Microscopic expression for the stress tensor

2 Microscopic expression for die stress tensor Let us now study the viscoelastic properties using molecular models. As was discussed in Chapter 3, the macroscofnc stress of the polymer solutions is written as (see eqn (3.133)) 

Here the factor c/N accounts for the number of polymers in the unit volume. 

The underlined term gives the isotropic stress kgT6 p by integration by parts, and can be dropped in the incompressible fluid (see Section 3.7.2). 

In a good solvent, one has to add the excluded volume potential eqn (4.65) to (4.132). However, the stress arising from this potential can be neglected because 

The first term is zero, and the second term can be omitted because it is isotropic. Therefore eqn (4.134) holds even for the chain with the excluded volume effect. (This of course does not mean that the excluded volume interaction plays no part in the viscoelastic properties. The excluded volume does affect the viscoelastic properties through the distribution function over which the average in eqn (4.134) is taken.) 

---

Expression for the stress tensor. The microscopic expression for the stress tensor can be obtained by taking the average of eqn (7.4) for a given conformation of the primitive chain. Alternatively, it can derived by an elementary argument explained in Fig. 7.10. In both cases the result is... 

---