We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality as the numerical evaluation of Marko’s and Siggia’s variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests, that our analytical expressions for the finite-chain length corrections are of similar quality. As an application of our results we discuss the possibility of inferring the changing number of nicks in a double-stranded DNA molecule in single-molecule stretching experiments from the accompanying changes in the effective chain length.
Download a copy of the article (preprint version)