Viscoelastic of polymers

Equation (2.56) not only enables us to understand the basis for the first-power dependence of rj on M, but also presents us with a new and important theoretical parameter, the segmental friction factor. We shall see in the next chapter that it is a quantity which can also be extracted from measurements of the viscoelasticity of polymers. 

Ferry, J.D. (1980) Viscoelasticity of Polymers, 3rd edition (Wiley, New York). 

First approaches at modeling the viscoelasticity of polymer solutions on the basis of a molecular theory can be traced back to Rouse [33], who derived the so-called bead-spring model for flexible coiled polymers. It is assumed that the macromolecules can be treated as threads consisting of N beads freely jointed by (N-l) springs. Furthermore, it is considered that the solution is ideally dilute, so that intermolecular interactions can be neglected. 

The methods described above give continuous distributions of relaxation times. However, the molecular theories of Viscoelasticity of polymers as... 

Drag reduction is caused by the viscoelasticity of polymer solutions (61). PIB is oil soluble and is thus interesting as a drag reducing additive for the transport of crude oil in pipelines (62). 

The investigation of viscoelasticity of dilute blends confirms that the reptation dynamics does not determine correctly the terminal quantities characterising viscoelasticity of linear polymers. The reason for this, as has already been noted, that the reptation effect is an effect due to terms of order higher than the first in the equation of motion of the macromolecule, and it is actually the first-order terms that dominate the relaxation phenomena. Attempts to describe viscoelasticity without the leading linear terms lead to a distorted picture, so that one begins to understand the lack of success of the reptation model in the description of the viscoelasticity of polymers. Reptation is important and have to be included when one considers the non-linear effects in viscoelasticity. 

Phillies GDJ (1995) Hydrodynamic scaling of viscosity and viscoelasticity of polymer solutions, including chain architecture and solvent quality effects. Macromolecules 28(24) 8198-8208... 

H. Umebayashi and M. Otomo Volume viscoelasticity of polymers and other highly dissipative materials. J. Phys. Soc. Japan 15, 2324—2334 (1960). 

When reptation is used to develop a description of the linear viscoelasticity of polymer melts [5, 6], the same underlying hypothesis ismade, and the same phenomenological parameter Ng appears. Basically, to describe the relaxation after a step strain, for example, each chain is assumed to first reorganise inside its deformed tube, with a Rouse-like dynamics, and then to slowly return to isotropy, relaxing the deformed tube by reptation (see the paper by Montfort et al in this book). Along these lines, the plateau relaxation modulus, the steady state compliance and the zero shear viscosity should be respectively ... 

J. D. Ferry. Viscoelasticity of Polymers, Third Edition, John Wiley and Sons eds., New York (1980). 

Further discussion of models of the elasticity of gels is beyond the scope of the present work the interested reader can find a thorough description of the elasticity and viscoelasticity of polymer chemical gels in Ferry (1980), Treloar (1975), and Flory (1953). 

In most non-crystalline linear polymers described to date, the relaxation mechanism (in the absence of such extraneous factors as degradation) is the simple molecular flow, or the a mechanism. Exceptions have been found, for instance in the case of the polysulfides (4,54,56,57) or pol5mrethanes (57) in which far above the gla transition temperature a ixmd interchange mechanism was observed. For a number of reasons (which will be described below), it is of interest to study viscoelasticity of polymers which are subject to both mechanisms, i. e., a and (as bond-interchange will be called due to the intrinsically chemical nature of the reaction), particularly if both mechanisms occur with comparable relaxation times. Among the benefits of such a study, particularly in the case of the ionic inorganic polymers would be ... 

We will not go into the non-linear viscoelasticity of polymer solutions in this paper, although it is a related problem, concerned with viscoelastic properties observed under large as well as relatively fast deformations in the case of fluids. This field includes many publications but two review papers by Bird et al. (6,7) cover the techniques and qualitative nature of the measured quantities for polymer solutions. 

Linear Viscoelasticity of Polymer Tethered Highly Grafted Nanoparticles... 

Teichroeb, J. H., and Forrest, J. A., Direct imaging of nanoparticle embedding to probe viscoelasticity of polymer surfaces, Phys. Rev. Lett., 91, 016104-1 to 016104-4 (2003). 

Higuchi, H., Jamieson, A. M., and Simha, R., Eree volume quantities and viscoelasticity of polymer glasses, J. Polym. Sci. Polym. Phys., 34, 1423 (1996). 

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