Polymer-bridged gels of nanoparticles in solutions of adsorbing polymers

Abstract

We use a combination of polymer mean field theory and Monte Carlo simulations to study the polymer-bridged gelation, clustering behavior, and elastic moduli of polymer-nanoparticle mixtures. Polymer self-consistent field theory is first numerically implemented to quantify both the polymer induced interparticle interaction potentials and the conformational statistics of polymer chains between two spherical particles. Subsequently, the formation and structure of polymer-bridged nanoparticle gels are examined using Monte Carlo simulations. Our results indicate a universality in the fractal structure for the polymer-bridged networks over a wide range of parametric conditions. Explicitly, near the gelation transition, the fractal dimension d(f) ranges between 2.2 and 2.5, and above the gelation thresholds, the elastic moduli are found to follow a universal power law G(') proportional, variant(eta-eta(c))(nu(eta) ) with a critical exponent nu(eta) approximately 1.82. The latter suggests strong similarities between polymer-bridging induced percolation and classical elastic resistor network percolation. Our results show a very good agreement with the experimental results for polymer-particle mixtures and suggest a possible framework for experimentally distinguishing the origins of gelation phenomena observed in polymer-particle mixtures.

Analytical theory of polymer-network-mediated interaction between colloidal particles

“…The interaction is dominated by bridging or steric repulsion in networks of adsorbing polymers. Consistent with our results, short-range attraction between colloids has been described by the polymer reference interaction site model (PRISM) integral equations theory (29,30) and confirmed by extensive computer simulations studies (31)(32)(33)(34)(35)(36)(37)(38) for the case of equilibrium dense polymer solutions and melts. In particular, Hooper and Schweizer (29,30) describe four types of polymer-mediated colloidal forces, including contact depletion interaction, direct polymer bridging, and steric repulsion.…”

“…Thereby, the idea of polymer bridging was introduced to explain such effects (24,26,27). In more recent years, extensive numerical studies have been devoted to clarify the origin of effective interactions between nanoparticles dispersed in concentrated polymer solutions or melts, also for the case of adsorbing polymers (28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38).In those limits the mixture can be treated globally using the tools of equilibrium statistical mechanics, which is justified as long as the polymers are not cross-linked and their concentration is far away from the glassy regime. However, when the nanoparticles are embedded in a polymer network the system as a whole is intrinsically far from equilibrium.…”

Mean-field models of structure and dispersion of polymer-nanoparticle mixtures

“…Instead simpler model interaction potentials are used to characterize the interactions between segments of the polymer and the particle fillers. Such simplifying assumptions have enabled the implementation of analytical theories and/or long time and length scale simulations which allow one to discern the equilibrium 39,41,43,44,47 and nonequilibrium 45,46 structural characteristics of the nanofiller dispersion in polymer matrices. We note that the main utility of such coarse-grained approaches lies in their ability to distill and characterize physical phenomena of interest in terms of a few macroscopic parameters.…”

“…Specifically, we focus on three issues: (i) dispersion and phase behavior of nanoparticles in homopolymer matrices; 39,41,43,44,47 (ii) dispersion in mixtures of homopolymers with grafted nanoparticles; (iii) self-assembly and organization of nanoparticles in block copolymer matrices. 42 Each of these topics serve to illustrate that the dispersability of nanoparticles may exhibit far more complexities than the simple miscibility trends one may deduce using the results of Fig.…”

Some issues in polymer nanocomposites: Theoretical and modeling opportunities for polymer physics

“…Most such theories and models use a coarse-grained perspective where simple micromechanical representations are used for the polymers and fillers, with their interactions represented by few coarse-grained parameters. Using such representations, theories and simulations based on PRISM, [16][17][18] self-consistent field approaches, [19][20][21][22] field-theoretic, 23 and molecular dynamics simulations [24][25][26] have addressed the equilibrium structure and phase behavior of mixtures of (mostly) spherical nanofiller units dispersed in homopolymers, polymer blends, and block copolymers. Despite these advances, a number of open issues relevant to PNCs still remain:…”