  Electrostatic interactions in polymeric systems are responsible for a wide
range of liquid-liquid phase transitions that are of importance for biology and
materials science. Such transitions are referred to as complex coacervation,
and recent studies have sought to understand the underlying physics and
chemistry. Most theoretical and simulation efforts to date have focused on
oppositely charged linear polyelectrolytes, which adopt nearly ideal-coil
conformations in the condensed phase. However, when one of the coacervate
components is a globular protein, a better model of complexation should replace
one of the species with a spherical charged particle or colloid. In this work,
we perform coarse-grained simulations of colloid-polyelectrolyte coacervation
using a spherical model for the colloid. Simulation results indicate that the
electroneutral cell of the resulting (hybrid) coacervates consists of a
polyelectrolyte layer adsorbed on the colloid. Power laws for the structure and
the density of the condensed phase, which are extracted from simulations, are
found to be consistent with the adsorption-based scaling theory of
coacervation. The coacervates remain amorphous (disordered) at a moderate
colloid charge, $Q$, while an intra-coacervate colloidal crystal is formed
above a certain threshold, at $Q > Q^{*}$. In the disordered coacervate, if $Q$
is sufficiently low, colloids diffuse as neutral non-sticky nanoparticles in
the semidilute polymer solution. For higher $Q$, adsorption is strong and
colloids become effectively sticky. Our findings are relevant for the
coacervation of polyelectrolytes with proteins, spherical micelles of ionic
surfactants, and solid organic or inorganic nanoparticles.
