Eur. Phys. J. B 2, 341–345 (1998) T HE EUROPEAN P HYSICAL JOURNAL B c  EDP Sciences Springer-Verlag 1998 The eﬀect of added salt on polyelectrolyte structure M.J. Stevens a and S.J. Plimpton P.O. Box 5800, MS 1111, Sandia National Laboratories, Albuquerque, NM 87185, USA Received: 9 July 1997 / Revised: 3 November 1997 / Accepted: 30 November 1997 Abstract. We present results of molecular dynamics simulations of strong, ﬂexible polyelectrolyte chains in solution with added salt. The eﬀect of added salt on the polyelectrolyte chain structure is fully treated for the ﬁrst time as a function of polymer density. Systems above and below the Manning condensation limit are studied. The chain structure is intimately tied to the ion density near the chain even for chains in the counterion condensation (CC) regime. The end-to-end distance is demonstrated to be a function of the inverse Debye screening length and the Bjerrum length. The ion density near the polymer chain depends on the amount of added salt, and above the condensation limit the chains signiﬁcantly contract due to added salt. PACS. 61.25.Hq Macromolecular and polymer solutions; polymers melts; swelling – 36.20.Ey Conforma- tion (statistics and dynamics) – 87.15.He Molecular dynamics and conformational changes 1 Introduction Polyelectrolytes are a very important class of polymers, because they are one set of water-soluble polymers. They include biopolymers such as DNA, RNA, and polysaccha- rides. Their water solubility makes polyelectrolytes an im- portant class of synthetic, commercial polymers used for example, as the key water absorbing ingredient in dispos- able diapers. The addition of salt is a key means to alter structure and properties. Our understanding of polyelec- trolyte structure is limited, and consequently, so is our un- derstanding of polyelectrolyte system properties [1–5]. Re- cently, simulations have calculated the structure of strong, ﬂexible polyelectrolytes in salt-free solution [3]. Here, we present results of polyelectrolyte simulations with added salt. In particular we examine the inﬂuence of the ionic distribution on the chain structure. Our understanding of polyelectrolytes has been poor because of the diﬃculties these systems present to both experiment and theory. Direct measurements of the sin- gle chain structure, particularly at dilute concentrations have yet to be done. Recent molecular dynamics (MD) simulations of salt-free polyelectrolyte systems have over- come major theoretical diﬃculties [3,6]. The picture of polyelectrolyte structure [3,5] has been shown to be more complicated than the two early theories [7] predicted. Past theoretical works tended to neglect entropy, in part be- cause they focused on DNA which is intrinsically very stiﬀ. For stiﬀ chains entropy is a small contribution to the free energy. In contrast, for ﬂexible polyelectrolytes, treating entropy along with the Coulomb interactions is essential and has only been done properly in simulations [3,5]. More a e-mail: mjsteve@cs.sandia.gov recently, self-consistent ﬁeld theory [8] and PRISM [9] cal- culations also treat entropy and are promising. One of the major theoretical diﬃculties is the calcula- tion of the ionic density about the chain. Almost all calcu- lations of chain structure use the Debye-H¨ uckel (DH) ap- proximation. Moreover, to date analytic calculations have been for ﬁxed shapes (e.g. cylinders). This approximation is a linearization of the Poisson-Boltzmann (PB) equa- tion, valid when the Coulomb interaction energy is much less than k B T . Yet, polyelectrolytes are highly charged and the Coulomb energies are often stronger than k B T . The PB equation [10–12] is a mean ﬁeld approximation that neglects ion correlations, and is valid when typical counterion separations are larger than the Bjerrum length, λ = e 2 /ǫk B T , where ǫ is the dielectric constant of the so- lution (water) and e is the electron charge. By performing MD simulations, we can treat the fundamental polyelectrolyte problem without any of the above approximations. Previously, using MD one of us has successfully characterized strong, ﬂexible polyelectrolytes in salt-free solution [3,6]. Experimental measurements of the osmotic pressure and the peak position in the inter- chain structure factor were reproduced by these simu- lations. Furthermore, it was shown that polyelectrolyte structure is fundamentally diﬀerent from previous theoret- ical predictions. In particular, the chains contract below the overlap density, ρ * . The chains are not fully extended or rodlike at dilute concentrations. For fully ﬂexible chains and λ/a ∼ 1 entropy is not dominated by the Coulomb interactions. While the end-to-end distance is much larger than for neutral chains, the dilute conformation exhibits signiﬁcant bending at large length scales.