End-To-End Distribution Function Function of Stiff Polymers for all Persistence Lengths

Abstract

We set up recursion relations for calculating all even moments of the end-to-end distance of a Porod-Kratky wormlike chains in $D$ dimensions. From these moments we derive a simple analytic expression for the end-to-end distribution in three dimensions valid for all peristence lengths. It is in excellent agreement with Monte Carlo data for stiff chains and goes properly over into the Gaussian random-walk distributions for low stiffness.