Torsional deformation

Torsion. Torsional deformation of an isolated equilibrium str ucture means twisting it so as to change the dihedral angle connecting two atoms. The dihedral angle... 

VVuv (ffl). Within the series, one tenn dominates, for example, the n 2 term for ethylene. Ethylene strongly resists torsional deformation to any angle other than 0 and 7t (180") (Fig. 4-10). 

The rotational relaxation of DNA from 1 to 150 ns is due mainly to Brownian torsional (twisting) deformations of the elastic filament. Partial relaxation of the FPA on a 30-ns time scale was observed and qualitatively attributed to torsional deformations already in 1970.(15) However, our quantitative understanding of DNA motions in the 0- to 150-ns time range has come from more accurate time-resolved measurements of the FPA in conjunction with new theory and has developed entirely since 1979. In that year, the first theoretical treatments of FPA relaxation by spontaneous torsional deformations appeared. 16 171 and the first commercial synch-pump dye laser systems were delivered. Experimental confirmation of the predicted FPA decay function and determination of the torsional rigidity of DNA were first reported in 1980.(18) Other labs 19 21" subsequently reported similar results, although their anisotropy formulas were not entirely correct, and they did not so rigorously test the predicted decay function or attempt to fit likely alternatives. The development of new instrumentation, new data analysis techniques, and new theory and their application to different DNAs in various circumstances have continued to advance this field up to the present time. 

It is conceivable that diffusion of kinks, or overdamped solitons, along the DNA could act to relax the FPA with a time dependence similar to that predicted for torsional deformation/31 32) High levels of intercalated dyes would be expected to alter both the equilibrium population of kinks and their mobility along the DNA. Hence, this question is addressed by examining the effect of intercalating dyes on the torsional dynamics. 

The effective potential governing torsional deformations could conceivably be quite anharmonic, so that overwinding is much more strongly resisted than underwinding for finite deformations. This question is addressed by examining the dependence of the torsion constant on temperature(40) and on superhelix density. 

The absence of segmental motion in the FPA relaxation and the invariance of a with respect to changes in base composition and temperature provide very strong arguments that DNA undergoes torsional deformations in a smooth rather than segmental manner (cf. Figure 4.2). 

Torsional deformation of a planar-oriented layer in the direction of the initial director, n, characterised by n rot n tO. 

Determine the appropriate multiplicity that would be used to calculate the torsion deformation energy arising from rotation about a Co-N bond in [Co(NH3)6]3+. (Note it is generally assumed that the energy barrier to such a rotation is so low that it need not be included in the force field). 

Again, reliable creep modulus data have to be available in order to apply the deflection equations. Tables 25.2 and 25.3 (see also Fig. 25.3) give the expressions for the deflections and torsional deformations of bars. By means of these equations the modulus of engineering materials may be determined from deflection and torsion experiments. The reader is also referred to, e.g. Ferry (1980), McCrum et al. (1997), Whorlow (1992) and Te Nijenhuis (1980, 2007). 

The hard-ray diffraction technique allows a fast characterization of the lattice distortions for sample size in the centimeter range or more. The spatial resolution is low, but this technique showed the predominance of excess screw dislocations to accommodate the torsion deformation in all deformed crystals. A negligible contribution of edge dislocations was evidenced, which is consistent with the loading conditions. 

Bridgehead Double Bonds. Typical bridgehead olefins represented by 44 (cf. Table 4) have been extensively discussed by Bredt (3). Inspection of molecular models, which do not allow for rehybridization at the carbon atoms of the double bond, suggest that structure 68 should prefer extensive torsional deformations. Extended Hiickel calculations showed, however, that the structure of a bridgehead double bond is best described by the overlap of a spx hybridized orbital at the bridgehead with an orbital at the adjacent carbon atom of high p character. This type of n bond is favored over a structure with two strongly pyramidalized carbon atoms (79). 

It was mentioned earlier that the strain of a molecule is distributed over various degrees of freedom. Nevertheless, it is possible to distinguish olefins with preferential if not exclusive in-plane distortions from those with out-of-plane bending and torsional deformations. 

Thus 8.2 x 103 kg (roughly 9 tons) placed on the sample pan in Figure 2-9 would cause the pointer to move down 0.40 cm in KT4 s. Clearly all the apparatus is assumed to have an infinite modulus and inertial effects are ignored. Clearly, this is not the preferred way to run a shear creep experiment on such a polymer. Torsional deformation of a rod would be a much better choice. 

In earlier studies the gradient thresholds for CAS geometry convergence were often weaker than those used here, and accurate analytic frequencies were unavailable to detect false (transition state) stationary points. The slight effects of B-state torsional deformation (if present at lower CAS levels) may therefore have fallen within the numerical uncertainties. 

Table 7.9 Torsional deformation and shear stress formulas...

The shear modulus of fibers in torsional deformation has been measured for cotton, jute, ramie, and sisal, etc., as shown in Table 8.22. The data for ramie appear to be contradictory the reason for the contradiction may lie in the differences in the theoretical models (hence assumptions) and the experimental techniques used by the two sets of investigators. Therefore, caution is advised in the use of such data. 

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