Effective interaction and second virial coefficient

The effective interaction of the various parts of an isolated polymer with one another can be measured by the second virial coefficient which defines the repulsion of two polymers in very dilute solutions. This is a physically important quantity which we also encounter when studying the structure functions of dilute polymer solutions. 

We showed in the preceding chapter, that from a physical point of view, it is reasonable to write the osmotic pressure by using as a length scale the size X of an isolated chain, defined by 

We can also write the first two terms in the form of a [1/1] Pade approximant 

A better method consists of calculating g as a root of an equation in g, by proceeding as indicated in Chapter 11, Section 3.3. We define w(z) by the equality 

Contenting ourselves with the first three terms of the expansion, we find 

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