Self-Consistent PRISM Theory−Monte Carlo Simulation Studies of Copolymer Grafted Nanoparticles in a Homopolymer Matrix

Abstract

We have used a self-consistent PRISM−Monte Carlo (MC) approach to study copolymer functionalized nanoparticles in a homopolymer matrix and to calculate the potential of mean force (PMF) between the grafted particles (at low grafting density) for varying monomer sequences in the grafted polymer, matrix packing fraction, molecular weight of the grafted and matrix chains, attraction strength between one set of like-monomers, and the nanoparticle diameter. We find that the monomer sequence (alternating and diblock) in the grafted chains dictates how the attractive monomers aggregate and how those aggregates help or hinder matrix-induced direct contacts between the grafted particles, and thus the strength and location of attraction or repulsion in the PMF between two grafted particles. At weak like-monomer attraction strengths (0.2kT), the alternating copolymer-grafted particles exhibit a PMF similar to athermal homopolymer-grafted particles. For the diblock copolymer-grafted particles, if the monomers in the block closer to the surface are attractive, the PMF is repulsive at contact and weakly attractive at larger interparticle distances; if the monomers in the outer block are attractive, the PMF is attractive at contact and repulsive at larger interparticle distances. The effect of monomer sequence on the PMF is enhanced by increasing the graft chain length and suppressed by either increasing the matrix packing fraction or using larger nanoparticles. For example, the PMF becomes strongly attractive at contact (a) when the amount of matrix is increased such that the matrix-induced depletion-like attraction between the particles prevails over the steric hindrance from the grafted chains or (b) when the ratio of particle diameter to graft length is increased such that the graft is too short and the grafted monomers can no longer shield the surface from direct interparticle contact. This study demonstrates that grafting copolymers on nanoparticles allows for precise tuning of the magnitude, nature and location of attraction or repulsion in the PMF, which is needed for the tailored assembly of these functionalized nanoparticles in polymer nanocomposites for use in photonics, electronics, and photovoltaic applications.