Chain-end Dynamics Whip Model

Segments located in blocks near the chain ends are expected to be subject to molecular motions different from those in the central block provided that the molecular mass of the chain is above the critical value, so that entangled dynamics is established in principle. The dynamics of segments in the chain-end blocks should generally be faster than those in the central block. Actually, in a transverse relaxation study of a polystyrene-polyisoprene-polystyrene three-block copolymer with a monomer ratio of 10 1600 10, this dynamical heterogeneity could be demonstrated qualitatively by selectively measuring signals specific for the polystyrene blocks and for the poly-isoprene block [141]. 

The same sort of three-block dynamics is also expected for homopolymers where different transverse relaxation components on these grounds show up, provided that the molecular weight distribution is practically monodisperse [36]. This suggests experimental investigations in a rather direct way. 

Two different scenarios for chain-end dynamics have been suggested. Doi [142] introduced the so-called contour length fluctuation (CLF) as a modification of the tube/reptation model. Due to the stochastic nature of chain modes in the tube, the chain ends are fluctuating back and forth a length proportional to the square root of the chain length and, hence, are subject to tube constraints to a much lower degree than the central part of the chain. The chain-end blocks are therefore expected to have a molecular mass obeying 

On the other hand, the mobile chain-end blocks may be identified as chain sections not subject to entanglements so that they move in a whip-like fashion. In view of the critical molecular mass Me indicating the minimum 

The transverse relaxation functions can be analyzed for two components related to the central and chain-end blocks according to 

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