| Nanoparticles display unique and size-dependent properties. The application of these properties frequently requires the ability to control particle aggregation when dispersed in a solvent. This control can be achieved through the use of ligands grafted to the particle surface. In light of this, it is desirable to know the grafting density for a particular ligand/nanoparticle system. Here we formulate a general method to calculate the relationship between ligand surface coverage and nanoparticle radius, using coarse-grain molecular dynamics simulations and a new free energy method. We have illustrated the use of this method by measuring the optimal number of poly(ethylene oxide) surfactants (C12E2, C12E5, C 12E8) tethered to the surface of a generic hydrophobic nanoparticle as a function of the particle's radius by evaluating the surface tension at the ligand/particle interface. Understanding the size-dependent nature of these systems should lead to better control of nanoparticle dispersions. |
