Torsion geometry

The techniques and test geometries that have been used to measure subcritical crack growth in ceramics are several, but they share a common principle, namely, the subjection of a well-defined crack to a well-defined stress intensity Ki, and a measurement of its velocity v. The technique considered here, the advantages of which are elaborated upon below, is the double torsion geometry shown in Fig. 12.8. For the double torsion specimen, K is given by... 

Rheological measurements were made with rectangular gel samples in a torsion geometry. The gel samples had dimensions of approximately 12 x 4.5 x 28 mm. The measurements were made on a Rheometric Scientific ARES instrument at a frequency of 1 Hz and a scan rate of 2 °C/min. An environmentally controlled chamber permitted determination of the modulus over temperatures from -100 to 70 C. Strain sweeps were conducted at various temperatures to ensure that the modulus was independent of strain. 

Dynamic measurements through the melting region of polymers can only be achieved with difficulty and require parallel-plate, simple-shear, or torsion geometry. Polyethylene shows at least two, if not three transitions [14, 15] which depend on polymer type (linear, linear low, etc.). Poly(chlorotrifluoro-ethylene) has also been studied in detail [16]. In reality these data are all related to the lamellar structures formed in these systems. Poly(ethylene oxide) also exhibits loss peaks through the melting region, but their amplitude has been observed to be strain-dependent. The polymer is non-linear viscoelastic, and quantification of the measurements is difficult. This probably applies to most ac relaxations. 

As the number of conformations increases exponentially with the number of rotatable bonds, for most molecules it is not feasible to take all possible conformations into account. However, a balanced sampling of the conformational space should be ensured if only subsets arc being considered. In order to restrict the number of geometries output, while retaining a maximum of conformational diversity, ROTATE offers the possibility of classifying the remaining conformations, i.c., similar conformations can be combined into classes. The classification is based on the RMS deviation between the conformations, either in Cartesian (RMS y 7if [A]) or torsion space in [ ], The RMS threshold, which decides whether two... 

The origin of a torsional barrier can be studied best in simple cases like ethane. Here, rotation about the central carbon-carbon bond results in three staggered and three eclipsed stationary points on the potential energy surface, at least when symmetry considerations are not taken into account. Quantum mechanically, the barrier of rotation is explained by anti-bonding interactions between the hydrogens attached to different carbon atoms. These interactions are small when the conformation of ethane is staggered, and reach a maximum value when the molecule approaches an eclipsed geometry. 

Another way is to define an improper torsion angle e- (for atoms 1-2-3-4 in Figure 7-11 in combination with a potential lihe V((r- = fc l-cos2fi.-), which has its minima at <> = 0 and 7t. This of course implies the risk that, if the starting geometry is far from reality, the optimi2 ation will perhaps lead to the wrong local minimum. 

You can include geometric restraints—for interatomic distances, bond angles, and torsion angles—in any molecular dynamics calculation or geometry optim i/.ation. Here are some applications of restrain ts ... 

Dmparison of various methods for searching conformational space has been performed cycloheptadecane (C17H34) [Saunders et al. 1990]. The methods compared were the ematic search, random search (both Cartesian and torsional), distance geometry and ecular dynamics. The number of unique minimum energy conformations found with 1 method within 3 kcal/mol of the global minimum after 30 days of computer processing e determined (the study was performed in 1990 on what would now be considered a / slow computer). The results are shown in Table 9.1. 

Cyclobutane has less angle strain than cyclopropane and can reduce the torsional strain that goes with a planar geometry by adopting the nonplanar puckered confer matron shown m Figure 3 11... 

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