We examine the structure of densely grafted polymer layers grown from the surfaces of spherical nanoparticles over a broad range of graft densities and chain lengths. Dynamic light scattering (DLS) experiments show that the hydrodynamic thickness of the polymer layer, h, scales as h µ N 4/5 for short chains and high grafting densities, that is, in the concentrated polymer brush (CPB) regime, whereas h µ N 3/5 for long enough chains (semidilute polymer brush, SDPB). The mean field theory of Wijmans and Zhulina is able to collapse approximately all of our data and those in the existing literature (even on other polymers) into an apparently universal form. From these findings, we conclude that the result h µ N 4/5 for the CPB is an intermediate crossover scaling, relevant to particles of finite curvature, analogous to the h µ N observed for concentrated flat brushes. Second, the scaling h µ N 3/5 uniquely reflects the increased space available to the chain segments as one proceeds away from a curved grafting surface. Under these situations, the chains experience less packing frustration as compared to a planar brush, and the semidilute polymer brush shows scaling behavior analogous to chains in good solvent, even though the chains are much more extended.

RAFT (reversible addition–fragmentation chain transfer) polymerization has been widely used to synthesize different polymer architectures such as polymer brushes on nanoparticles for incorporation into polymer nanocomposites. It is believed that these polymer brushes, with the same chemistry as the matrix polymer, can be employed to improve filler dispersion by compatibilizing unfavorable enthalpic interactions between the inorganic nanoparticles and their organic host matrices. However, monomodal brush graft nanoparticles are found to aggregate into a range of isotropic and anisotropic morphologies, formed due to a delicate balance between enthalpic and entropic interfacial interactions. This coupling of enthalpy and entropy leaves only a small window of graft densities and molecular weights to obtain randomly dispersed filler morphologies. These issues can be countered by using a bimodal polymer brush that contains a small number of long homopolymer chains that can entangle, and a high density of short brushes that screens the particle/particle attraction, thereby aiding in decoupling the interfacial enthalpic and entropic interactions. In the present work, we demonstrate a robust step-by-step technique using RAFT polymerization to synthesize these bidisperse/bimodal polymer brush-anchored nanoparticles. A layer of dense brush of the first population was initially prepared using surface-initiated RAFT polymerization from colloidal silica nanoparticles. After cleavage of the chain transfer agent from the first population of chain ends, a second RAFT agent was attached onto the silica nanoparticles and then a monomer, which may be the same or different from the first brush, was polymerized. This versatile and widely applicable route enables us to independently control the molecular variables of the attached chains, such as composition, molecular weights and graft densities of the individual populations. The bimodal brush-grafted colloidal silica nanoparticles show superior dispersion and interaction with a homopolymer matrix when compared to monomodal brush-grafted particles.

It has recently been proposed that the miscibility of nanoparticles with a polymer matrix can be controlled by grafting polymer chains to the nanoparticle surface. As a first step to study this situation, we have used molecular dynamics simulations on a single nanoparticle of radius R (4σ ≤R≤ 16σ , where σ is the diameter of a polymer monomer) grafted with chains of length 500 in a polymer melt of chains of length 1000. The grafting density Σ was varied between 0.04-0.32 chains/σ 2 . To facilitate equilibration a Monte Carlo doublebridging algorithm is applied -new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. For the long brush chains studied here, the structure of the brush assumes its large particle limit even for R as small as 8σ , which is 1 consistent with recent experimental findings. We study autophobic dewetting of the melt from the brush as a function of increasing Σ. Even these long brush and matrix chains of length 6 and 12 N e , respectively, (the entanglement length is N e ∼ 85) give somewhat ambiguous results for the interfacial width, showing that studies of two or more nanoparticles are necessary to properly understand these miscibility issues. Entanglement between the brush and melt chains were identified using the primitive path analysis. We find that the number of entanglements between the brush and melt chains scale simply with the product of the local monomer densities of brush and melt chains.

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