Anisotropy of the NMR Response When Molecular Motions Occur

3 ANISOTROPY OF THE NMR RESPONSE WHEN MOLECULAR MOTIONS OCCUR 

So far the discussion has been concerned with rigid lattice conditions such as pertain at low temperatures. At very high temperatures, such as at the melting point of the polymer, the NMR spectra are very narrow and are typical of a liquid-like structure. For intermediate temperatures, various types of molecular motion may arise, while the overall orientation distribution is maintained. 

If motion is occurring it can be shown (see Ref. 3, p. 62) that to calculate the second moment the dipolar interaction term 

To fix our ideas consider again the simple model for the polethylene fibre with full orientation, but where there is rotation of the chain around its axis (at a frequency greater than the line width in Hz, i.e. lO -lO Hz for proton resonance with Hq 10 kg). The length of the internuclear vector r is unchanged by the motion and we have for the proton pair interaction only  

The pioneering work of Slichter, and Hyndman and Origlio was followed by a systematic investigation of oriented linear polyethylene and oriented polyoxymethylene over a wide range of temperatures by Olf and 

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