Models for local dynamics

In polymers, due to the constraint resulting from the connectivity of the chain, the local motions are usually too complicated to be described by a single isotropic correlation time x, as discussed in chapter 4. Indeed, fluorescence anisotropy decay experiments, which directly yield the orientation autocorrelation function, have shown that the experimental data obtained on anthracene-labelled polybutadiene and polyisoprene in solution or in the melt cannot be represented by simple motional models. To account for the connectivity of the polymer backbone, specific autocorrelation functions, based on models in which conformational changes propagate along the chain according to a damped diffusional process, have been derived for local chain 

Among the various expressions that are based on a conformational jump model and have been proposed for the orientation autocorrelation function of a polymer chain, G t), the formula derived by Hall and Helfand (HH) [4] leads to a very good agreement with fluorescence anisotropy decay data. It is written as 

The expression for the autocorrelation function derived by Hall and Helfand can be identified, in a generalized diffusion and loss equation, with the orientation cross-correlation function of two neighbouring bonds inside the polymer chain. To account for motional coupling of non-neighbouring bonds, resulting for example from the presence of side-chains, Viovy et al (VMB) [5] have introduced cross-correlation functions of a pair of bonds separated by j bonds into the orientation autocorrelation function. These functions are written 

Another expression for the orientation autocorrelation function of chains undergoing three-bond jumps on a tetrahedral lattice has been developed by Jones and Stockmayer [7]. Analysis [10] of the derived orientation autocorrelation function has shown that this function can be considered as a particular case of expression (6.4). 

From a practical point of view, all the above expressions for the orientation autocorrelation function lead to very similar numerical results for NMR spin-lattice relaxation time () calculations. 

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In section 2, the different theoretical models for local dynamics are briefly reviewed, and their connection with spectroscopic experiments is recalled. The Fluorescence Anisotropy Decay technique and the synchrotron source are presented in section 3. The fourth section is concerned with two typical examples. Using a series of experiments performed on polystyrene dilute solutions and another one performed on melt poly butadiene, we show how the different theoretical models can be told apart, and we present new information about the processes responsible of backbone rearrangement which has been obtained using the cyclosynchrotron LURE-ACO at Orsay (France). 

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