Configuration of Polymer Molecules with Excluded Volume

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Abstract
The displacement distribution for a polymer molecule with excluded volume is derived by rejecting the unacceptable configurations available to random‐flight chains. The fraction of those configurations corresponding to a displacement length L which are acceptable is calculated through use of a model which considers the chain to be composed of a sequence of identical subchains. Interactions between the elements of a given subchain, and between these and elements of the various possible clusters of adjacent subchains, are summed to obtain the total interference for all elements of the chain. The average interference encountered by the elements of one subchain is calculated therefrom. The resulting displacement distribution is considerably sharper than the corresponding Gaussian distribution for positive values of the excluded volume, but somewhat more extended than the corresponding Gaussian for negative excluded volumes. When the present treatment is compared with that of Flory, the former predicts smaller values for the mean‐square displacement length, 〈L2〉, at both the low and the high ends of the molecular weight scale, and a more marked dependence of 〈L2〉 upon the thermodynamic interactions as embodied in the factor (½—χ12). Comparison with experiment confirms these predictions, and indicates the present treatment to be a significant improvement over that proposed earlier by Flory.

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