Polyelectrolyte-mediated bridging interactions: columnar macromolecular phases

Abstract

We present a mean-field theory for charged polymer chains in an external electrostatic fieldin the weak and strong coupling limits. We apply the theory to describe the statisticalmechanics of flexible polyelectrolyte chains in a hexagonal columnar lattice of stiffcylindrical macroions, such as DNA, in a bathing solution of a uni-univalent salt(e.g. NaCl). The salt effects are first described in the Debye–Hückel framework. This yieldsthe macroion electrostatic field in the screened Coulomb form, which we taketo represent the mean field into which the chains are immersed. We introducethe Green’s function for the polyelectrolyte chains and derive the correspondingEdwards equation which we solve numerically in the Wigner–Seitz cylindrical cellusing the ground state dominance ansatz. The solutions indicate the presence ofpolyelectrolyte bridging, which results in a like-charge attraction between stiffmacroions. Then we reformulate the Edwards theory for the strong coupling caseand use the standard Poisson–Boltzmann picture to describe the salt solution.We begin with the free energy which we minimize to obtain the Euler–Lagrangeequations. The solutions yield self-consistently determined monomer density andelectrostatic fields. We furthermore calculate the free energy density as well as the totalosmotic pressure in the system. We again show that bridging implicates like-chargeattractions of entropic origin between stiff cylindrical macroions. By analyzing theosmotic pressure we demonstrate that, in certain parts of the parameter space, aphase transition occurs between two phases of the same hexagonal symmetry.