Magnus Ullner, Bo Jönsson, Carsten Peterson, Ola Sommelius and Bo Söderberg The Electrostatic Persistence Length calculated from
Monte Carlo, Variational and Perturbation
Methods Journal of Chemical Physics
107, 1279-1287 (1997)Abstract: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-Hückel 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
(xi_{p})^{1/2}/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.LU TP 96-30 |