Configurational properties of self-interacting linear polymer chains in a three-dimensional continuum. I. End-to-end probability and molecular span

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Abstract
A diagrammatic method of comparable status to the exact enumeration machine techniques is developed for the determination of the configurational properties of isolated self-avoiding polymer chains of freely jointed hard sphere segments. A close upper bound on the exponent in (R1N2) approximately ngamma is determined to be 1.26> gamma >1.0, which is a substantial improvement upon earlier diagrammatic analyses ( gamma =2.0). Moreover, the end-to-end distribution function has a non-zero contact value, indicating the possible development of closed ring configurations-again contrary to earlier diagrammatic analyses.