Molecular rheology

Flow-induced degradation is intimately related to the nonequilibrium conformation of polymer coils and any attempt to interpret the process beyond the phenomenological stage would be incomplete without a sound understanding of chain dynamics. To make the paper self-contained and to provide a theoretical basis for the discussion, we have included some fundamental models of polymer dynamics in the next section which may also serve as a guideline for future work in the field of polymer degradation in flow. For the first-time reader, however, this section is not absolutely necessary. Further, any reader familiar with molecular rheology or interested only in experimental results can skip this section, only to go back whenever a reference is needed. 

Keywords. Viscoelasticity, Molecular rheology. Branched polymers. Tube model, Non-Newtonian flow... 

Ziabicki,A Molecular rheology of polymer systems. Pure Appl. Chem. 26, 481-497... 

T. E. Karis and M. S. Jhon, The relationship between PFPE molecular rheology and tribology,... 

Middleman S (1968) The flow of high polymers. Continuum and molecular rheology. Intersd Publ Wiley NY-London-Sydney-Toronto... 

Middleman, S., The Flow of High Polymers Continuum and Molecular Rheology. Interscience Publishers, New York, 1968. 

A very recent move to apply the structures emerging from molecular rheology to non-linear models of polydisperse complex-architecture melts has met with considerable success. The simple insight that the stress is a composite, not a structural, variable, with orientational and scalar components of different relaxation times, vastly improves the ability to model LDPE melts quantitatively. It also explains how such melts may be shear thinning yet extension-hardening. 

So far the closure problem for the system of Reynolds equations has not been theoretically solved in a conclusive way. In engineering calculations, various assumptions that the Reynolds stresses depend on the average turbulent flow parameters are often adopted as closure conditions. These conditions are usually formulated on the basis of experimental data, dimensional considerations, analogies with molecular rheological models, etc. 

Stress and strain expressed in the tensorial forms, which are essential to the molecular rheological theories and simulations as studied in the later chapters, will be discussed in Chapter 5. For the phenomenological description in the linear region, it is sufficient to discuss the stress-strain relation in terms of scalar quantities. 

Leonard , E, C. Derail, and G. Marin. 2005. Some applications of molecular rheology Polymer formulation and molecular design. Journal of Non-Newtonian Fluid Mechanics 128 50-61. 

This chapter is devoted to the molecular rheology of transient networks made up of associating polymers in which the network junctions break and recombine. After an introduction to theoretical description of the model networks, the linear response of the network to oscillatory deformations is studied in detail. The analysis is then developed to the nonlinear regime. Stationary nonhnear viscosity, and first and second normal stresses, are calculated and compared with the experiments. The criterion for thickening and thinning of the flows is presented in terms of the molecular parameters. Transient flows such as nonhnear relaxation, start-up flow, etc., are studied within the same theoretical framework. Macroscopic properties such as strain hardening and stress overshoot are related to the tension-elongation curve of the constituent network polymers. 

In this chapter, we focus on thetelechelic polymers, and construct a molecular rheology that contains only the molecular parameters whose origin can easily be identified [16-19]. 

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