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

Abstract

Nanostructured materials based on colloidal particles embedded in a polymer network are used in a variety of applications ranging from nanocomposite rubbers to organic-inorganic hybrid solar cells. Further, polymer-network-mediated colloidal interactions are highly relevant to biological studies whereby polymer hydrogels are commonly employed to probe the mechanical response of living cells, which can determine their biological function in physiological environments. The performance of nanomaterials crucially relies upon the spatial organization of the colloidal particles within the polymer network that depends, in turn, on the effective interactions between the particles in the medium. Existing models based on nonlocal equilibrium thermodynamics fail to clarify the nature of these interactions, precluding the way toward the rational design of polymer-composite materials. In this article, we present a predictive analytical theory of these interactions based on a coarse-grained model for polymer networks. We apply the theory to the case of colloids partially embedded in cross-linked polymer substrates and clarify the origin of attractive interactions recently observed experimentally. Monte Carlo simulation results that quantitatively confirm the theoretical predictions are also presented.polymer nanocomposites | polymer bridging | colloidal aggregation | depletion force I ncorporation of colloidal micro and nanoparticles in crosslinked polymeric materials can be used to tune their structural and electronic properties. For example, introducing inorganic nanoparticles is a well-established technique to reinforce rubbers. The mechanical properties of the material will strongly depend on the size and conformation of colloidal aggregates (1-5), and, in the last instance, on the polymer-network-mediated colloidal interactions. Semiconductor nanocolloids can be incorporated in polymer-based organic photovoltaic devices to improve efficiency (6-10), therefore, controlling the aggregation of colloids is needed to optimize the performances of materials for renewable energy production. For these reasons, there is an urgent need of tools to understand and control colloidal interactions in polymer networks, which is currently a bottleneck in the rational design of functional nanostructured materials.Besides technological applications, polymeric cross-linked hydrogels are often adopted as model systems to study changes in motility, differentiation, and morphology of living cells in response to variations in the compliance of their environment (11)(12)(13)(14)(15)(16)(17)(18). Recently, experimental evidence of short-range attractive interactions between silica colloids deposited on extremely soft polyacrylamide hydrogels have been reported. However, knowledge about the origin of these interactions is still missing (19).Colloidal interactions mediated by nonadsorbing polymers in dilute solutions have been successfully described in terms of depletion by the theory of Asakura and Oosawa (20). Scientific investigation then turned ...

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