Strain energy, defined

If the heat of fonnation parameters are derived on the basis of fitting to a large variety of compounds, a specific set of parameters is obtained. A slightly different set of parameters may be obtained if only certain strainless molecules are included in the parameterization. Typically molecules like straight chain alkanes and cyclohexane are defined as strainless. Using these strainless heat of formation parameters, a strain energy may be calculated as illustrated in Figure 2.14. 

It can be easily shown that equivalent expressions for the strain energy per unit volume are U=o e/2 and U = a2/2 E. The modulus of elastic resilience, Ur, of a material is defined as the strain energy absorbed per unit volume when it is stressed to its proportional limit. Thus,... 

Ring strain energy can be defined as the energy of the homodesmotic reaction. 

Owing to the chain orientation distribution the fracture mechanism of oriented polymer fibres is different from that of isotropic fibres. The presence of this distribution leads to a non-uniform distribution of the strain energy between the domains. The strain energy is defined by... 

Maier and Schleyer (220) have studied the problem of the stability of bridgehead double bonds in bi- and polycyclic systems. They define an olefinic strain (OS) as the difference in strain energy between the olefin and its parent saturated... 

What is necessary to compute a heat of formation, then, is to define the heat of formation of each hypothetical, unstrained atom type. The molecular heat of formation can then be computed as the sum of the heats of formation of all of the atom types plus the strain energy. Assigning atom-type heats of formation can be accomplished using additivity methods originally developed for organic functional groups (Cohen and Benson 1993). The process is typically iterative in conjunction with parameter determination. 

Next, we consider the symmetry operations of the system. The free energy is expanded as a function of the strains (as defined above) and the corresponding harmonic polynomials A (a,-). The resulting expression must be invariant under the symmetry transformations. If the symmetry is low enough, one can reduce further the vector space(s) introduced above, by choosing a suitable basis. The resulting irreducible subspaces are indicated... 

The coherency strain energy introduces an additional barrier to spinodal decomposition, which causes a shift on the temperature-composition phase diagram of the chemical spinodal, defined by d2filom/dc% = 0, to the coherent spinodal, defined by... 

The closeness of the numerical values for the strain energies of cyclopropane and cyclobutane can be recast in numerous ways. Among the simplest are the differences of the enthalpies of formation of real cyclopropane and cyclobutane with that equated with 3/6 and 4/6 of that of cyclohexane. These two values are 115.2 and 110.7 kJmol"1. Equivalently, the strain energy of a species c-(CH2) is defined as the enthalpy of the gas-phase reaction 34 ... 

We have once earlier used the term cycloethene for acetylene in the context of defining the strain energy of acetylene in terms of ethylene, i.e. AHf(g, C2H2) vs 2AH g, C,H4) AH g, C2H6)], in order to compare that quantity with the strain energies of cyclopropene and other cycloalkenes cf Reference 4, p. 94. 

Test can be made at a number of extensions and compounds can be compared in terms of fatigue life at the same strain or at the same strain energy. In the latter case, absolute comparisons can be made on compounds of different modulus. When comparing different rubbers, it is necessary to test at a number of strains or to define the severity of conditions which will occur in service, because with the number of variables (G, K, W, n and C0) the ranking order may vary with the maximum strain employed. 

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