Self-consistent field theories of the polymer excluded volume problem. III. A self-consistent solution

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Abstract
We summarize the self‐consistent field (SCF) approach of the excluded volume problem developed in two earlier articles. We emphasize that this approach leads to a hierarchy of SCF theories and that it resolves apparent conceptual conflicts between earlier SCF theories developed by Edwards and Reiss. We present an approximate solution to the simplest member of that hierarchy, and we demonstrate self‐consistency for the dominant part of the solution. From that solution we show the asymptotic dependence of the mean square end separation vector on chain length to be 〈R2〉 ∼ L6/(d+2) for 1?dd dimensions). Corrections to this asymptotic dependence, explicitly derived for d=2,3, demonstrate the crossover from the 6/5 law to the unperturbed (〈R2〉 ∼ L) behavior for finite chain lengths and for sufficiently weak excluded volume.

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