Dynamics of entangled polymers

M. Cates. Reptation of living polymers Dynamics of entangled polymers in the presence of reversible chain-scission reactions. Macromolecules 20 2289-2296, 1987. 

Restricted diffusion, correlated motion of spins, or any deviation from a free behavior of the molecules will result in a propagator shape different from a Gaussian one. A wide range of studies have dealt with such problems during the last two decades and NMR has turned out to be the method of choice for quantifying restricted diffusion phenomena such as for liquids in porous materials or dynamics of entangled polymer molecules. 

The various relaxation processes that occur in entangled chains may be so complex and coupled that only a smooth distribution or spectrum of relaxation times may actually exist. Nevertheless, the concept of modes and even models that are characterized by just one or two relaxation rimes is useful when you start out in this subject, as it gives you a good feel for what is going on. Just keep in mind that the dynamics of entangled polymer chains is a complex subject and one where we presently only have rough theoretical models. 

For t the dynamics of entangled polymer melts are described by the Rouse model. Owing to the fact that x, Eq. (11.33) can be written as... 

The Doi-Edwords equation [Eq. (9.20)] is the first attempt at a molecular model for viscoelasticity of entangled polymers. It ignores tube length fluctuation modes that relax some stress on shorter time scales. These modes significantly modify dynamics of entangled polymers, as described in Section 9.4.5. 

Watanabe, H. Viscoelasticity and dynamics of entangled polymers. Prog. Polym. Sci. 1999, 24, 1253-1403. 

P.G. DeGennes, "Dynamics of Entangled Polymer Solutions I. The Rouse Model," Macromolecules, 9, 587 (1976). 

DeGennes, P.G. Dynamics of entangled polymer solutions, n. Inclusion of hydrodynamic interactions. Macromolecules 1976, 9, 594. 

To quantify the anisotropy of motion, we plot the anisotropy coefficient of the center-of-mass motion with respect to the end-to-end vector Acm(t) as defined by eqn [54]. All four models have a very similar behavior the anisotropy reaches the peak value of approximately 0.3 at around the terminal time rj. The peak value is almost independent of the molecular weight (apart from the tube model that surprisingly has this peak deaeasing). We think that any model claiming to reproduce the dynamics of entangled polymers should be checked against observables similar to the ones shown in Figures 33 and 34. 

Robertson C H and Palade L I (2006) Unified application of the coupling model to segmental, Rouse, and terminal dynamics of entangled polymers, J Non-Cryst SoMs 352 342-348. 

In the second of his two well-known papers (of 1976) devoted to the dynamics of entangled polymer solutions, de Gennes used a "two-fluid model" to determine the effects of hydrodynamic interactions. Among the many results reported in this paper are two of particular interest to us here, viz., (1) that these interactions are not screened in the static, long wavelength limit and (2) that static screening does occur provided that the wavelength is less than the radius of the polymer chain. 

This paper is dedicated to Professor P.G. de Gennes, the inventor of the reptation model. This beautiful and simple idea significantly advanced our understanding of the dynamics of entangled polymers... 

Dynamics of entangled polymer chains (with L. Leger), Ann. Rev. Phvs. Chem.. 23, pp. 49-61 (1982). 

T. P. Lodge, N. A. Rotstein, and S. Prager. Dynamics of entangled polymer liquids. Do entangled chains reptate Adv. Chem. Phys., 79 (1990), 1-132. 

Kindt, P. and Briels, W.J. (2007) A single particle model to simulate the dynamics of entangled polymer melts. J. Chem. Phys., 127 (13), 134901. 

Sanchez-Reyes, J., Archer, LA. Step shear dynamics of entangled polymer liquids. Mflcromo/. (2002) 35, pp. 5194-5202... 

H. Watanabe, Viscoelasticity and Dynamics of Entangled Polymers fVug Polym. Sci. 24,1253-1403 (1999). 

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