Complex formation between a weak flexible polyelectrolyte chain and one positively charged nanoparticle in presence of explicit counterions and salt particles is investigated using Monte Carlo simulations. The influence of parameters such as the nanoparticle surface charge density, salt valency, and solution property such as the pH on the chain protonation/deprotonation process and monomer adsorption at the nanoparticle surface are systematically investigated. It is shown that the nanoparticle presence significantly modifies chain acid/base and polyelectrolyte conformational properties. The importance of the attractive electrostatic interactions between the chain and the nanoparticle clearly promotes the chain deprotonation leading, at high pH and nanoparticle charge density, to fully wrapped polyelectrolyte at the nanoparticle surface. When the nanoparticle bare charge is overcompensated by the polyelectrolyte charges, counterions and salt particles condense at the surface of the polyelectrolyte–nanoparticle complex to compensate for the excess of charges providing from the adsorbed polyelectrolyte chain. It is also shown that the complex formation is significantly affected by the salt valency. Indeed, with the presence of trivalent salt cations, competition is observed between the nanoparticle and the trivalent cations. As a result, the amount of adsorbed monomers is less important than in the monovalent and divalent case and chain conformations are different due to the collapse of polyelectrolyte segments around trivalent cations out of the nanoparticle adsorption layer

The electrostatic driven complex formation between a weak polyampholyte chain and one positively charged nanoparticle is investigated using Monte Carlo simulations. The influence of parameters such as the polyampholyte contour length, number and size of blocks, nanoparticle surface charge density, and solution properties, such as the pH and ionic concentration, on the PA titration curves is investigated. It is shown that the presence of one positively charged nanoparticle significantly modifies the acid/base properties of the weak polyampholyte by, on the one hand, promoting the formation of negatively charged monomers and, on the other hand, limiting the number of positively charged monomers. The electrostatic interactions of this system can be modified by pH, ionic concentration, and nanoparticle surface charge. The competition between attractive and repulsive, intramolecular and intermolecular electrostatic interactions leads to a wide range of possible PA conformations at the nanoparticle surface, which have a direct impact on the nanoparticle stabilized or destabilized solutions. Extended conformations, electrostatic rosettes, and dense multiplayer structures are observed. Nonetheless, the intramolecular interactions between the positively and negatively charged PA monomers, in particular at the isoelectric point, are found to play important and subtle roles for both the isolated and adsorbed chain conformations. It is also found that nanoparticle charge inversion is an important ingredient for the formation of multilayer structures at the nanoparticle surface.

Acid/base and conformational properties of a weak polyelectrolyte chain surrounded by explicit ions (counterions and salt particles) are investigated using Monte Carlo simulations. The influence of the pH, monomer size, presence of explicit ions, salt particles, salt size, and valency on the polyelectrolyte titration process is systematically investigated. It is shown that the presence of explicit ions, the increase in pH and monomer sizes, and the decrease in salt radius are parameters that favor the monomer deprotonation processes hence affecting the global acid/base polyelectrolyte chain properties. The competition between attractive and repulsive, long-range and local electrostatic interactions leads to a heterogeneous distribution of charges and ions along the polyelectrolyte backbones. This subtle electrostatic competition leads to equilibrated chain conformations ranging from extended to globular conformations. A simple screening effect is achieved with monovalent salt resulting in a slight limitation of the formation of extended structures at high pH values. Focusing on trivalent salt, the local complexation of several chain monomers around each trivalent cation leads to the formation of collapsed structures. The decrease in the size of trivalent cations promotes the deprotonation process, in particular, when trivalent salt cations are smaller than the monomer size.

Monte Carlo simulations have been used to study two different models of a weak linear polyelectrolyte surrounded by explicit counterions and salt particles: (i) a rigid rod and (ii) a flexible chain. We focused on the influence of the pH, chain stiffness, salt concentration, and valency on the polyelectrolyte titration process and conformational properties. It is shown that chain acid-base properties and conformational properties are strongly modified when multivalent salt concentration variation ranges below the charge equivalence. Increasing chain stiffness allows to minimize intramolecular electrostatic monomer interactions hence improving the deprotonation process. The presence of di and trivalent salt cations clearly promotes the chain degree of ionization but has only a limited effect at very low salt concentration ranges. Moreover, folded structures of fully charged chains are only observed when multivalent salt at a concentration equal or above charge equivalence is considered. Long-range electrostatic potential is found to influence the distribution of charges along and around the polyelectrolyte backbones hence resulting in a higher degree of ionization and a lower attraction of counterions and salt particles at the chain extremities.

The conformational properties and formation of a complex between a weak flexible biomacromolecule chain of variable hydrophobicity and one negatively charged nanoparticle in the presence of explicit counterions are investigated here using Monte Carlo simulations. The influence of the charge distribution and hydrophobicity, monomer distribution of the chain as well as the pH of the solution are systematically investigated. It is shown that the isolated chain conformations, built with random and block distribution of carboxylic, amino and hydrophobic groups, are the result of the subtle competition between intrachain attractive and repulsive electrostatic interactions as well as intrachain attractive short-range interactions due to hydrophobic properties. Extended conformations are found at low and high pH and folded conformations at physiological pH when hydrophilic and block polymer chains are considered. On the other hand, hydrophobic chain conformations do not show pH dependency and remain folded. The intrachain attractive electrostatic interactions clearly promote the deprotonation of carboxylic groups at low pH and the protonation of amino groups at high pH with higher efficiency for hydrophilic chains. The additional set of electrostatic interactions due to the presence of one negatively charged nanoparticle limits the deprotonation of carboxylic groups at low pH. Moreover, the attractive interactions between the biomacromolecule and the nanoparticle allow to observe the formation of a complex considering intermediate and hydrophilic chains even close to the chain isoelectric point due to the charge inhomogeneity distribution. Hydrophobic chain segments are not affected by the presence of the nanoparticle and remain desorbed. In all cases, the presence of one nanoparticle influences the biomacromolecule structures and acid/base properties, leading to more stretched conformations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.

Biomacromolecule activity is usually related to its ability to keep a specific structure. However, in solution, many parameters (pH, ionic strength) and external compounds (polyelectrolytes, nanoparticles) can modify biomacromolecule structure as well as acid/base properties, thus resulting in a loss of activity and denaturation. In this paper, the impact of neutral and charged nanoparticles (NPs) is investigated by Monte Carlo simulations on polypeptide (PP) chains with primary structure based on bovine serum albumin. The influence of pH, salt valency, and NP surface charge density is systematically studied. It is found that the PP is extended at extreme pH, when no complex formation is observed, and folded at physiological pH. PP adsorption around oppositely-charged NPs strongly limits chain structural changes and modifies its acid/base properties. At physiological pH, the complex formation occurs only with positively-charged NPs. The presence of salts, in particular those with trivalent cations, introduces additional electrostatic interactions, resulting in a mitigation of the impact of negative NPs. Thus, the corona structure is less dense with locally-desorbed segments. On the contrary, very limited impact of salt cation valency is observed when NPs are positive, due to the absence of competitive effects between multivalent cations and NP.

Nanoparticle surface charge properties represent key parameters to predict their fate, reactivity, and complexation in natural, biological, and industrial dispersions. In this context, we present here an original approach to better understand the surface charge electrostatic properties of spherical nanoparticles (NPs). The ion distribution around one nanoparticle is investigated using Monte Carlo simulations and by adjusting a wide range of parameters including NP properties (surface charge density and site distribution), salt concentration (ionic strength and cation concentration), and salt valency (mono-, di-, and trivalent salt). A canonical Metropolis Monte Carlo method is used to reach equilibrium states and a primitive Coulomb model is applied to describe the electrostatic interactions between explicit discrete sites, counterions, and salt particles. Our results show that the presence of explicit surface charges on the NP and in solution has a strong influence on the local ion distribution and on the effective surface charge of the nanoparticles. The increase of surface charge density reduces the NP effective charge by the formation of a condensation layer around the nanoparticle. However, a limit of condensation is achieved due to steric effects and electrostatic repulsions. The presence of di- and trivalent cations is also found to strongly modify the effective charge and improve condensation state as long as electrostatic repulsion between the cations close to the surface are not so strong. At high trivalent cation concentration, the NP effective charge is greatly reduced and the local environment around the nanoparticle becomes more structured with the formation of a multi layer structure composed by anions and cations.