The Lagrangian theory of polymer solutions at intermediate concentrations

2014 De Gennes has shown that the properties of an isolated polymer in a solution (a chain with excluded volume) can be deduced within the framework of a Lagrangian theory for a zero component field in the absence of an external field. This result in generalized to the case of polymer solutions at intermediate concentrations. It is shown that a grand ensemble of polymers can be described by using a Lagrangian theory for a zero component field coupled to an external field. The concentrations Cp of polymers (chains) and Cm of monomers (links) are fixed by two chemical potentials. It is shown that the osmotic pressure obeys a scaling law of the form (P/KTCp) = F(Cp N303BD) where N is the mean number of monomers per polymer (N = Cp/Cm) and 03BD the critical index defining the size of a long isolated polymer. The function F(03BB) can be expanded in powers of 03BB and it is given implicitly by the generating functional of the zero-momentum vertex functions derived from the Lagrangian theory. The results seem to be in good agreement with experiments. Tome 36 N° 4 AVRIL 1975 Classification Physics Abstracts 1.650 7.480