Distribution in the Grafting Density of End-Functionalized Polymer Chains Adsorbed onto Nanoparticle Surfaces

We have developed a simple model to quantify the role of curvature on the surface composition of polymer-nanoparticle hybrids formed as a result of the adsorption of end-functionalized homopolymer chains onto spherical nanoparticles in dilute polymer solutions. The analytic model incorporates relevant contributions from changes in the translational and conformational entropies of the polymer chains, and the enthalpy gained during adsorption, to derive an expression for the distribution of the grafting density as a function of nanoparticle curvature and solution properties of the end-adsorbing chains. Our model predicts that the grafting density distribution is Gaussian. The mean grafting density is found to increase with increasing nanoparticle curvature and polymer concentration. However, the degree of polydispersity in the grafting density is also found to increase with curvature, suggesting the near impossibility of synthesizing monodispersed polymer-tethered nanoparticle hybrids via the grafting-to technique as the radius of the nanoparticles approaches the unperturbed radius of gyration of the polymer chains in the solution.