Dumbbell Model for Dilute and Semi-Dilute Solutions

Abstract

Dumbbell models are very crude representations of polymer molecules. Too crude to be of much interest to a polymer chemist, since it in no way accounts for the details of the molecular architecture. It certainly does not have enough internal degrees of freedom to describe the very rapid motions that contribute, for example, to the complex viscosity at high frequencies. On the other hand, the elastic dumbbell is orientable and stretchable, and these two properties are essential for the qualitative description of steady-state rheological properties and those involving slow changes with time. For dumbbell models one can go through the entire program of endeavor – from molecular model to fluid dynamics – for illustrative purposes, in order to point the way towards the task that has ultimately to be performed for more realistic models. According to [4], dumbbell models must, to some extend then, be regarded as mechanical playthings, somewhat disconnected from the real world of polymers. When used intelligently, however, they can be useful pedagocically and very helpful in developing a qualitative understading of rheological phenomens.