Orientation auto correlation functions

The Fluorescence Anistorpy Decay technique, performed either on pol3oners labelled with fluorescent groups or on fluorescent probes dissolved in a bulk pol3n ner matrix, can yield unique information on the type of orientation auto-correlation function able to describe the segmental motion of the pol3niier chain as well as on the nature of the motion performed by the probe molecule. 

FAD studies on concentrated solutions have shown that the same orientation auto correlation functions which are used in dilute solutions can be satisfactorily applied. So, it is interesting to investigate bulk poljmiers to check if the constraints arising from the surrounding in a dense medium would yield a different type of OACF. Furthermore, it is questionable if the segmental motions observed by FAD can be related to the molecular processes involved in the glass-rubber transition. 

Here, it is assumed that the distance r is a constant independent of time. After the time-consuming calculations for Equations (3.3)-(3.5) and (3.11), Ti, T2, and NOE can finally be expressed by the auto-correlation functions G (t) of the orientation functions F, which describe the random time fluctuation of the C—H vector, or by the spectral densities Jq(o)) that are the Fourier transforms of G,(t) with frequency <0 as follows ... 

As a result of the intermolecular origin of the field gradients it is much more difficult to calculate the spectral densities for ions than for the cases considered in Chapter 2. Let us first consider the situation which appears to best rationalize the experimental results, i,e, we assume that there is a random orientation of the water molecules around the relaxing ion. This corresponds to a weakly hydrated ion and would be approximately valid for chloride, bromide and iodide ions. The total auto-correlation function is for the case of random orientational dipole distribution around the relaxing ion obtained by integration to be... 

One might suppose that the problem is now to solve this system of 2N coupled equations however, one is actually interested in only two aspects of the solution, which are the auto and the total (auto + mutual) orientational correlation functions Consequently, one keeps the two equations for the autocorrelations and < j l (0)6 j (t)>, but sums the equations for the correlations... 

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