  In solutions of star-branched polyelectrolytes, electrostatic interactions
between charged arms on neighboring stars can compete with intra-star
interactions and rotational entropy to induce anisotropy in the orientational
distribution of arms. For model stars comprising rigid rodlike arms with evenly
spaced charged monomers interacting via an effective screened-Coulomb (Yukawa)
potential, we explore the influence of arm orientational anisotropy on
effective star-star interactions. Monte Carlo simulation and density-functional
theory are used to compute arm orientational distributions and effective pair
potentials between weakly charged stars. 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
inter-star 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 intra- and inter-star 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, C. N. Likos, and H.
Lowen, Phys. Rev. Lett. 88, 018301 (2002); J. Chem. Phys. 116, 11011 (2002)].
