Stress in polymeric liquids

To understand the mechanical properties of materials, it is important to consider first the microscopic origin of stress. In the usual gas or liquid of small molecules, the stress comes from the momentum transfer due to the intermolecular collision. In polymeric liquids, the stress is mainly due to the intramolecular force, and is directly related to the orientation of the bond vectors of the polymer. This idea, originated from the theory of rubber elasticity, is fundamental in the physics of polymeric materials.  

To demonstrate the point, let us fimt consider a dilute polymer solution. As shown in Section 4.5.2, the stress tensor is written as 

This is directly related to the orientation of the vector R ldn, and it is this term that gives the viscoelasticity of dilute solutions. 

In the dilute solution, the viscoelasticity has only a small effect the major contribution to the stress is the purely viscous stress given by the first term in eqn (7.2). The situation changes with increasing polyma concentration. The contribution of increases steeply (because the polymers become more easily oriented due to the entanglement), 4iile the contribution of the first term remains essentially unchanged. When dominates the first term, the total stress is simply related to the orientation of the bond vectors  

Note that eqn (7.4) is valid even if the excluded volume effect is accounted for since, as shown in eqn (4.135), the pseudo-potential described by the delta function does not change the expression for the stress tensor (apart from the isotropic stress, i.e., the pressure). 

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