Long Chain Dynamics

This second order expression accounts for experimental results with  

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Long-chain dynamics in the presence of fixed stress points (entanglements)... 

Fig. 21. Comparison of the dynamic structure factors from long PTHF chains in a matrix of long chains (x) with that in a matrix of short chains ( ). The Q-value of the experiment was Q = 0.09 A-1, the temperature T = 418 K (Reprinted with permission from [57]. Copyright 1985 Royal Society of Chemistry, Cambridge, UK)...

Rostov, K.S. Freed, K.F., Mode coupling theory for calculating the memory functions of flexible chain molecules influence on the long time dynamics of oligoglycines, J. Chem. Phys. 1997,106, 771-783... 

This author is perfectly aware that he could add very little to the work done by these workers if an attempt was made to focus on intramolecular catalysis phenomena or on the relevance to cyclisation of available models of chain conformation and chain dynamics instead, the aim will be the presentation of a general treatment of the subject, namely, one that includes the cyclisation of very short chains as well as that of very long chains of, say, 100 atoms or more. With a subject as vast as this, an encyclopaedic review would be a hopeless task. Therefore, the subject will be treated in a systematic and critical way, with more concentration on reaction series with regular and wide variations in structure, rather than on scattered examples. The aim will be to show that the field of intramolecular reactions is a mature area in which the merging of concepts from both physical organic chemistry and polymer chemistry leads to a unified treatment of cyclisation rates and equilibria in terms of a few simple generalisations and theories. 

The long side chains of a homopolypeptide have remarkable motional freedom about multiple bonds, while the main chain forms the secondary regular conformation such as a-helix, /1-sheet, and turn, which are rigid structures. The macroscopic properties of the rigid a-helical polypeptide, therefore, highly depends on the dynamic structure of the side chains so that a lot of studies on the side chain dynamics of the a-helical polypeptides have been carried out in the solid and solution states.12,14,29 66... 

Chem. Phys., 107, 4751 (1997). Local Dynamics in a Long-Chain Alkane Melt from Molecular Dynamics Simulations and Neutron Scattering Experiments. 

From the foregoing it will be clear that whenever entanglements and long chain branching are both present the dynamics in a polymer melt are highly co-operative. The orientational relaxation time of chain segments is exponentially dependent on both the contour distance to the nearest effective free end and on the effective entanglement density of its enviroiunent at all previous timescales. 

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