Potential of mean force and transient states in polyelectrolyte complexation

Abstract: 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.