Interaction strain

These examples show how heats of combustion and of hydrogenation of isomeric compounds, or of a homologous series, can be used to determine the relative strain energies which exist in the compounds. Strain energies can be divided, somewhat artificially, but usefully into three different types angular strain, due to compression of the angle normal to the particular type of carbon hybridization interaction strain, due to repulsion between non-bonded atoms and, finally, torsional strain of double bonds out of the plane where the greatest orbital overlap can occur. 

Equation (102) shows that MAQO can provide important information about the electronic parameters (extremal Fermi surface cross-sectional area, effective masses, electronic relaxation times) and about the electron-phonon interaction (strain derivatives of the cross-sectional area for different symmetry strains). With the help of this technique, combined with de Haas-van Alphen susceptibility measurements, one can put the deformation potential interaction and the temperature dependence of the elastic constants, discussed above in sect. 3.2, on a solid basis. In the following we discuss some compounds. 

Sun, Z., Howard, D. and Moatamedi, M., 2005. Finite element analysis of footwear and ground interaction. Strain, 41(3), 113-15. 

Torsional strain (also called eclipsed interaction strain) Strain that arises when atoms separated by three bonds are forced from a staggered conformation to an eclipsed conformation. 

There are many other nonplanar conformations of cyclohexane, one of which is the boat conformation. You can visualize the interconversion of a chair conformation to a boat conformation by twisting the ring as illustrated in Figure 3.9. A boat conformation is considerably less stable than a chair conformation. In a boat conformation, torsional strain is created by four sets of eclipsed hydrogen interactions, and steric strain is created by the one set of flagpole interactions. Steric strain (also called nonbonded interaction strain) results when nonbonded atoms separated by four or more bonds are forced abnormally close to each other—that is, when they are forced closer than their atomic (contact) radii allow. The difference in potential energy between chair and boat conformations is approximately 27 kj/mol (6.5 kcal/mol), which means that, at room temperature, approximately 99.99% of all cyclohexane molecules are in the chair conformation. 

Angle strain that results when a bond angle in a molecule is either expanded or compressed compared with its optimal values, and Steric strain (also called nonbonded interaction strain) that results when nonbonded atoms separated... 

Cis alkenes are less stable than their irons isomers because of nonbonded interaction strain between alkyl substituents on the same side of the double bond in the cis isomer, as can be seen in space-filling models of the cis and irons isomers of 2-butene. This is the same type of steric strain that results in the preference for equatorial methylcyclohexane over axial methylcyclohexane (Section 3.6B). 

These features of a hydrogenation reaction allow us to compare the stabilities and reactivities of any two alkenes that would yield the same product upon hydrogenation. Thus we explain the greater stability of trans alkenes relative to cis alkenes in terms of nonbonded interaction strain. In ar-2-butene, the two —CH3 groups are sufficiently close to each other that there is repulsion between their electron clouds. This repulsion is reflected in the larger heat of hydrogenation (decreased stability) of d -2-butene compared with that of frawfr2-butene (approximately 4.2 kJ/mol). 

Additional forces accompany particle displacements in piezoelectric solids due to the fact that macroscopic charge separation (polarization) occurs within the solid. Such charge separation results in the establishment of electrical field gradients in the material. The application of electric fields across the boundaries of a piezoelectric crystal always results in the creation of particle displacement and strains, so the effect is reversible. To account for these additional interactions, strain and its electromagnetic analogue electric displacement, D, can be equated to the stress and electrical forces acting on a solid particle via the following equations ... 

The difference in energy between an eclipsed conformation and a staggered conformation of ethane is approximately 12.6 kJ (3.0 kcal)/mol (approximately 4.2 kJ (1.0 kcal)/mol for each eclipsed H/H) and is referred to as torsional strain. Torsional strain (also called eclipsed-interaction strain) arises when nonbonded atoms separated by three bonds are forced from a staggered conformation to an eclipsed conformation. In ethane, for example, torsional strain occurs when pairs of hydrogens H(4)-H(6), H(5)-H(8), and H(3)-H(7) on adjacent carbons are forced into eclipsed positions. The models shown here represent only one of the three different but equivalent eclipsed conformations of ethane. 

The strain that arises when nonbonded atoms separated by four or more bonds are forced closer to each other than their atomic (contact) radu would allow. Steric strain is also called nonbonded interaction strain or van der Waals strain. 

Measure the CH3, CH3 distance in the energy-minimized model of ds-2-butene and the CHj, H distance in the energy-minimized model of trans-2-butene. In which isomer is the nonbonded interaction strain greater ... 

The minimum distance of approach to an atom that does not cause nonbonded interaction strain. 

The classical treatment for the quantitative determination of the steric effects operative in molecules was developed by Westheimer. Steric effects were considered as the sum of various independent strain producing mechanisms (bond strain, angle strain, torsional strain, non-bonded interaction strain). Westheimer s assumptions proved to be the fundamental basis for the BIGSTRN program as well as for all subsequent molecular mechanics treatments of neutral hydrocarbons and carbocations. Reactivities ranging over 10 ° could be correlated by the strain differences between cation and the neutral precursor. Gleicher and Schleyer s work was a historical breakthrough in the development of molecular mechanics and provided the basis for the predictions of rate constants of solvolysis reactions. For the first time chemical reactions could reliably be predicted by the means of computational chemistry. 

Creep-fatigue interaction, strain ratcheting, irradiation effects, high temperature effects... 

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