Potential strain energy

Because passage of an elastic wave causes tune-harmonic deformatitMi of a crystal, each unit volume through which the wave passes has time-varying potential (strain) energy and kinetic energy. At any point in the crystal, the time-varying... 

The interaction potential (R) describes both bonding and non-bon ding in teraction s. Th e bon dm g interactions arc u snally form u -lated as a strain energy that is zero at some ideal configuration of the atoms and describe how the energy increases as the ideal con-figu ration is deform ed. Don d in g in teraction s ii su ally refer to atom s in the following relationships ... 

If we assume that there are certain ideal val ues for bond angles bond distances and so on itfol lows that deviations from these ideal values will destabilize a particular structure and increase its po tential energy This increase in potential energy is re ferred to as the strain energy of the structure Other terms for this increase include steric energy and steric strain Arithmetically the total strain energy ( ) of an alkane or cycloalkane can be considered as... 

The stiffness matrix, Cy, has 36 constants in Equation (2.1). However, less than 36 of the constants can be shown to actually be independent for elastic materials when important characteristics of the strain energy are considered. Elastic materials for which an elastic potential or strain energy density function exists have incremental work per unit volume of... 

The basis for the determination of an upper bound on the apparent Young s modulus is the principle of minimum potential energy which can be stated as Let the displacements be specified over the surface of the body except where the corresponding traction is 2ero. Let e, Tjy, be any compatible state of strain that satisfies the specified displacement boundary conditions, l.e., an admissible-strain tieldr Let U be the strain energy of the strain state TetcTby use of the stress-strain relations... 

Cyclopentenones. from 1.4-diketones. 886-887 Cyclopropane, angle strain in, 115 bent bonds in. 115 from alkenes. 227-229 molecular model of, 111. 115 strain energy of, 114 torsional strain in, 115 Cystathionine, cysteine from. 1177 Cysteine, biosynthesis of, 1177 disulfide bridges from, 1029 structure and properties of, 1018 Cytosine, electrostatic potential map of, 1104... 

The less strain energy inherent in the four-membered ring sulfoxides and sulfones, their less distorted geometries and the lack of potential aromatic -type conjugation effects make the comparison of their physical and chemical properties with other cyclic and... 

Plastic deformation is a transport process in which elements of displacement are moved by a shear stress from one position to another. Unlike the case of elastic deformation, these displacements are irreversible. Therefore, they do not have potential energy (elastic strain energy) associated with them. Thus, although the deformation associated with them is often called plastic strain, it is a fundamentally different entity than an elastic strain. In this book, therefore, it will be called plastic deformation, and the word strain will be reserved for elastic deformation. 

The structure of CNTs can be understood as sheets of graphene (i.e. monolayers of sp2 hybridized carbon, see Chapter 2) rolled-up into concentric cylinders. This results in the saturation of part of the dangling bonds of graphene and thus in a decrease of potential energy, which counterbalances strain energy induced by curvature and thus stabilizes the CNTs. Further stabilization can be achieved by saturating the dangling bonds at the tips of the tubes so that in most cases CNTs are terminated by fullerene caps. Consequently, the smallest stable fullerene, i.e. C60, which is - 0.7 nm in diameter, thus determines the diameter of the smallest CNT. The fullerene caps can be opened by chemical and heat treatment, as described in Section 1.5. 

The molecular mechanics technique has been called by many different names, including Westheimer method, strain-energy method, conformational energy calculations, empirical potential energy calculations, atom-atom pair potential method, and force field calculations. Empirical force field is widely used, but somewhat long, and many authors omit empirical, leading to confusion with spectroscopic force field calculations. Molecular mechanics (11) now appears to be favored (10a) and is used (abbreviated as MM) throu out this chapter. 

Polynitro derivatives of pentacyclo[5.4.0.0 .0 °.0 ]undecane have attracted interest as potential high-energy explosives. Molecular strain in this caged system could arise from both the constrained norbomyl moiety and the cyclobutane ring. Additional strain would be expected from nonbonding interactions if the S-endo and 1 l-endo positions were substituted with gm-dinitro groups. 

A (average) for the ds-a-isomer. Potential energy minimization calculations have been carried out for the three isomers and the strain energy was found to decrease in the sequence cis-a > trans > ds-[3. The electronic... 

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