Theory of Moderately Concentrated Polymer Solutions

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Abstract
The transition between the theories of the thermodynamic properties of dilute and concentrated polymer solutions is investigated using the random‐flight model with explicit consideration of segment—segment interactions. It begins with a qualitative discussion of the transition. Supposing the individual segments, instead of the entire polymer molecules, to be solute molecules, a general expression for the osmotic pressure π is derived by the method of Green. Then the apparent second virial coefficient Γ defined by Γ=π/RTc2−1/Mc, where c is the concentration and M the polymer molecular weight, is evaluated by a coupling‐parameter method. The evaluation consists of solving differential equations which can be derived approximately from the Kirkwood integral equations for the distribution functions. The result is expressed as a function of c and α, where α is the linear expansion factor of the polymer molecule at finite concentrations. Thus, α is also evaluated as a function of c, though the expression is incomplete at very high concentrations. For good solvent systems, it is predicted that as α is decreased to unity with increasing concentration and then becomes independent of concentration, Γ increases first rapidly and then gradually, passing through the transition region. This prediction is in fairly good agreement with experiment for polyisobutylene in cyclohexane. For poor solvent systems, the theory is invalid except at low concentrations.

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