Rheology of Polymeric Liquids

We begin by considering the liquid state conformation of a typical synthetic polymer, such as a polymer chain consisting of n bonds of identical length / joined at fixed valence angles 9. Linear polyethylene or vinyl polymers (-CH2 — —), fit this model 

Now we must realize that the polymer chain conformation is dynamic, constantly changing as a result of Brownian movement. If we wish to deal with some equilibrium conformational property of a macromolecule, we must define average properties such as 

If the chain were completely freely jointed (9 unrestricted), then the average projection of one bond vector on any other, given by the average dot product / //, would be zero. Then 

Thejmportant result here is that the mean-square, end-to-end vector H is proportional to chain length (molecular weight), n. This result also can be derived firom consideration of a random walk of n steps of length / (Flory, 1953). If fixed valence angle 6 is considered, the result is 

Equations 11.2.4-11.2.6 describe what are termed the unperturbed dimensions of polymer molecules, in reference to the conformation obtained in the absence of interactions with solvent or some imposed field, such as velocity gradient Unperturbed dimensions exist in bulk amorphous or molten polymers or in solutions at the so-called theta temperature, For most synthetic polymers a characteristic ratio can be defined as 

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See for example Tirrell, M., Rheology of polymeric liquids , Chapter 11 in Macosco,... 

Fluid Dynamics Fluid Mixing Liquids, Structure and Dynamics Reactors in Process Engineering Rheology of Polymeric Liquids... 

Te Nijenhuis K, "Rheology of Polymeric Liquids", 4th impression, Delft, 2nd Ed, 2005. 

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