Charged Nanoparticle Attraction in Multivalent Salt Solution: A Classical-Fluids Density Functional Theory and Molecular Dynamics Study

Unveiling the Role of Electrostatic Forces on Attraction between Opposing Polyelectrolyte Brushes

Electrostatic interaction and molecular excluded-volume effects are responsible for a plethora of nonintuitive phenomena in soft-matter systems, including local charge inversion and attraction between similar charges. In the current work, we study the surface forces and swelling behavior of opposing polyelectrolyte brushes using a classical density functional theory that accounts for electrostatic and excluded-volume correlations. We observe that the detachment pressure between similarly charged brushes is sensitive to salt concentration in both the osmotic and salted regimes and can be negative in the presence of multivalent counterions. A comparison of the theoretical results with the mean-field predictions unravels the role of correlation effects in determining the surface forces and brush structure. For systems containing multivalent counterions, the detachment pressure attains negative values at an intermediate brush-brush separation, and the attractive region in the pressure vs distance plot is magnified in terms of both the depth and width of attraction with increasing counterion valency. However, the interbrush attraction vanishes when the size-induced correlations are switched off. We also investigated the role of counterion size and polymer chain length on the detachment pressure. It is found that smaller counterions are more effective in neutralizing the polymer charge than bigger counterions, leading to a reduced interbrush repulsion and, in some cases, attraction between like-charged brushes at intermediate distances. Meanwhile, varying the chain length of the grafted polymers only shifts the location of the attraction basin, with little influence on the interaction strength. The theoretical predictions show qualitative agreement with experimental observations and offer valuable insights into the interaction between similarly charged polymer brushes in the presence of multivalent ions.

Multivalent Ion-Mediated Attraction between Like-Charged Colloidal Particles: Nonmonotonic Dependence on the Particle Charge

Ion-mediated effective interactions are important for the structure and stability of charged particles such as colloids and nucleic acids. It has been known that the intrinsic electrostatic repulsion between like-charged particles can be modulated into effective attraction by multivalent ions. In this work, we examined the dependence of multivalent ion-mediated attraction between like-charged colloidal particles on the particle charge in a wide range by extensive Monte Carlo simulations. Our calculations show that for both divalent and trivalent salts, the effective attraction between like-charged colloidal particles becomes stronger with the increase of the particle charge, whereas it gradually becomes weakened when the particle charge exceeds a "critical" value. Correspondingly, as the particle charge is increased, the driving force for such effective attraction transits from an attractive electrostatic force to an attractive depletion force, and the attraction weakening by high particle charges is attributed to the transition of electrostatic force from attraction to repulsion. Our analyses suggest that the attractive depletion force and the repulsive electrostatic force at high particle charges result from the Coulomb depletion which suppresses the counterion condensation in the limited region between two like-charged colloidal particles. Moreover, our extensive calculations indicate that the "critical" particle charge decreases apparently for larger ions and smaller colloidal particles due to stronger Coulomb depletion and decreases slightly at higher salt concentrations due to the slightly enhanced Coulomb depletion in the intervening space between colloidal particles. Encouragingly, we derived an analytical formula for the "critical" particle charge based on the Lindemann melting law.

Unraveling Chiral Selection in the Self-assembly of Chiral Fullerene Macroions: Effects of Small Chiral Components Including Counterions, Co-ions, or Neutral Molecules

Lactic acid-functionalized chiral fullerene (C₆₀) molecules are used as models to understand chiral selection in macroionic solutions involving chiral macroions, chiral counterions, and/or chiral co-ions. With the addition of Zn²⁺ cations, the C₆₀ macroions exhibit slow self-assembly behavior into hollow, spherical, blackberry-type structures, as confirmed by laser light scattering (LLS), transmission electron microscopy (TEM), and atomic force microscopy (AFM) techniques. Chiral counterions with high charge density show no selection to the chirality of AC₆₀ macroions (LAC₆₀ and DAC₆₀) during their self-assembly process, while obvious chiral discrimination between the assemblies of LAC₆₀ and DAC₆₀ is observed when chiral counterions with low charge density are present. Compared with chiral counterions, chiral co-ions show weaker effects on chiral selection with larger amounts needed to trigger the chiral discrimination between LAC₆₀ and DAC₆₀. However, they can induce a higher degree of discrimination when abundant chiral co-ions are present in solution. Furthermore, the self-assembly of chiral AC₆₀ macroions is fully suppressed by adding significant amounts of neutral molecules with opposite chirality. Thermodynamic parameters from isothermal titration calorimetry (ITC) reveal that chiral selection is controlled by the ion pairing and the destruction of solvent shells between ions, and meanwhile originates from the delicate balance between electrostatic interaction and molecular chirality.

Electrostatics of Nanoparticle-Wall Interactions within Nanochannels: Role of Double-Layer Structure and Ion-Ion Correlations

We perform computational investigations of the electrolyte-mediated interactions of charged nanoparticles with the walls of nanochannels. We investigate the role of discrete ion effects, valence, and electrolyte strength on nanoparticle-wall interactions. We find for some of the multivalent charge regimes that the like-charged nanoparticles and walls can have attractive interactions. We study in detail these interactions and the free-energy profile for the nanoparticle-wall separation. We find there are energy barriers and energy minima giving preferred nanoparticle locations in the channel near the center and at a distance near to but separated from the channel walls. We characterize contributions from surface overcharging, condensed layers, and overlap of ion double layers. We perform our investigations using coarse-grained particle-level simulations with Brownian dynamics, classical density functional theory, and the mean-field Poisson-Boltzmann theory. We discuss the implications of our results for phenomena in nanoscale devices.