  The association between polyelectrolytes (PEs) of the same size but opposite
charge is systematically studied in terms of the potential of mean force (PMF)
along their center-of-mass reaction coordinate via coarse-grained,
implicit-solvent, explicit-salt computer simulations. The focus is set on the
onset and the intermediate, transient stages of complexation. At conditions
above the counterion-condensation threshold, the PE association process
exhibits a distinct sliding-rod-like behavior where the polymer chains approach
each other by first stretching out at a critical distance close to their
contour length, then 'shaking hand' and sliding along each other in a parallel
fashion, before eventually folding into a neutral complex. The essential part
of the PMF for highly charged PEs can be very well described by a simple theory
based on sliding charged `Debye--H\"uckel' rods with renormalized charges in
addition to an explicit entropy contribution owing to the release of condensed
counterions. Interestingly, at the onset of complex formation, the mean force
between the PE chains is found to be discontinuous, reflecting a bimodal
structural behavior that arises from the coexistence of interconnected-rod and
isolated-coil states. These two microstates of the PE complex are balanced by
subtle counterion release effects and separated by a free-energy barrier due to
unfavorable stretching entropy.
