The strong and weak collision regimes

The laboratory frame spin-lattice relaxation time T is related to the molecular rotation correlation time xc by the expression 

In order to study molecular motions effectively in systems in which they occur in the kHz region or below, the obvious thing to do is to lower HQ and thereby the resonance frequency. This method is only useful over a limited range of Hq, typically down to a Larmor frequency of a few MHz, because the sensitivity is approx- 

The BPP expression was derived under the assumptions that the dipolar interactions formed a perturbation on the Zeeman levels and that the time dependent part of the dipolar interaction could be treated by time dependent perturbation theory or equivalently the density matrix approach to determine the relaxation expression. This does not rule out a BPP type expression for relaxation in the rotating frame. Specifically, a BPP type approach can be used to derive the following expression for T due to rotational motion under basically 

In the expression above, (1-q) is the fraction of the mean square local field which is time dependent and therefore participates in the relaxation process. When u)qTc 1, the T expression is more complicated. See Look and Lowe (1965) for a derivation. The restriction tc T2j l w ere Tc s the rotational correlation time is that of the weak collision regime. Specifically, it requires that, on the average, many motions occur before the nuclei on a given molecule relaxes. 

A relaxation time versus temperature plot for cyclohexane, is sketched below. It reveals two minima, one influenced predominantly by molecular translation and the other by molecular rotation. The strong collision regime is applicable below 170° and the weak collision regime above this temperature (Roeder and Douglass, 1970). 

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