Reptation-like behavior

Figure 11.3 Schematic curves showing the times at which Rouse-like behavior smoothly crosses over reptation behavior (t = Xg) and the region (t > in which disentanglement of the chains from the tube occurs (from Ref. 3.).

The reptation time T ep is a strongly increasing function of and c cf. Sections 7.5.1.2 and 7.5.2.2). Therefore the condition corresponding to liquid-like behavior, is reached for... 

Because of the interaction of the two complicated and not well-understood fields, turbulent flow and non-Newtonian fluids, understanding of DR mechanism(s) is still quite limited. Cates and coworkers (for example, Refs. " ) and a number of other investigators have done theoretical studies of the dynamics of self-assemblies of worm-like micelles. Because these so-called living polymers are subject to reversible scission and recombination, their relaxation behavior differs from reptating polymer chains. An additional form of stress relaxation is provided by continuous breaking and repair of the micellar chains. Thus, stress relaxation in micellar networks occurs through a combination of reptation and breaking. For rapid scission kinetics, linear viscoelastic (Maxwell) behavior is predicted and is observed for some surfactant systems at low frequencies. In many cationic surfactant systems, however, the observed behavior in Cole-Cole plots does not fit the Maxwell model. 

Although theories of the Rouse-Bueche-Zimm type have been very successful in rationalizing the behavior of polymeric systems from a molecular point of view, another class of theories is presently commanding the most attention. These theories treat the motion of polymer molecules in terms of reptation, a reptile-like diffusive motion of each polymer molecule through a matrix formed by its neighbors. To a considerable extent, this new approach has overcome some of the most important shortcomings of the normal-mode theories, which... 

The objectives of the present research were (i) to develop a solvent transport model accounting for diffusional and relaxational mechanisms, in addition to effects of the viscoelastic properties of the polymer on the dissolution behavior (ii) to perform a molecular analysis of the polymer chain disentanglement mechanism, and study the influence of various molecular parameters like the reptation diffusion coefficient, the disentanglement rate and die gel layer thickness on the phenomenon and (iii) to experimentally characterize the dissolution phenomenon by measuring the temporal evolution of the various fronts in the problem. 

Panagiotopoulos and coworkers [51] use the same parameters as Larson for the study of phase behavior, but with two different simulation methodologies. The first technique is the Gibbs ensemble method, in which each bulk phase is simulated in a separate cell and molecules are interchanged and volumes adjusted between the two for equilibration of the system [52]. The second is a standard canonical ensemble simulation, like Larson s, but employs the configurational bias Monte Carlo method. The configurational bias Monte Carlo method is much more efficient than the ones based on reptation and other local moves but is not useful if any dynamic information is sought from the simulations. 

Polymer melts and semidilute and concentrated solutions of polymer are highly viscous. Even at a concentration of 1 wt %, solutions of polymer with a molecular weight greater than several million g/mol can flow only slowly. Their behaviors are even elastic like rubber at accessible time and frequency ranges. These exquisite properties had eluded researchers for decades until the tube model and the reptation theory elegantly solved the mystery. The tube model and the reptation theory were introduced by de Gennes." They were refined and applied to the viscoelasticity of semidilute solutions of polymers and polymer melts in the late 1970s by Doi and Edwards." Until then, there had been no molecular theory to explain these phenomena. We will leam the tube model and the reptation theory here. 

Like Leonardi et al [52] Van Ruymbeke et al [53] accounted for non-reptational mechanisms in their method, but they used different models for the relaxation processes. They inverted a model that they had previously proposed [54] for the calculation of rheological behavior from the molecular weight distribution. For the Rouse modes they used a modified version of an expression proposed by Pattamaprom et al [55]. Their modified equation is shown below. 

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