The Electrostatic Persistence Length Calculated from Monte Carlo, Variational and Perturbation Methods

TL;DR

This study uses Monte Carlo, variational, and perturbation methods to analyze the electrostatic persistence length of polyelectrolyte chains, revealing different regimes of dependence on salt screening length and confirming some theoretical predictions.

Contribution

It provides a comprehensive comparison of simulation and analytical methods to determine electrostatic persistence length across various regimes, including flexible and stiff chains.

Findings

Electrostatic persistence length scales as sqrt(ξ_p)/κ for flexible chains at intermediate salt concentrations.

In the short screening length regime, the dependence becomes quadratic according to variational calculations.

For stiff chains, the persistence length varies quadratically with the Debye length, aligning with previous theories.

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-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.