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

ABSTRACT: 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.

SUBMITTER: Lin C

PROVIDER: S-EPMC8047654 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:We conduct Metropolis Monte Carlo simulations on models of dilute colloidal dispersions, where the particles interact via isotropic potentials of mean force (PMFs) that display a long-ranged repulsion, combined with a short-ranged and narrow attraction. Such systems are known to form anisotropic clusters. There are two main conclusions from this work. First, we demonstrate that the width of the attractive region has a significant impact on the type of structures that are formed. A narrow attractive well tends to produce clusters in which particles possess fewer neighbors than in systems where the attraction is wider. Second, metastable clusters appear to persist in the absence of specific simulation moves designed to overcome large energy barriers to particle accumulation. The so-called "Aggregation-Volume Bias Monte Carlo" moves were previously developed by Chen and Siepmann, and they facilitate particle exchanges between clusters via unphysical moves that bypass high energy intermediate states. These facilitate the progression of metastable clusters to equilibrium clusters. Metastable clusters are generally large with significant branching of thin filaments of aggregated particles, while stable clusters have thicker backbones and tend to be more compact with significantly fewer particles. This general behavior is observed in both two- and three-dimensional systems. In two dimensions, less anisotropic clusters with backbones possessing lattice structures will occur, particularly for systems where the particles interact with a PMF that has a relatively wide attractive region. We compare our results with PMF calculations established from a more specific model, namely weakly charged polystyrene particles, which carry a thin surface layer of grafted polyethylene oxide polymers in aqueous solution. We hope that our investigations can serve as crude guidelines for experimental research, aiming to construct linear or branched polymers in aqueous solution built up by colloidal monomers that are large enough to be studied by confocal microscopy. We suggest that metastable clusters are more relevant to experimental scenarios where the energetic barriers are too large to be surmounted over typical timescales.

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

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