Rotational motions

Irrotational flow occurs when the fluid motion rotates about its axis (e.g., water flowing in a bend in a pipe). 

Kreis-ausschnitt. m. sector, -bahn, /. circular path orbit, -bewegung,/. circular motion, rotation, revolution, -blende, /. (Photog.) iris diaphragm, -bogen, m. arc of a circle circular arch. 

Rad, n. wheel, -achse, /. axle or shaft of a wheel, -arm, m. spoke (of a wheel), -be-wegung, /. rotary motion, rotation, -dre-hnng, /. rotation torsion. 

Goldman, S.A., Bruno, G.V., and Freed, J.H. 1972. Estimating slow-motional rotational correlation times for nitroxides by electron spin resonance. The Journal of Physical Chemistry 76 1858-1860. 

Lord Kelvin lla> recognized that the term asymmetry does not reflect the essential features, and he introduced the concept of chiralty. He defined a geometrical object as chiral, if it is not superimposable onto its mirror image by rigid motions (rotation and translation). Chirality requires the absence of symmetry elements of the second kind (a- and Sn-operations) lu>>. In the gaseous or liquid state an optically active compound has always chiral molecules, but the reverse is not necessarily true. 

We determined earlier (page 63) that the irreducible components of this representation are three A, one A2. two and three B3 species. To obtain from this total set the representations for vibration only, it is necessary to subtract (he representations for the other two forms of motion rotation and translation. We can identify them by referring to the C2t character table. The three translational modes will belong to the same representations as the x, y, and z basis functions, and the rotational modes will transform as Ry, and Rs. Subtraction gives... 

Internal Molecular Motion Rotation of Methyl Groups... 

The appearance, at T > 160 K, of a channel of decay with a relatively high activation energy, 2 ", can be accounted for, e.g. by a defreezing of some additional type of motion (rotation, vibration, or conformational transition) creating still more favourable conditions for electron tunneling than the channel with activation energy E A. 

As with alkenes, in general, anti-addition is often the course of reaction, especially when halonium ions are involved109-112. However, as mentioned earlier, syn addition can take place in the bromination of /Tsilylslyrenes. This stereochemistry is explained by stabilization of the open-chain carbocation by the aromatic group, compared to the cyclic bromonium ion. In this case the conformer 83 has the maximum hyperconjugative stabilization, and is formed by the least motion rotation about the carbon-carbon bond. 

The production of the (Z)-haloalkenes is thought to proceed via initial exchange of the tetrafluoroborate and halide ions and collapse of the resulting vinyliodonium halides by the addition-elimination (Ad-E) mechanism (equations 203 and 204)84. As with Ad-E reactions of moderately activated vinyl halides (X = Cl, Br), which typically occur with configurational retention (> 95%)143 145, the intermediate carbanions apparently prefer a least motion rotation of 60° prior to the expulsion of iodobenzene. It has been demonstrated by an NMR study that anion exchange between (Z)-(2)-phenylsulfonyl-l-decenyl)-phenyliodonium tetrafluoroborate and tetrabutylammonium chloride occurs instantaneously in deuteriochloroform84. Furthermore, when authentic halide salts of the... 

The product distribution is also time dependent. Listed in Table 8.2 is the time dependence of the s/a and Ur ratios for the trajectories initiated at the three TSs. Trajectories from TS(si) show strong preference for s over a in the short trajectories. These are trajectories that essentially directly travel a least-motion rotation of the vinyl gronp to the product. Over longer times, the TSfi O trajectories lose specificity. 

From the dynamic point of view, the motion (rotation) of the substituent takes place in the femtosecond range with a frequency of >10 Hz. If any chemical reaction is faster than this motion, the... 

The existence of chiral pathways in this molecule is made possible by the existence of the two independent degrees of freedom that govern internal motion, rotation, and inversion. As molecular complexity increases, the number of degrees of freedom also increases and, unless an achiral pathway is energetically much preferred, it becomes more and more likely that enantiomerization proceeds by a chiral pathway. For example, it is extremely improbable that reversal of helicity in a polymeric chain involves an achiral intermediate or transition state. There is a strong resemblance here to the stochastic achirality of ensembles of achiral molecules discussed previously. 

If a gas is contained in a vessel and then heated thermally, the constituent atoms of the gas gain thermal energy upon striking the hot walls of the containment vessel. The heat energy transferred to molecules increases their thermal motions (rotation, vibration, translation). Under equilibrium... 

Because gas molecules are in motion (rotating as well), they experience only a weak net attraction because of occasional alignment. 

In related studies, two maxima were observed in the deuteron 1/Ti as a function of temperature (at ca. 60 and 10 K measured at 9 T, 58 MHz) in the NMR of the fully deuterated form of Mnl2 by Dalai and co-workers, and they suggested that molecular motion (rotation of CD3 groups) could be responsible for the high temperature maximum [58,59]. Although they subsequently supported this conclusion with NMR studies on oriented samples of the -labelled analogue of Mnl2 (in which a peak is also ob-... 

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