CONFIGURATIONAL PROPERTIES OF SELF-INTERACTING LINEAR POLYMER-CHAINS IN A 3-DIMENSIONAL CONTINUUM .1. END-TO-END PROBABILITY AND MOLECULAR SPAN

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.