Chain entanglements general

In 1944, Flory (3) noted that the moduli of cross-linked butyl rubbers generally differ somewhat from values calculated from the crosslink density according to the kinetic theory of rubber elasticity. In many cases, the modulus also depends on the primary (uncross-linked) molecular weight distribution of the polymer. He attributed both observations to three kinds of network defects chain ends, loops, and chain entanglements. The latter are latent in the system prior to cross-linking and become permanent features of the network when cross-links are added. 

Generally, T2 relaxation times are very sensitive to slower relative translational motions of the polymer chains and can provide information on intramolecular couplings, such as chemical crosslinks and chain entanglements. Numerous studies on both permanent and temporary networks are presented in a series of papers by Charlesby and co-workers 74,86 94). In the case of extracted polymer networks, T2s relaxation is observed in the crosslinked (gel) fraction, while T2 relaxation occurs in the soluble fraction of the irradiated polymer86 . It is shown that the fraction of more mobile protons, (1-f). has the same general trend with increasing... 

The natural generalization of the problem considered above is the calculation of the partition function for the chain entangled with many obstacles on the plane. At first sight, it seems that the approach presented above allows one to solve the problem easily. Actually, let us replace the function f(z) in Eq. (4) by the... 

Polymer concentration affects particle size and morphology because it influences polymer chain entanglements and solution viscosity. The size of the particle generally decreases as the polymer concentration decreases because of the decrease in the fraction of solid material for a defined volume of solution. A further decrease in concentration creates irregular or biconcave particle shapes. 

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