Deformation analysis torsion

The skeletal deformation and torsional vibration bands were expected in the range of 150-330 cm It was supposed that in some cases, these vibrations may be coupled with internal modes of side groups and the spectral parameters of the absorption bands in this region would be dependent on conformational state of macromolecules. In the analysis of the spectra and signment of bands, various theoretical and experimental data were taken into consitkration. 

A direct analysis of the low-frequency vibrations of the hydrogen bonds in synthetic polymers is rare. Up till now, a considerable amount of information on FIR spectra of liquids with H-bonds (carboxylic acids, alcohols, phenols, etc.) has been accumulated [14,141], which significantly facilitates the identification of absorption bands of H-bond vibration in the far infrared spectra. In low-molecular weight systems, e.g. alcohols and phenols, the H-bond stretching vibrations are manifested usually at 110-180 cm" while in carboxylic acids at 190-250 cm" the frequencies of deformation and torsional vibrations of H-bonds are 100-150cm" and 40-fi0 cm", respectively [142]. We present below some examples of FIR spectra of polymers with H-bonds. 

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. 

Exhaustive catalytic hydrogenation of triptycene affords an equilibrium mixture of perhydrotriptycene isomers. As expected, Boyd s force field (37) calculations, with a modified torsional constant, reproduced the observed composition fairly well (Table 6). All important conformations were taken into account for each isomer. The most stable conformations agree with the results of the X-ray analysis (131) and have the characteristic that the cyclohexane rings are invariably either boat or deformed chair. The most stable conformation of all is 20 (ttt). The predominant conformation of ccc, in which all cyclohexane rings are boat, has an enthalpy only 2.56 kcal/mol above that of 20. The difference is virtually all due to angle and torsional terms. 

In thermomechanical analysis (TMA) the deformation of the sample under stress is monitored against time or temperature while the temperature increases or decreases proportionally to time. Changes are detected by mechanical, optical, or electrical transducers. The stress may be a compression, penetration, tension, flexure, or torsion. Generally the instruments are also able to measure the sample dimensions, a technique called thermodilatometry. The stress F/A) expressed in N/m or Pa may be a normal tensile stress cr, a tangential shearing stress x, or a pressure change Ap the force applied is F and A is the area. 

Strain the amount by which the sample is deformed. In oscillatory rheometry, the strain is horizontal (torsional) and is measured in radians, whereas in dynamic mechanical thermal analysis, the strain is termed amplitude (distance) owing to the vertical nature of the deformation. 

Using differential geometry, a curve can be reconstructed from the knowledge of its curvature and torsional functions (the Frenet-Serret formulas). Therefore, these two functions give a concise shape description, provided one associates an everywhere-differentiable curve to the molecular skeleton. This approach has been employed in the analysis of protein shape. Moreover, this technique allows one to represent the dynamics of molecular chains or loops in terms of the deformation of elastic bodies. We return to this point when we discuss a number of purely topological descriptors of molecular curves. 

We shall now extend the theory of the Freedericksz effect to study the dynamical behaviour when the magnetic field is switched on or off suddenly. The analysis is particularly simple for a twist deformation (fig. 3.4.1 b)) because the torsion exerted on the director does not result in a translational motion of the centres of gravity of the molecules. Neglecting director inertia in (3.3.2) we obtain the following equation of motion for this geometry ... 

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