Grand canonical ensembles osmotic pressure and structure of continuous chains

GRAND CANONICAL ENSEMBLES OSMOTIC PRESSURE AND STRUCTURE FUNCTIONS OF CONTINUOUS CHAINS 

In the monodisperse case, the (connected) grand partition function reads [see (9.4.12)] 

The osmotic pressure TI and the number C(S) of polymers per unit volume and per unit area are given by 

Consequently, the first terms of the virial expansion are obtained by eliminating the fugacities in terms of which the osmotic pressure and the concentrations are expressed. In the monodisperse case, we set 

---