Interactions and Aggregation of Charged Nanoparticles in Uncharged Polymer Solutions

Abstract

We employ an extension of the single chain in mean field simulation method to study mixtures of charged particles and uncharged polymers. We examine the effect of particle charge, polymer concentration, and particle volume fraction on the resulting particle aggregates. The structures of aggregates were characterized using particle-particle radial distribution functions and cluster size distributions. We observe that the level of aggregation between particles increases with increasing particle volume fraction and polymer concentration and decreasing particle charge. At intermediate regimes of particle volume fraction and polymer concentrations, we observe the formation of equilibrium clusters with a preferred size. We also examined the influence of manybody effects on the structure of a charged particle-polymer system. Our results indicate that the effective two-body approximation overpredicts the aggregation between particles even at dilute particle concentrations. Such effects are thought to be a consequence of the interplay between the respective manybody effects on the depletion and electrostatic interactions.

Tuning the phase diagram of colloid-polymer mixtures via Yukawa interactions

“…Equivalently, added repulsions increase the required depletant concentration for phase coexistence. The latter is in qualitative agreement with computer simulations and experimental results for charged nanoparticles in polymeric solutions [16,32,34,35]. Not surprising, the difference in the phase diagram with respect to the HS cases is more dramatic for larger values of |β | and q Y .…”

“…The strength and range of attraction between nanoparticles can be controlled via the depletant concentration and the depletant-to-colloid size ratio (q D ). The depletion interaction is used to rationalize both fundamental as well as practical issues [15][16][17][18][19].…”

“…However, limited theories are available for dispersed colloidal particles with realistic interactions and added free polymers (acting as depletants). Available approaches focused on short-range repulsive colloids [16,[32][33][34][35]. In real systems, more involved (soft) interactions are often present.…”

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

“…For instance, recent experiments and theories have suggested the formation of equilibrium cluster phases in systems possessing long-range electrostatic interactions in conjunction with the polymer-mediated depletion attraction. 187 While some studies have made progress in the incorporation of such interactions, 188,189 the behavior expected in a vast parameter space of particle/polymer sizes and concentrations remains to be clarified. Understandably, most theories and simulations of polymer-NP mixtures have concerned themselves with spherical particles and flexible polymer chains.…”

Fluids with competing interactions. II. Validating a free energy model for equilibrium cluster size

“…where βA MAX is the maximum electrostatic barrier between particles at contact, κ −1 /d is the Debye-Hückel screening length, Z is the total surface charge per monomer, and λ B /d is the Bjerrum length of the solvent. Crucially, this formulation neglects any long-range multi-body interactions 40,41 , and any charge renormalization due to counterion condensation [42][43][44][45] or close monomer association 18,29 . As our goal here is to test how even the simplest clustering systems might be described from a free energy perspective, we reserve incorporation of these phenomena for future studies.…”