The Electrostatic Persistence Length Calculated from Monte Carlo,   Variational and Perturbation Methods
  Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions.   For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-H\"{u}ckel screening length, $\kappa^{-1}$.As long as the salt content is low and $\kappa^{-1}$ is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with $\kappa^{-1}$. Decreasing the screening length, a controversial region is entered. We find that the electrostatic persistence length scales as $sqrt{\xi_p}/\kappa$, in agreement with experiment on flexible polyelectrolytes, where $\xi_p$ is a strength parameter measuring the electrostatic interactions within the polyelectrolyte. For screening lengths much shorter than the bond length, the $\kappa^{-1}$ dependence becomes quadratic in the variational calculation. The simulations suffer from numerical problems in this regime, but seem to give a relationship half-way between linear and quadratic.   A low temperature expansion only reproduces the first regime and a high temperature expansion, which treats the electrostatic interactions as a perturbation to a Gaussian chain, gives a quadratic dependence on the Debye length.   For a sufficiently stiff chain, the persistence length varies quadratically with $\kappa^{-1}$ in agreement with earlier theories. 
M. Ullner, B. J\"onsson (Dept. of Chemistry, Lund U.), C. Peterson, O.   Sommelius, B. S\"oderberg (Dept. of Theoretical Phy...