Résumé:

We will review recent results on primitive models of oppositely charged polyions and present a new, ultrasoft core model of interpenetrating polycations and polyanions with continuous Gaussian charge distributions. The model aims at investigating the aggregation process ("complex coacervation") of ultrasoft polyelectrolytes in dilute and semi-dilute solutions, in the absence and presence of added salt. In the salt-free case, the effective interaction between the polyions is given by a bounded potential at short distances and a long-range Coulomb interaction. By means of numerical simulations, we show that the topology of the phase diagram of the symmetric version of the model (the ``ultrasoft restricted primitive model'') differ from that of the widely studied ``restricted primitive model'' (RPM), where ions have hard cores. At sufficiently low temperatures and densities, oppositely charged polyions form weakly interacting, polarizable neutral pairs, leading to a sharp conductor-insulator transition. The conductor-insulator transition line terminates near the top of a first order coexistence curve separating a high-density liquid phase from a low-density vapor phase. The simulation data thus hint at a tricritical behavior, reminiscent of that observed in the two-dimensional Coulomb Gas, which contrasts with the Ising criticality of its three-dimensional counterpart, the RPM. The effect of salt addition on the physical properties of the model and the possible aggregation patterns in the asymmetric version of the model will be briefly discussed.