The effects of ionic concentration, colloid size, polyelectrolyte length, charge, and intrinsic flexibility on the conformation of a polyelectrolyte like DNA in the presence of an oppositely charged polymer have been investigated using an MC approach. Monte Carlo simulations constitute a rewarding and invaluable approach. In fact, it has been shown that computer simulations and theory can isolate in good agreement the molecular factors that control polyelectrolyte conformation in solution and at the interface, the adsorption limit, and overcharging issue, and thus can be used to address the optimization of colloid-polymer mixtures and guide new experiments.
FIG. 20 Number of monomers in trains (a), loops (b), and tails (c) as a function of the linear charge density (LCD) at different ionic concentration for the polyelectrolyte-par-ticle complex.
Adsorption occurs if the loss of entropy of the chain is at least compensated by the gain of energy. Thus, most favorable conditions to achieve adsorption are obtained by considering long chains. Our simulations point out the importance of two competing effects when the ionic concentration increases; on the one hand, the particle capacitance increases and so much monomer can be adsorbed; on the other hand, the electrostatic attraction between the particle and the monomer becomes less important, giving the monomers and the polyelectro-lyte the opportunity to leave the particle surface. Polyelectrolyte conformational changes resulting from adsorption are found to be dependent on the polyelectro-lyte size. Maximal chain deformation is achieved in the low screened limit and when the ratio of the mean end to end distance of the free polyelectrolyte to the particle radius is close to 20. By further increasing the chain length, excluded electrostatic volume prevents any additional monomer adsorption on the surface. As a result, an extended tail is formed in solution. Our MC results demonstrate that the complexation between a polyelectrolyte and a charged sphere can lead to overcharging when N > N°. We find a perfect agreement with the NS model both in the salt-free case and in the case of added salt. Variations in the number of adsorbed monomers as a function of the total number of monomers support
a first-order transition with the spontaneous formation of a protuding tail in solution.
Adsorption of charged polymers is not only controlled by ionic concentration but also by particle diameter. Surface curvature effects clearly limit the amount of adsorbed monomers; large particles allow the polyelectrolyte to spread on the surface; small particles limit the number of adsorbed monomers that may be attached to it. When small particles are considered, the low-salt regime is dominated by the monomer-monomer repulsions forcing the polyelectrolyte to form extended tails in opposite directions. When the particle size is equal to or greater than the radius of gyration of the charged polymers, polyelectrolytes can wrap fully around the particle. Under such conditions, trains are favored whereas loops become more frequent when increasing ionic strength before the adsorption-desorption limit. MC results also demonstrate that the complexation between a polyelectrolyte and a charged sphere can lead to overcharging when the polymer size is large enough. In the case of added salt, our simulations point out the importance of charge inversion with the increase of ionic concentration because of the increase of particle capacitance as well as the key role of the charged polymer size.
The influence of polyelectrolyte intrinsic stiffness and ionic concentration on the adsorption-desorption limit, polyelectrolyte conformation, and monomer distribution on the particle surface was presented. Chain stiffness modifies the conformation of isolated and adsorbed chains by locally destroying a large amount of monomer entropy. As a result, chain stiffness influences the amount of adsorbed monomers, monomer distribution at the particle surface, and adsorption-desorption limit. The amount of adsorbed monomers has a maximal value for the semiflexible chains in the low-salt-concentration regime. Under such conditions, the polyelectrolyte is strongly adsorbed at the particle surface as a solenoid and the confinement energy does not contribute to the formation of tails in solution. When the chain intrinsic stiffness is small, tennis ball-like conformations are achieved. At the opposite, when rigid chains are considered the polyelectrolyte becomes tangent to the particle. Hence, adsorption is promoted by decreasing the chain stiffness or decreasing the salt concentration for a given chain length.
Polyelectrolyte adsorption is promoted by increasing its LCD or/and decreasing the ionic concentration to promote electrostatic attractive effects. Calculating the adsorption-desorption limit, we found the LCDcrit scales as LCDcnt ~ k2. By focusing on the variations of the LCD and probability of contact, we found a sharp transition at the adsorption-desorption limit that appears to be more gradual by increasing the ionic strength. Adsorption occurred when the mean attractive energy per monomer is more negative than -0.4kT. By analyzing the monomer fraction in loops, tails, and trains, we demonstrated that at small values of the LCD and low ionic strength, a large amount of monomer is present in loops and tails. By increasing the LCD, the amount of monomers in trains reaches a maximal value and polyelectrolytes adopt flat conformations at the particle surface.
The simulations reported here are a preliminary step toward a more precise modeling of the problem to get insight into the behavior of more concentrated polymer solutions (systems with several chains) and thus flocculation/stabiliza-tion processes of polymer-particle mixtures. A simple model involving one chain interacting with one particle has been described, but it can be extended to more concentrated systems involving several chains (and/or colloidal particles). Nonetheless, the computational description of adsorption processes is still part of a great challenge. A Debye-Huckel approach involving one charged polymer interacting with one spherical particle has been investigated, but it can be extended to more precise modeling of the phenomena (e.g., by including explicit counterions, hydrophobic interactions), polydisperse systems (sizes and shapes), and more concentrated solutions. We hope that the observations made in this study are particularly useful for choosing an appropriate polymer or biopolymer for applications such as steric stabilization of dispersed particles.
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