Polyelectrolyte adsorption on charged particles in the Debye-Huckel approximation. A Monte Carlo approach

Monte Carlo simulations are used to study in the Debye-Huckel approximation the complexation between a polyelectrolyte and an oppositely charged spher ical particle. Attention is focused on the effect of chain length and ionic concentration on (i) the adsorption/desorption limit, (ii) the interfacial structure of the adsorbed layer, and (iii) the overcharging issue. In part icular, we are interested in polyelectrolyte adsorption on particles whose surface area is small to allow the polyelectrolyte to spread to the same ex tent on a flat surface. The extent of polyelectrolyte adsorption is found t o be the result of two competing effects: the electrostatic repulsion betwe en the chain monomers which forces the polyelectrolyte to adopt extended co nformations in solutions and limits the number of monomers which may be att ached to the particle, and the electrostatic attractive interactions betwee n the particle and the monomers forcing the chain to undergo a structural t ransition and collapse at the particle surface. To overcome the loss of ent ropy per monomer due to adsorption, it is shown that a stronger electrostat ic attraction, with decreasing ionic concentration, is needed for the short chains. Below that critical ionic concentration, it is found that the degr ee of adsorption increases with the decrease in both the chain length and i onic strength. Trains are favored at low degrees of chain polymerization wh ile loops are favored more when increasing the size of the chain. Above a c ritical chain length, electrostatic repulsions between the adsorbed monomer s force the polyelectrolyte to form a protuding tail in solution. Charge in version is also observed. Indeed, depending on the polyelectrolyte length, the number of monomers close to the particle surface is higher than it is n ecessary to neutralize it. Charge inversion is found to increase with the i onic concentration of the solution.