Structure of Polyelectrolytes in Poor Solvent

– We present molecular dynamics simulations on strongly charged polyelectrolytes in poor solvent. The resulting pearl-necklace conformations are analyzed in detail. Fluctuations in the number of pearls and their sizes lead only to small signatures in the form factor and the force-extension relation, which is a severe obstacle for experimental observations. We find that the position of the first peak in the structure factor varies with the monomer density as ≈ ρ m for all densities. This is a qualitative difference to polyelectrolyte solutions in good solvent which scale as ρ 1/3 m and ρ 1/2 m in the dilute and semi-dilute concentration regime, respectively. Polyelectrolytes (PEs) are polymers that carry ionizable groups that dissociate ions in aqueous solution. Technical applications range from viscosity modifiers, precipitation agents, superabsorbers to leak protectors [1]. In biochemistry and molecular biology they are of great importance because virtually all proteins, as well as DNA, are PEs. Many PEs contain a non-polar hydrocarbon backbone, for which water is a poor solvent. Therefore, in aqueous solution, there is a competition between the tendency to precipitate, the Coulomb interaction and the entropic degrees of freedom. This can lead to elongated strings of locally collapsed structures (pearls). Such necklace conformations have been predicted on the basis of scaling arguments in ref. [2] for a weakly charged single chain PE, and have been confirmed by simulations using the Debye-Hückel approximation [2, 3] and with explicit counterions [4]. The formation of the necklace structure is due to the Rayleigh instability of a charged droplet, which leads to a split once a critical charge is reached. The size of the pearls is determined by the balance between electrostatic repulsion and surface tension. The distance between two pearls is governed by the balance of the electrostatic pearl-pearl repulsion and the surface tension. However, there is up to now no clear experimental proof for the existence of necklace chains [5,6]. Our previous papers [4] dealt with smaller system sizes and showed that necklaces exist also in the presence of counterions and exhibit a variety of conformational transitions as a function of density. The focus of the present paper is to analyze by extensive computer simulations in detail three possible experimental observables, namely the form factor, the structure factor and the force-extension relation, which can be probed by scattering and AFM techniques. Analyzing the fluctuations of necklace structures we find an extended coexistence regime between different necklace structures and broad distributions for the pearl sizes and the pearl-pearl distances that smear out the necklace signatures. In addition we find that the peak in the structure factor of the solution scales proportional to