Twists, unsymmetrical

Unsymmetric laminates with multiple specially orthotropic layers can be shown to have the force and moment resultants in Equations (4.59) and (4.60) but with different A22, B22, and D22 korn B.,., and Dll, respectively. That is, there are no shear-extensiorTcoupling terms nor any bend-twist coupling terms, so the solution of problems with this kind of lamination is about as easy as with isotropic layers. 

Bend-twist coupling is a totally different animal. The governing stiffnesses, D g and D2g, simply are never zero for any laminate that is more complicated than a cross-ply laminate. You cannot force those stiffnesses to go to zero unless you do something else to the laminate. You can make them go to zero if you let the laminate be unsymmetric, but that is robbing Peter to pay Paul. In fact, it is not very difficult in most contemporary analyses to include the influence of those bend-twist cou-... 

Figure 4.76 Side and end views of the 90°-twisted ethylene complex (0.5 kcal mol-1 above the untwisted equilibrium complex, Fig. 4.74(b)), showing the interaction of the unsymmetric pi bond with Ti.

Figure 5.118 Twisting, bending, and shear of an unsymmetrical laminate under direct stress. Reprinted, by permission, from P. C. Powell and A. J. I. Housz, Engineering with Polymers, p. 201. Copyright 1998 by Stanley Thomed Publishers.

Kao and Huang employed molecular mechanics and ab initio molecular orbital (MO) theory to determine the structure, energies, and conformations of the (Z)- (40, R = H) and ( )- (12, R1 - R4 = H) isomers. For the (Z)-isomer, an unsymmetrical conformation (67) is favored by at least 6 kcal over symmetrical chair, boat, and twist forms, which suffer from ethane-type and other H-H repulsions. In the case of ( )-isomer, the twist... 

Ab initio calculations at HF/6-31+G level of theory for geometry optimization and MP2/6-31+G //HF/6-31+G level for single-point total energy calculations were reported for lenthionine (1,2,3,5,6-pentathiepane). The unsymmetrical twist-chair conformation is the most stable conformation of lenthionine. The unsymmetrical twist-boat form is 33.0 kj mol-1 less stable. Conformational racemization of twist-chair conformation can take place via plane symmetrical chair geometry as transition state and requires 50.7 kj mol 1 <2003JMT225>. 

In single crystals of OMCTS,53 two conformers - the chair-(Al) and the boat-form (A2) - are found (see Fig. 15). The calculated most stable twist conformation A appears only in the unsymmetrical [(Me3C)2Si-NH-SiMe2NH]2. 

An electrochemical study has shown reversible reduction to Mn" and oxidation to Mnlv species and a H NMR study shows that isomerization, of the compounds of unsymmetrical ligands such as MePhdtc, is slow on the NMR time scale at - 60°C and occurs via a trigonal twist mechanism rather than a dissociative one. 

X-substituted phenyl ring which in turn will be enforced to be further out of the plane. In unsymmetrically substituted cases, the stronger cation-stabilizing aryl ring should be less twisted from the plane of the carbocation centre and the other ring should be twisted even more out of the plane. 

Hendrickson has investigated symmetrical interconversion pathways between cyclooctane conformations. In some cases at least, these paths are probably not as low-energy as unsymmetrical paths, which unfortunately are more difficult to calculate. In the crown family, which includes the chair-chair and twist-chair-chair forms, the situation is quite clear. The twist-chair-chair is of lowest energy and conversion to the chair-chair form involves only the energy difference between the two forms. Thus the chair-chair is a transition state for the degenerate interconversion of twist-chair-... 

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