Effect of Polymer Ligand Molecular Weight on Polymer-Coated Nanoparticle Location in Block Copolymers

Gold nanoparticles (Au−PS) coated with an areal chain density Σ of end-attached polystyrene (PS) chains of different molecular weights ( M n ) are added to a lamellar diblock copolymer of poly(styrene- b -2-vinylpyridine) (PS- b -P2VP) to determine the critical areal chain density Σ C below which the Au−PS nanoparticles adsorb to the PS- b -P2VP interface. Gold nanoparticles coated by thiol end functional polystyrene homopolymers (PS−SH) with M n ranging from 1.5 to 13 kg/mol are synthesized with various areal densities of PS−SH chains on the nanoparticle surface. The particles are incorporated into a PS- b -P2VP diblock copolymer with M n = 196 kg/mol. The P2VP block has a more favorable interaction with a bare gold particle surface than does the PS block, and this interaction becomes important as the coverage of gold particles by PS−SH decreases, leading to adsorption of the Au−PS to the interface below a critical areal chain density Σ C . Σ C decreases from 3.1 to 0.9 chains/nm 2 as the M n of PS−SH chains increases from 1.5 to 13 kg/mol, leading to a scaling relation, ∑ C ∼ R g -1 ∼ M n -0.6, which is very different from the behavior expected for polymer chains tethered to a flat surface, ∑ C ∼ R g -2 ∼ M n -1, where R g is the radius of gyration of the end-attached chains. A simple scaling relationship, Σ C ∼ (( R + R g )/ RR g ) 2 that takes into account the high curvature of the Au nanoparticle core of radius R, is derived and is shown to describe the data very well. For Σ ≈ Σ C, there is a slight tendency for the larger particles within the particle size distribution to adsorb preferentially to the PS/P2VP interface, a tendency that can be qualitatively understood by the fact that the absorption free energy per particle is predicted to scale roughly as R 2 .