Sphere, excluded volume viscosity

The effective hard sphere diameter may be used to estimate the excluded volume of the particles, and hence the low shear limiting viscosity by modifying Equation (3.56). The liquid/solid transition of these charged particles will occur at... 

If the branching density is sufficiently high to hinder segmental flexibility and impose strong excluded volume and even steric interactions, molecular dimensions become rigid. Measurements of solution and melt viscosity showed that the properties of dendritic molecules approached that of solid spheres as the... 

We have seen that polymers, like all opaque fractals, have a number of characteristic effects on a fluid. They produce osmotic pressure and viscosity in the fluid, and they individually experience hydrodynamic drag. Each of these effects can be quantified by a length. For the osmotic pressure this was the thermodynamic radius Rt, the radius of a sphere with the same excluded volume as the polymer. For the viscosity it was the viscometric radius R. For the drag coefficient it was the hydrodynamic radius R. All these radii have roughly the same size, and like the geometric size R they grow with the molecular weight M as where D is the fractal dimension. In the... 

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