Fractal liquid viscosity

The discrepancy indicated requires the application of principally differing approaches to the polymer nanocomposites melt viscosity description. Such an approach can be fractal analysis, within the ffamewoik of which, the authors used the following relationship for fractal liquid viscosity (h) estimation ... 

Goldstein and Mosolov [8] offered the general relationship for estimation of fractal liquid viscosity t (/) ... 

However, polymer coils overlap and dominate most of the physical properties of semidilute solutions (such as viscosity). Thus, adding a very small amount of polymer to a solvent can create a liquid with drastically different properties than the solvent. This unique feature of polymer overlap is due to their open conformations. Linear polymers in solution are fractals with fractal dimension I) < 3. In semidilute solutions, both solvent and other chains are found in the pervaded volume of a given coil. The overlap parameter P is the average number of chains in a pervaded volume that is randomly placed in the solution ... 

The results observed in this ehapter emphasize that the microcomposites rheology description models do not give adequate treatment of melt viscosity for particulate-filled nanocomposites. The correct description of the nanocomposites rheological properties can be obtained within the frameworks of viscous liquid flow fractal models. It is significant, that such an approach differs principally from the used ones to describe microcomposites. So, nanofiller particles aggregation reduces both melt viscosity and elastic modulus of nanocomposites in the solid-phase state. For microcomposites, melt viscosity enhancement is accompanied by elastic modulus increase. 

Hence, the results stated above confirmed that the models, developed for the microcomposites rheology description, did not give melt viscosity adequate treatment for nanocomposites polymer/oiganoclay as well. And as earlier, the indieated nanoeomposites iheologieal properties deseription ean be obtained within the fiamewoik of a viseous liquid flow fractal model. Na -montmorillonite plates aggregation in paekets (tactoids) simultaneously reduces both melt viscosity and elasticity modulus in solid-phase state of nanocomposites. 

As the adduced above data have shown, the polymer nanocomposites with three main types of inorganic nanofiller and also polymer-polymeric nanocomposites melt viscosity caimot be described adequately within the fiamework of models, developed for the description of microcomposites melt viscosity. This task can be solved successfully within the framework of the fractal model of viscous liquid flow, if in it the used nanofiller special feature is taken into account correctly. Let us note that unlike microcomposites nanofiller cotents enhancement does not result in melt viscosity increase, but, on the contrary, reduces it. It is obvious, that this aspect is very important from the practical point of view. 

Since fractals increase dissipation they increase the effective viscosity of the fluid more external work more force or pressure - is required to maintain a given flow when the fractals are added to the liquid. The macroscopic viscosity rj is that required to account for the power dissipated in a volume O P =... 

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