rXXXX American Chemical Society A dx.doi.org/10.1021/ma2007943 | Macromolecules XXXX, XXX, 000–000 ARTICLE pubs.acs.org/Macromolecules Polyelectrolytes in Salt Solutions: Molecular Dynamics Simulations Jan-Michael Y. Carrillo and Andrey V. Dobrynin* Polymer Program, Institute of Materials Science and Department of Physics, University of Connecticut, Storrs, Connecticut 06269, United States 1. INTRODUCTION Polyelectrolytes are macromolecules with ionizable groups. In aqueous solutions charged groups dissociate, leaving charges on the chain and releasing counterions into solution. Common polyelectrolytes include poly(acrylic acid) and poly(methacrylic acid) and their salts, poly(styrenesulfonate), DNA, RNA, and other polyacids and polybases. 19 Polyelectrolytes play an important role in a diverse number of fields ranging from materials science and colloids to biophysics. These polymers are used as rheology modifiers, adsorbents, coatings, biomedical implants, colloidal stabilizing agents, and suspending agents for pharmaceutical delivery systems. Electrostatic interactions between charges lead to the rich behavior of these polymeric systems (see for review refs 15 and 7). For example, in salt-free polyelectrolyte solutions the electrostatic interactions between charged groups on the poly- mer backbone result in a strong chain elongation with chain size scaling almost linearly with the chain degree of polymerization. Because of this strong dependence of the chain size on the chain degree of polymerization, the crossover to semidilute polyelec- trolyte solution regime occurs at much low polymer concentra- tions than in solutions of neutral polymers. 1,5,6,8,10 The main contribution to the osmotic pressure in polyelectrolyte solutions comes from the ionic component. 9,1115 Polyelectrolyte con- formations are sensitive to the solvent quality for the polymer backbone. In poor solvent conditions for the polymer backbone a polyelectrolyte chain forms an unusual necklace-like structure of dense polymeric beads connected by strings of monomers. 1,1630 Similar necklace-like structure can be formed in hydrophobically modified polyelectrolytes in which a hydrophobic side chains are attached to the polyelectrolyte backbone. 31 Addition of salt leads to screening of the electrostatic interac- tions between ionized groups reducing the polyelectrolyte effect (see for review refs 1 and 2). At high salt concentrations properties of polyelectrolyte solutions are similar to those of neutral polymers with effective second virial coefficient between monomers which strength is determined by the salt concentra- tion and by the fraction of the ionized groups along the poly- mer backbone. While there is a significant number of experi- mental studies of polyelectrolytes in salt solutions (see for review refs 1, 2, and 6) the computational studies of the salt effect on the properties of polyelectrolyte solutions are lagging behind. 3,3241 The computer simulations of the polyelectrolyte solutions in the presence of salt were limited to investigation of the salt effect on the single chain properties. 3337 The salt ions in these simula- tions were taken into account either explicitly or implicitly by modeling the screening effect of the salt ions by representing the electrostatic interactions between charged monomers by the Received: April 5, 2011 Revised: June 6, 2011 ABSTRACT: We present results of the molecular dynamics simulations of salt solutions of polyelectrolyte chains with number of monomers N = 300. Polyelectrolyte solutions are modeled as an ensemble of beadspring chains of charged Lennard-Jones particles with explicit counterions and salt ions. Our simulations show that in dilute and semidilute polyelectrolyte solutions the electrostatic induced chain persistence length scales with the solution ionic strength as I 1/2 . This dependence of the chain persistence length is due to counterion condensation on the polymer backbone. In dilute polyelectrolyte solutions the chain size decreases with increasing the salt concentration as R µ I 1/5 . This is in agreement with the scaling of the chain persistence length on the solution ionic strength, l p µ I 1/2 . In semidilute solution regime at low salt concentrations the chain size decreases with increasing polymer concentration, R µ c p 1/4 , while at high salt concentrations we observed a weaker dependence of the chain size on the solution ionic strength, R µ I 1/8 . Our simulations also confirmed that the peak position in the polymer scattering function scales with the polymer concentration in dilute polyelectrolyte solutions as c p 1/3 . In semidilute polyelectrolyte solutions at low salt concentrations the location of the peak in the scattering function shifts toward the large values of q* µ c p 1/2 while at high salt concentrations the peak location depends on the solution ionic strength as I 1/4 . Analysis of the simulation data throughout the studied salt and polymer concentration ranges shows that there exist general scaling relations between multiple quantities X(I) in salt solutions and corresponding quantities X(I 0 ) in salt-free solutions, X(I)= X(I 0 )(I/I 0 ) β . The exponent β = 1/2 for chain persistence length l p , β = 1/4 for solution correlation length ξ, and β = 1/5 and β = 1/8 for chain size R in dilute and semidilute solution regimes, respectively.