experiment are used as boundary conditions for the finite-element stress analysis. The stability of the method is examined with data from simple numerical models one of which corresponded to the stress analysis of a pin-loaded plate with friction. These studies show that the method requires the sensivity of moiré interferometry for successful implementation, i.e., displacement data accuracy within 0.1 μm or 4 μin. This localized hybrid method of stress analysis provides a powerful and efficient method for the reduction of experimental data.     

A Benzylation Study of 2,3-Dichloronaphthazarin

Depending on different reaction time and temperature employed, benzylation of 2,3-dichloronaphthazarin (I) using silver oxide as the catalyst can form either exclusively 5,8-dibenzyloxy-6,7-dichloronaphthalene-1,4-dione (II), or exclusively 5-benzyloxy-2,3-dichloro-8-hydroxynaphthalene-1,4-dione (IV); or a mixture of II and 5,8-dibenzyloxy-2,3-dichloronaphthalene-1,4-dione (III). Structures of these compounds were identified by nmr analysis.