Model of the excluded volume chain

In real polymers, the nature of the long range interaction is quite complicated the interaction will include steric effects, van der Waals attraction, and also may involve other specific interactions mediated by solvent molecules. However, as far as the property of large length scale is concerned, the detail of the interaction will not matter because the excluded volume effect is controlled by the interaction between distant parts of the chain. Thus the interaction between the polymer segments n and m can be expressed by a short range function 

This expression indicates that eqn (2.87) is the first term in the virial expansion of the free energy with respect to the local concentration c(r). Therefore the excluded volume parameter v can be regarded as the virial coefficient between the segments. 

In principle the virial expansion can be continued to include higher 

However, the higher order terms may be neglected since the segment density inside the polymer coil is small the segment density is estimated as 

For a given combination of polymer and solvent, v varies with temperature and can be zero at a certain temperature, called the 0 or Flory temperature. At the 0 temperature, the chain becomes nearly ideal.t 

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