In
the present work, we study the equilibrium conformations of
linear polyelectrolytes tethered onto a spherical, oppositely charged
core in equilibrium with an ionic reservoir of fixed concentration.
Particular focus is placed on the situation of stretched chains, where
the monomer concentration is known to display an inverse square-law
decay far away from the spherical surface, which is then further extrapolated
all the way down to the grafting core. While the equilibrium distributions
of mobile ions are computed in the framework of a classical density
functional theory (cDFT) that incorporates both their size and electrostatic
correlations within the grafted polyelectrolyte, the equilibrium configuration
of the latter is described by its average radius of gyration, which
is taken as a variational parameter that guarantees mechanical equilibrium
across the polymer–solvent interface. The average particle
size is then analyzed over a wide range of polymerization degrees,
ionic concentrations, and functionality of the polymer backbones.
Two distinct regimes can be identified: at high ionic strengths, swelling
of the grafted polymers is dominated by ionic entropic contribution
as well as polymer size effects, whereas at low ionic concentrations,
a balance between electrostatic and entropic effects is the main driven
mechanism for particle stretching. Using Monte Carlo simulations,
we then proceed to investigate the effects of charge regulation when
the brush core is further decorated with active functional sites randomly
distributed over its surface, which act as receptors onto which dissolved
acidic ions can be adsorbed.