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In infinitely dilute solutions, macromolecules exhibit non-Gaussian distributions for their end-to-end separations. This occurs under such circumstances because intramolecular interactions are more important than intermolecular forces. On the other hand, when a macromolecular solution becomes so concentrated that it approaches its bulk phase, then the end-to-end length distribution becomes substantially Gaussian. A theoretical explanation for the observed behavior is obtained by taking cognizance of a balance between inter-and intramolecular forces acting on self-avoiding random chains. Such a balance causes the chains to behave very much like random walks of order 2-that is to say, walks for which the only restriction against double occupancy is that identified with immediate return steps. This is demonstrated by taking Monte Carlo data for chains of various concentrations and analyzing the distributions of a component of length by using expansions involving orthogonal vectors. Although Gaussian behavior is more or less achieved for bulk polymers, slight deviations from that behavior still persist at the origin.

Self-avoiding random walks at finite concentrations: The bulk phase limit