Effective electrostatic interactions in solutions of polyelectrolyte stars with rigid rodlike arms.

In solutions of star-branched polyelectrolytes, electrostatic interactions between charged arms on neighboring stars can compete with intrastar interactions and rotational entropy to induce anisotropy in the orientational distribution of arms. We explore the influence of arm orientational anisotropy on effective star-star interactions for model stars comprising rigid rodlike arms with evenly spaced charged monomers interacting via an effective screened-Coulomb (Yukawa) potential. Monte Carlo simulation and density-functional theory are used to compute the arm orientational distributions and effective pair potentials between weakly charged stars. For comparison, a torque balance analysis is performed to obtain the configuration and energy of the ground state, in which the torque vanishes on each arm of the two-star system. The degree of anisotropy is found to increase with the strength of electrostatic interactions and proximity of the stars. As two stars begin to overlap, the forward arms are pushed back by interstar arm-arm repulsion, but partially interdigitate due to rotational entropy. At center-center separations approaching complete overlap, the arms relax to an isotropic distribution. For nonoverlapping stars, anisotropy-induced changes in the intra- and interstar arm-arm interactions largely cancel and the effective pair interactions are then well approximated by a simple Yukawa potential, as predicted by linear-response theory for a continuum model of isotropic stars [A. R. Denton, Phys. Rev. E 67, 11804 (2003)]. For overlapping stars, the effective pair interactions in the simple rigid-arm-Yukawa model agree closely with simulations of a molecular model that includes flexible arms and explicit counterions [A. Jusufi et al., Phys. Rev. Lett. 88, 018301 (2002); J. Chem. Phys. 116, 11011 (2002)].