Molecular modelling of entangled polymer fluids under flow The ...

Chapter 1
Introduction
1.1 Overview
Rheology is the study of the deformation of matter. In particular, it is the term
used to describe the study of complex fluids such as polymer melts, polymer solutions
and colloidal suspensions. The aim of theoretical rheology is to develop constitutive
equations that relate stress within the material to its deformation history. Constitutive
equations together with mass and momentum conservation can be used to predict
the flow of the material. Molecular rheology aims to derive and understand these
constitutive equations from the underlying microscopic physics of the material.
Polymer are large macromolecules. They consist of many chemical repeat units
covalently bonded into long chains. Chain with N = 10 2 − 10 4 repeat units can be
synthesised and polymer of length N = 10 9 −10 10 occur in nature. The topology of the
chain can vary from a simple linear chain to a complex branched structure. Chemically
identical materials with the same molecular weight but different topologies often have
radically different rheology. Conversely materials with different chemistries but with
molecules of globally the same shape often exhibit evidence of universal behaviour.
Molecular rheology of polymers has a long history [Bird et al. (1977), Larson (1988),
de Gennes (1979)]. However, work in this area has intensified in the last twenty years.
Understanding polymer rheology is important not only from the point of view of fundamental
science but because its applications often have very useful industrial consequences.
A good understanding of the link between the molecular constituents of a
polymer liquid and its rheological behaviour is a long term goal of molecular rheology.
This would allow the production of materials with a rheology that is tailored to their
application.
There are many processing problems which are thought to be avoidable if a material
has the correct rheology. For example, in a film blowing process small areas of thinning
in the film may grow in amplitude leading to rupture of the film. By changing the
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