The complex formation between a weak polyelectrolyte chain and an oppositely charged nanoparticle is investigated using Monte Carlo simulations. Global structural parameters such as the polyelectrolyte length, nanoparticle size, solution pH, and ionic concentration as well as local features, such as the nanoparticle surface charge density and polyelectrolyte intrinsic stiffness influences, are systematically investigated. Phase states of the polyelectrolyte/nanoparticle complexes are presented, and to bridge the gap with experiments, titration curves are calculated. It is shown that the presence of one oppositely charged nanoparticle significantly modifies the acid/base properties of the weak polyelectrolyte as well as the charge distribution along the polymer backbone and that the solution pH and ionic concentration largely control the polyelectrolyte conformation at the nanoparticle surface. Chain stiffness promotes the polyelectrolyte expansion as well as ionization but penalizes the polyelectrolyte adsorption at the nanoparticle surface, hence affecting its acid/base behavior.

Monte Carlo simulations have been used to study two different models for a weak linear polyelectrolyte in the presence of nanoparticles: (i) a rodlike and (ii) a flexible polyelectrolytes. The use of simulated annealing has made it possible to simulate a polyelectrolyte chain in the presence of several nanoparticles by improving conformation sampling and avoiding multiple minima problems when dense conformations are produced. Nanoparticle distributions along the polymer backbone were analyzed versus the ionic concentration, polyelectrolyte stiffness, and nanoparticle surface charge. Titration curves were calculated and the influences of the ionic concentration, solution pH, and number of adsorbed nanoparticles on the acid/base polyelectrolyte properties have been systematically investigated. The subtle balance of attractive and repulsive interactions has been discussed, and some characteristic conformations are presented. The comparison of the two limit models provides a good representation of the stiffness influence on the complex formation. In some conditions, overcharging was obtained and presented with respect to both the polyelectrolyte and nanoparticle as the central element. Finally, the charge mobility influence along the polyelectrolyte backbone was investigated by considering annealed and quenched polyelectrolyte chains.