We simulate interactions between charged flat Surfaces in the presence of block polymers, where the end blocks carry a charge opposite to the surfaces. Using a recently developed simulation technique, we allow full equilibrium, i.e. the chemical potential of the polyelectrolyte is retained as the separation is changed. In general, the block polyions will adsorb strongly enough to overcharge the surfaces. This results in a double layer repulsion at large separation, with a concomitant free energy barrier. At short separations, the surfaces are Pulled together by bridging forces. We make some efforts to theoretically design the polymers to be efficient flocculants, i.e. minimize the free energy barrier and still allow for a long-ranged bridging attraction. Here, we also take into account the possibility of nonequilibrium circumstances, which may be relevant in practice. Our results suggest that short chains, with small charged end blocks and a (relatively speaking) long neutral mid block, are likely to promote rapid flocculation. (C) 2008 Elsevier Inc. All rights reserved.