A Renormalization of the interaction parameters

For our associating blends clusters are characterized by the set of two figures so that the sum over a can be replaced by the sum over the type Hence we have 

From the material conservation laws (5.27a) and (5.27b), it is possible to expand v and y in powers of the volume fraction of the A component (polymer) as 

Obviously, = l,yo = l,yi = — 1, and other coefficients are 0 if there is no association. We first split the total number density of the clusters in accordance with the power of x 

The function go y) is related to the association within the B component (solvent), i(y) is related to the adsorption of the B molecules onto the polymers, and g2(y) is related to the pairwise cross-links of polymers by B component molecules. The fraction of the B molecules associated to the polymers is related to gi (y) by 

Substituting these power expansions into as (5.39), and expanding it in powers of the concentration, we find 

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