Stretching motions

Extensional flows occur when fluid deformation is the result of a stretching motion. Extensional viscosity is related to the stress required for the stretching. This stress is necessary to increase the normalized distance between two material entities in the same plane when the separation is s and the relative velocity is ds/dt. The deformation rate is the extensional strain rate, which is given by equation 13 (108) ... 

The infrared spectra of alcohols change markedly with increasing concentration. For example, at very low concentration, the infrared spectrum of te/t-butyl alcohol in carbon tetrachloride contains a single sharp band at approximately 3600 cm corresponding to the OH stretching motion. As the alcohol s concentration increases (by adding more alcohol to the sample), a second broad OH stretch band grows in at approximately 3400 cm and eventually replaces the other band. 

First of all, we have to take account of every bond-stretching motion. We could write a simple harmonic potential for each bond, as discussed above. For a bond A-B, we would therefore write... 

I The region from 4000 to 2500 cm"1 corresponds to absorptions caused by N-H, C-H, and O-H single-bond stretching motions. N—H and O—H bonds absorb in the 3300 to 3600 cm-1 range C-H bond-stretching occurs near 3000 cm"1. 

FIGURE 2 la The three normal vibrational modes of 11,0. Two of these modes are principally stretching motions of the bonds, but mode v2 is primarily bending, (b) The four normal vibrational modes of C02. The first two are symmetrical and antisymmetrical stretching motions, and the last two are perpendicular bending motions. 

Carbon dioxide absorbs infrared energy during bending or stretching motions that are accompanied by a change in dipole moment (from zero). Which of the transitions pictured in Fig. 2b... 

Bending motions are easier than stretching motions ... 

Fig. 17 Plot of the calculated secondary deuterium KIE versus the extent of O—H bond formation for the model elimination reaction at 45°C Models 1 and 2 have different imaginary frequencies and no coupling of the Ca—D bending vibrational motion with the C0—H stretching motion in the transition state. Models 3,4 and 5 have increasing extents of coupling between the Ca—D bending and C —H stretching motion in the transition state. Reproduced, with permission, from Saunders (1997).

Figure 1.4 The very anharmonic energy levels of the C6H6 - Ar stretch motion (cf. Figure 0.3) (adapted from Neusser, Sussman, Smith, Riedle, and Weber, 1992). The computed values of the rotational constant Bv [the coefficient of 1(1+1) in the expression for the energy eigenvalues] are given in the figure, as are the vibrational spacings.

Figure 4.4 Coordinates x, y appropriate to water superposed on the contours of the potential energy for the stretch motion. See also Lawton and Child (1980).

Figure 0.3 The structure of the van der Waals molecule C6H6 Ar as determined by very high-resolution spectroscopy. (Adapted from Weber, van Bargen, Riedle, and Neusser, 1990.) The potential along the C6H6 - Ar stretch motion is shown in Figure 1.4.

Having called attention to the similarity in the values of vi for H20(as) and ice Ih, we must now call attention to the difference. In the case of the fully coupled OH stretching motion this is 25 cm-1 in the case of the uncoupled OH stretching motion this is also 25 cm-1 in the same direction [n H20(as) >n (ice Ih)]. It is interesting that the uncoupled value of vi in ice II is 3373,3357 and 3323 cm-1, in ice III is 3318 cm-1, in ice V is 3350 cm-1 and in ice VI is 3338 cm-1 27h Each of these ice forms has a more complex crystal structure than ice Ih. In general ices II-VIII have higher density than ice Ih, and have some severely bent... 

On this theory, it is assumed (a) that the motion of the reactant-state C-H/D bonds can be thought of as one stretching and two bending motions, and (b) that the bending motions are httle different in the transition state than in the reactant state. Then, the maximum possible isotope effect will be determined by the isotopic zero-point energy difference in the reactant-state C-H/D motion. For a stretching motion with a C-H frequency of 2900 and CD frequency 2130 cm , the isotopic... 

Values for Mn(CO)sH distorted by coupling between C—O and Mn—H stretching motions. 

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