Strain, angular torsional

Fig. 6 Reaction energy profile for reactions 34a/34b (A), 35a/35b (B), and 36a/36b (C). (A) and (B) Aromatic stabilization of the transition state is greater than that of benzene or cyclopentadienyl anion, respectively. (C) Anti-aromatic destabilization (positive ASE) of the transition state is less than that of cyclobutadiene the high barrier results from the additional contribution by angular and torsional strain at the transition state.

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. 

The thermal reaction, at room temperature, of A -bicyclo[2A0]hexene (277) gave, besides polymeric material, a dimer now identified as 2,5-dimethylenetricyclo-[4,2,2,0 ]decane (278). Reaction of (277) with irons, frans-dimethyl-2,5-hexadiene gave the olefin (279) and reduction of both (278) and (279) gave cis-2,5-dimethyltri-cyclo[4,2,2,0 ]decane. The reactive double bond in (277) differs from that usually associated with thermal olefin dimerizations. In most cases, such reactivity has been associated with double bonds which are torsionally strained. In (277) the torsion angle about the double bond must be zero and the reactivity must be associated with angular deformation at the olefinic carbons. Addition of ketene to (277) gave 3-methyl-6-methylenecyclohex-2-ene-l-one. In both reaction with ketene and dimerization, [2,2,2]propellanes would appear to be reasonable intermediates. 

Dynamic Mechanical Testing. Composite samples were tested in the dynamic torsional mode of a Rheometrics Mechanical Spectrometer (RMS 800) using an angular frequency of 10 rad/s, a strain of 1%, and a nitrogen atmosphere. The dynamic storage and loss moduli of 45 mm long rectangular samples (8 mm x 1.5 mm) were recorded as a function of temperature. The temperature was increased from 50 to 250 C at constant rates and then decreased at the same rates. 

Shear or Rigidity Modulus. When successive layers of material are moved or sheared by tangential surface force or a torsional force, the magnitude of strain is determined by the shear modulus or modulus of rigidity. The angular strain, 0 radians, induced in a rod of radius r, length I, by a torque C is given by... 

Nematic liquid crystals having no translational order will not support extensional or shear strains, but they will support torsional strain which results from application of a torque. The torsional strain is conveniently represented in terms of the angular... 

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