(565f) Obtaining Specific Ion Binding Free Energies on Polyelectrolytes Using Atomistic Molecular Dynamics Experiments

Using full atomistic molecular dynamics (MD) simulations of aqueous solutions of potassium salt ions and partially charged polyelectrolytes of varying charge fraction, we extract the ion-binding free energy from the radial distribution function of salt ion around the charged monomer. We compare these results with the predictions of a model in which the (effective) ion binding free energy is governed by intrinsic binding free energy and electrostatic correlations, captured by random phase approximation (RPA). The electrostatic correlations within the RPA depend on the polyelectrolyte chain configuration. An increase of the polyelectrolyte charge fraction increases the electrostatic repulsions among charged monomers leading to extended configurations of the polyelectrolyte and, simultaneously, stronger ion binding to the polyelectrolyte to relieve these repulsions. Using a rodlike chain configuration, the model yields quantitative predictions of ion binding at high polyelectrolyte charge fractions, where the intrinsic ion binding free energy is measured from separate MD simulations.