Coulomb Correlation Between Counterions in the Double Layer Around Cylindrical Polyions

Monte Carlo simulation and theoretical results on some aspects of structure and thermodynamics of polyelectrolyte solutions at room temperature are presented. The solution is mimicked by an infinitely long cylindrical polyion surrounded by point counterions. Both standard histogram method and Widom’s particle insertion method are utilized in the simulations based on the cylindrical cell model. The osmotic coefficient is determined via different equations (approaches) to determine the internal consistency of the equations as also the numerical accuracy of the calculations. Contributions to the osmotic coefficient arising out of polyion-counterion and counterioncounterion interactions are explicitly evaluated. The study clearly demonstrates (i) that the good agreement between the Poisson-Boltzmann predictions and the simulations is partly due to some serendipitous cancellation of errors, and (ii) that it is the neglect of the inter-ionic correlations in the mean field approach that leads to a partial compensation of the shortcomings of the Poisson-Boltzmann osmotic equation. Simulations results are also reported for the ion-ion correlations in the inhomogeneous diffuse double layer surrounding the polyion.