Dielectric pearl‐necklace model of flexible polyelectrolytes for electrostatic solvation energy calculations

Abstract

The electrostatic component of the solvation free energy of polyelectrolytes in the description of dilute polymer solutions through the introduction of a dielectric dependent pearl-necklace model is taken into account. In this twodielectric model, the solvent is assumed to have a high dielectric constant while the pearls are modeled as charged spheres with low dielectric constant (e in ). Generalized Born (GB) models of electrostatic solvation give approximate solutions to the Poisson electrostatic problem through the Born radii of the pearls. Explicit calculations of the mean dimensions of the molecule, as a function of the solvation free energy, are performed on a minimal polyelectrolyte model (MPM), consisting of three identical beads with a single degree of freedom-the bond angle. Born radii calculated from the GB-Z 6 model (based on Kirkwood electrostatics) and from the GB-Z 4 model (based on the Coulomb Field Approximation) are compared with "perfect" radii (calculated from the Green's function of finite difference Poisson equation (PE)) in a wide range of molecular conformations. The best agreement is obtained with the first GB model. The descreening effect described by GB is demonstrated in both, good and poor solvent conditions, described with Lennard-Jones nonpolar interaction and variable dielectric constant of the pearls of the necklace. It is found that the electrostatic expansion factor of the mean squared end-to-end distance depends on the electric charge Q of the beads and the dielectric constant of the molecule. This function displays, in good and poor solvents, a maximum at high values of Q (10) and the height increases with lower e in . For instance, in the good solvent regime, the electrostatic swelling of the molecule is 6% in a one-dielectric model but it amounts to 12% in the two-dielectric model with GB-Z 6 electrostatic solvation when e in 5 7 (or increases up to 26% for e in 5 1), for Q 5 10. The electrostatic swelling is less relevant for lower values of electric charge (Q 1).