Properties of polyelectrolyte chains from analysis of angular correlation functions

An empirical expression for the angular correlation function (ACF) of charged (Debye–Hückel) wormlike chains (WLC) with excluded volume (EV) is introduced. It reproduces the Monte Carlo (MC) data of a previous study very well. Using this expression analytical calculations for the persistence length $(Lp),$ radius of gyration $(Rg),$ and end-to-end distance $(R)$ are given in the form of Taylor series. It is shown that the above quantities can be expressed as a weighted sum over the corresponding quantities $(Lph,$ $Rgh,$ $Rh)$ of a set of ideal wormlike chains ${Ch}$ $h=0,1,… .$ Both the set ${Ch}$ and the coefficients in the Taylor expansions are defined as functions of three parameters which are determined by fitting the ACF expression to the MC data. A comparison of the calculated $Rg$ and R shows excellent agreement with the corresponding sampled values. The persistence length $Lp$ is in good agreement with the values determined by fitting the sampled scattering functions by model expressions for neutral chains with excluded volume interactions, provided that a contribution due to EV is subtracted from $Lp.$ Moreover, the method here proposed allows one to determine the persistence length of very short chains which is not possible by fitting the scattering function. The new expression for the angular correlation function, as well as the expressions derived for $Rg$ and R are a natural generalization of well known results for ideal WLC, when EV and/or electrostatic interactions are present.