  We introduce an ultrasoft core model of interpenetrating polycations and
polyanions with continuous Gaussian charge distributions, to investigate
polyelectrolyte aggregation in dilute and semi-dilute, salt-free solutions. The
model is studied by a combination of approximate theories (random phase
approximation and hypernetted chain theory) and numerical simulations. The
calculated pair structure, thermodynamics, phase diagram and polyion dynamics
of the symmetric version of the model (the "ultrasoft restricted primitive
model" or UPRM) differ from the corresponding properties 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. The clustering probabilities,
dielectric behavior and electrical conductivity point to a line of sharp
conductor-insulator transitions in the density-temperature plane. At very low
temperatures 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 hint at a tricritical behavior,
reminiscent of that observed of the two-dimensional Coulomb Gas, which
contrasts with the Ising criticality of its three-dimensional counterpart, the
RPM.
