Multibody Interactions, Phase Behavior, and Clustering in Nanoparticle–Polyelectrolyte Mixtures

Abstract

We present the results of a computational study of the interactions, phase-behavior and aggregation characteristics of charged nanoparticles (CNPs) suspended in solution of oppositely charged polyelectrolytes (PEs). We used an extension of the mean-field polymer self-consistent field theory (SCFT) model presented in our earlier work ( Macromolecules , 2014 , 47 , 6095 - 6112 ) to explicitly characterize the multibody interactions in such systems. For dilute-moderate particle volume fractions, the magnitudes of three and higher multibody interactions were seen to be weak relative to the contributions from pair interactions. On the basis of such results, we embeded the pair-interaction potentials within a thermodynamic perturbation theory approach to identify the phase behavior of such systems. The results of such a framework suggested that the gas and FCC crystal phases were thermodynamically stable, whereas the fluidlike phase was metastable in such systems. To complement the parameters studied using SCFT, we used a recently developed multibody simulation approach to study the aggregation and cluster morphologies in CNP-PE mixtures. For low particle charges, such systems mainly exhibited clusters arising from direct contact aggregation between CNPs. However, for higher particle and PE charges and low PE concentrations, large regions of PE-bridged clusters were seen to form. We present a morphological phase diagram summarizing such results.

Recent progress in the science of complex coacervation

“…Recently, fundamental numerical theory has provided an alternative picture to the counterion release mechanisms of Record, et al 280 and Manning, ıet al 281 to understand polymer-particle and polymer-protein coacervation. [302][303][304][305] These efforts have used polymer self-consistent field theory to determine pairwise and three-body interaction potentials between charged particles. These efforts were used to predict phase boundaries for these asymmetric systems, which not only consider the electrostatic interactions but other competing effects such as polymer depletion and colloidal radius.…”

“…These efforts were used to predict phase boundaries for these asymmetric systems, which not only consider the electrostatic interactions but other competing effects such as polymer depletion and colloidal radius. [303][304][305] Finally, extensions to particles with oppositely-charged patches provides insights into proteinpolymer coacervation. 302…”

“…12,14,76,284,285,287,289,296,305,[322][323][324][325][326][327] Here, molecular geometry and surface-charge patterning will play a significant role in the prediction of coacervate properties; it will no longer be possible to take advantage of (i) the symmetry between the larger charged species and (ii) the highly interpenetrating conformations, both of which help the theoretical development of polyelectrolytepolyelectrolyte systems. Only a few theoretical or computational papers have considered these systems, 302,303,[328][329][330] with the bulk of the work performed experimentally. Much of the insight developed in recent advances in coacervate theory could be modified to account for these more complicated scenarios; however, many of the methods may need to be combined in new ways.…”

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.…”