Torsional sensitivity

Fig. 7.4 Surface plot of the contour diagram given in Fig. 7.3, illustrating the concept of torsional sensitivity. The numerical values were taken from M. Cao and L. Schafer, J. Mol. Struct., 284 (1993) 235.

Whether a staggered model will reproduce the torsion sensitive distance distribution with sufficient accuracy for intermediate barriers, or a weighted sum over Gaussian peaks has to be applied, will also depend on the total change in the torsion dependent distance compared to the u-values of the said distance. 

It is deemed that with this provision, issues of torsionally sensitive storeys are addressed. 

Mechanical Properties. Although wool has a compHcated hierarchical stmcture (see Fig. 1), the mechanical properties of the fiber are largely understood in terms of a two-phase composite model (27—29). In these models, water-impenetrable crystalline regions (generally associated with the intermediate filaments) oriented parallel to the fiber axis are embedded in a water-sensitive matrix to form a semicrystalline biopolymer. The parallel arrangement of these filaments produces a fiber that is highly anisotropic. Whereas the longitudinal modulus of the fiber decreases by a factor of 3 from dry to wet, the torsional modulus, a measure of the matrix stiffness, decreases by a factor of 10 (30). 

Once the driver and driven equipment have been chosen and it is deter mined that none of the items will be subject to any lateral vibration problems, the system torsional analysis is performed. If a calculated torsional natural frequency coincides with any possible source of excitation (Table 9-21, the system must be de-tuned in order to assure reliable operation. A good technique to add to the torsional analysis was presented by Doughty [8 j, and provides a means of gauging the relative sensitivity of changes in each stiffness and inertia in the system at the resonance in question. 

Doughty, S., Sensitivity of Torsional Natural Frequencies, ASME 7h-WA/DE 18, New York American Society of Mechanical Engineer., ... 

The changes in the sulfur-carbon bonds appear to be especially sensitive to the nature of the R groups1 °. As R is usually a group of atoms, the relative conformation of these groups in terms of torsion angles with respect to the S—C bonds is often important. 

Methyl rotors pose relatively simple, fundamental questions about the nature of noncovalent interactions within molecules. The discovery in the late 1930s1 of the 1025 cm-1 potential energy barrier to internal rotation in ethane was surprising, since no covalent chemical bonds are formed or broken as methyl rotates. By now it is clear that the methyl torsional potential depends sensitively on the local chemical environment. The barrier is 690 cm-1 in propene,2 comparable to ethane,... 

In this section, we present a unified picture of the different electronic effects that combine to determine methyl rotor potentials in the S0, Sp and D0 electronic states of different substituted toluenes. Our approach is based on analysis of ab initio wavefunctions using the natural bond orbitals (NBOs)33 of Weinhold and cowork-ers. We will attempt to decompose the methyl torsional potential into two dominant contributions. The first is repulsive steric interactions, which are important only when an ortho substituent is present. The second is attractive donor-acceptor interactions between CH bond pairs and empty antibonding orbitals vicinal to the CH bonds. In the NBO basis, these attractive interactions dominate the barrier in ethane (1025 cm-1) and in 2-methylpropene (1010 cm-1) see Figure 3. By analogy, donor-acceptor attractions are important in toluenes whenever there is a substantial difference in bond order between the two ring CC bonds adjacent to the C-CH3 bond. Viewed the other way around, we can use the measured methyl rotor potential as a sensitive probe of local ring geometry. 

A particularly interesting sensitivity to intermolecular interactions occurs when a torsional group (e.g., R = CH3) is attached to the central atom of a resonance-stabilized allylic-like system,... 

Figure 5.65 provides theoretical evidence that resonance-assisted H-bonding can serve as an effective mechanism for switching a methyl rotor from one preferred conformation to another, or for controlling the stiffness of torsional motions in alkylated amides. In particular, the torsional potentials of proteins (more specifically, the Ramachandran b angle at Ca) should be sensitive to N—H- O and related H-bonding interactions involving the amide backbone. In principle, this electronic... 

---