Angular displacements, ring rotations

The ring rotations generate total angular displacements of about 40° (for substituent s in the ortho position) to 70° (for bulky non-polar substituents in the para position). 

Consider the example of motions of phenyl rings [53]. Two different motional models are possible. Reorientation about the chain ring C -Cv bond axis may occur either by 180° flips 0umps between two indistinguishable conformations) or by fast-diffusional rotational motion with small angular displacements. The principal axis system is shown in Fig. 8.12. 

From (8.23) and (8.24) one can see two special cases when the potential becomes separable. In the first case c12 = 0, we have two independent anharmonic modes, each having two equilibrium positions. In the second case, the angular part of the potential (8.23) Vr is zero, and the motion breaks up into radial vibration in the double well V0(q) and a free rotation, i.e. propagation of the waves of transverse displacements along the ring. The latter case is called free pseudorotation. Since the displacements of atomic groups in the wave are purely transverse, they do not contribute to the total angular momentum. 

---