Twist strain theory

In the case of electrophilic addition, the reactions of tricyclic dienes 1 with several electrophilic reagents have been investigated.1 7 Interestingly, some of these compounds undergo addition reactions with remarkable syn stereoselectivity. For example, the reaction of dimethyl tricy-clo[4.2.2.02,5]deca-3,9-diene-7,8-dicarboxylate with iodine azide solution, prepared in situ from an excess of sodium azide and iodine monochloride, in acetonitrile at — 5 C provided the. yyn-4-azido-3-iodo derivative 2 (Table 1) in 90% yield.1,2,4,6 The formation of the 5,>,n-4-azido-3-iodo derivative 2 is thought to be the first example of a syn addition of iodine azide to an alkene.1,2 The formation of the syn-product is best explained by the twist strain theory,8 according to which the syn transition structure A is favored over the an/7-coplanar transition structure B.1... 

One optical feature of helicoidal structures is the ability to rotate the plane of incident polarized light. Since most of the characteristic optical properties of chiral liquid crystals result from the helicoidal structure, it is necessary to understand the origin of the chiral interactions responsible for the twisted structures. The continuum theory of liquid crystals is based on the Frank-Oseen approach to curvature elasticity in anisotropic fluids. It is assumed that the free energy is a quadratic function of curvature elastic strain, and for positive elastic constants the equilibrium state in the absence of surface or external forces is one of zero deformation with a uniform, parallel director. If a term linear in the twist strain is permitted, then spontaneously twisted structures can result, characterized by a pitch p, or wave-vector q=27tp i, where i is the axis of the helicoidal structure. For the simplest case of a nematic, the twist elastic free energy density can be written as ... 

At the MP2 level of theory, the half-chair conformer of 4//-l,3-dithiin 55 is 2.0kcalmoP more stable than the boat conformer (Equation 4) <1998JCC1064> and has a calculated twist angle of 33.2° the relative stability of the halfchair conformer was attributed to absent lone-pair-lone-pair repulsions and a decrease of torsional strain owing to an... 

Another important aspect of finite elasticity theory is the ability to measure the strain energy fimction derivatives Wi = dW/dli and W2 = BW/9I2. Penn and Kearsley (94) showed how this is done nsing data from torsional experiments. An interesting aspect about torsion in finite deformations is that in order to maintain the cylinder at a constant length, it is necessary to apply normal forces at the ends of the cylinder. If the cylinder is left imrestrained, it will lengthen in an effect referred to as the Poynting (95) effect, first observed early in the last century in experiments with metal wires. When a cylinder of length L is twisted by an amount... 

There are conditions of loading a product that is subjected to a combination of tensile, compressive, and/or shear stresses. For example, a shaft that is simultaneously bent and twisted is subjected to combined stresses, namely, longitudinal tension and compression, and torsional shear. For the purposes of analysis it is convenient to reduce such systems of combined stresses to a basic system of stress coordinates known as principal stresses. These stresses act on axes that differ in general from the axes along which the applied stresses are acting and represent the maximum and minimum values of the normal stresses for the particular point considered. There are different theories that relate to these stresses. They include Mohr s Circle, Rankine s, Saint Venant, Guest, Hencky-Von Mises, and Strain-Energy. 

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