Dielectric Pearl-Necklace Model of Flexible Polyelectrolytes for Electrostatic Solvation Energy Calculations Alejandro R. Roig, 1 Jos e Luis Alessandrini 2 1 Facultad de Ingenier  ıa, Universidad Nacional de La Plata (UNLP), La Plata, Argentina 2 Departamento de F  ısica e Instituto de F  ısica de La Plata (IFLP), Facultad de Ciencias Exactas, UNLP, La Plata, Argentina Correspondence to: J. L. Alessandrini (E - mail: alessan@fisica.unlp.edu.ar) Received 15 October 2015; accepted 12 April 2016; published online 00 Month 2016 DOI: 10.1002/polb.24078 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 two- dielectric model, the solvent is assumed to have a high dielec- tric 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 per- formed 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 con- stant of the pearls of the necklace. It is found that the electro- static 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 elec- trostatic swelling is less relevant for lower values of electric charge (Q 1). V C 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 00, 000–000 KEYWORDS: electrostatic solvation; generalized Born model; solution properties; polyelectrolytes; statistical mechanics INTRODUCTION The understanding of the behavior of charged macromolecules in solution is still a subject of renewed interest because of the long-range nature of the electrostatic interactions, which alters the polymer structure in compari- son with neutral polymers. The electric charges introduce a greater complexity in the study of the conformations of sin- gle polymers because the total system is electrically neutral and weak polyelectrolytes in solution are then described as a ternary system composed of the charged polymer, the sol- vent, and the counterions. An additional forth component (coion) is incorporated in solutions with added salt. 1,2 Analytical theories of the conformation properties of charged polymers treat the solvent as a continuous medium with uni- form dielectric constant e. Charged polymers are classified as weak or strong polyelec- trolytes according to the strength of the Coulomb interaction, measured as the ratio k between the Bjerrum length l B (l B 5 e 2 /e k B T , with e the elemental electric charge and k B T , the thermal energy) and the distance, a, between charges on the polymer skeleton (k 5 l B /a). A strong (weak) polyelectro- lyte is defined as k  1(k « 1), respectively. In both cases, the Coulomb interaction tends to dominate the structure of the charged polymer. For instance, in strong polyelectrolytes the end-to-end distance R follows a rod-like limit, R  N 1 in the case of an isolated charged chain with N monomers (i.e., in the absence of counterions). Weak polyelectrolytes exhibit similar behavior, but preserving the intrinsic flexibility of the neutral chain. Counterions were introduced using mean field arguments through Debye–Huckel theory and their effect Additional Supporting Information may be found in the online version of this article. V C 2016 Wiley Periodicals, Inc. WWW.MATERIALSVIEWS.COM JOURNAL OF POLYMER SCIENCE, PART B: POLYMER PHYSICS 2016, 00, 000–000 1 JOURNAL OF POLYMER SCIENCE WWW.POLYMERPHYSICS.ORG FULL PAPER