Direct evaluation of the order parameter fluctuations

A more general version of the theory of P+LMW L systems, which expresses the Gibbs potential of mixing with due account of the order parameter s fluctuations (the concentration of polymer segments) has been put forward by Muthukumar (1986) on the basis of Eldwards (1965, 1966) formalism and their mutual paper (1982) (see Equations 5.1-246... 268). 

et us consider a P-f-LMWL system containing n chains of length L — Nl and Ns 

In the mean field approximation and in view of the ternary interactions, the Gibbs potential of mixing is written in the form 

As the second virial coefficient of the osmotic pressure expansion, the quantity (1/2 — y) is accepted here, while the difference between the characteristic parameter of the ternary interactions w and the trivial factor 1/6 acts as the third virial coefficient (sec 

The correction to Equation 1 due to the fluctuations in the order parameter must have the form 

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