Mean field theory of polymer crossover behavior

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Abstract
An argument is presented that the exponent previously employed to describe crossover behavior of either a linear or randomly branched polymer from the theta region to the swollen or collapsed state is inconsistent with the mean field description of the polymer free energy. In place of the conventional exponent φ(d)=[2−dνθ(d)], it is suggested that mean field theory compels use of the exponent ψ(d)=[νθ(d)d−1], where νθ(d) is the index which describes the dependence of polymer length on molecular weight in the theta region. The consequences of this different choice of crossover index are discussed for crossover behavior of the polymer length and for phase separation behavior. Comparison of the results of the different predictions with both Flory–Huggins theory and ε-expansion calculations is included. For linear chains in two dimensions striking differences are found for the predicted behavior of the phase separation curve at high monomer concentrations.

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