Self-consistent field theories of the polymer excluded volume problem. IV. The linear polymer

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Abstract
The previous abstract formulation of self‐consistent field (SCF) theories of polymer excluded volume is extended and generalized to provide a SCF theory for the moments of the end‐vector distribution such as 〈R2n〉. The nonlinear integrodifferential equations of the SCF theory are considered for a linear polymer where the SCF’s, V2n, are shown to be spherically symmetric, and the dominant part of V2n is obtained and shown to be self‐consistent. The 〈R2n〉 are obtained and have asymptotic long chain limits conforming to the Flory–Edwards power laws. Contributions from fluctuations about the SCF are considered and are shown to alter the total number of chain configurations but not to change the long chain limits for 〈R2n〉 for n≳0. A discussion is presented of the relationship of the SCF results to those obtained by use of the renormalization group method.