Angle strain definition

Compounds 63 and 64 have been prepared174 as crystalline solids at -80°C. Nmr spectra show that all the hydrogens lie in the olefinic region and neither compound is aromatic. From 13C and proton nmr spectra it has been deduced that neither is planar. However, that the angle strain is not insurmountable has been demonstrated by the preparation of several compounds that have large angles but that are definitely planar 10-electron aromatic systems. 

Can one definitely prove the occurrence of non-isolable short-lived cycloalkynes Throughout this article the expression angle strained cycloalkynes is used. 

The experimental data in Table 3.1 show that the calculated values of total angle strain are approximately correct only for cyclopropane, cyclobutane, and cyclopentane. Cyclohexane is definitely not the strained compound Baeyer s theory predicts, and the larger ring compounds are also not very strained. Any chemist today can explain the discrepancy between these calculated and experimental values of strain energy cyclohexane is not planar. In either the chair or boat conformations (Figure 3.12), all bond angles can be approximately 109.5°. In the chair conformation of cyclohexane, all bonds are staggered, and there are no apparent van der Waals repulsions in the molecule. ... 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

Like many other chemical concepts the concept of strain is only semi-quantitative and lacks precise definition. Molecules are considered strained if they contain internal coordinates (interatomic distances (bond lengths, distances between non-bonded atoms), bond angles, torsion angles) which deviate from values regarded as normal and strain-free . For instance, the normal bond angle at the tetra-coordinated carbon atom is close to the tetrahedral value of 109.47°. In the course of force field calculations these normal values are defined more satisfactorily, though in a somewhat different way, as force field parameters. 

Figure 2.6 shows that the element distorts (shears) as well as dilates. The next task is to develop expressions for the shear strain rates, rz and ezr. By convention, the definition of the two-dimensional shear strain rate is taken as the average rate at which the angles defining the element sides decrease. Thus... 

The shear-strain rate r = e r is given by the average rate at which the vertex angle decreases, which is the same definition as in the r-z plane ... 

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