A Nondestructive Method to Quantify Polymer Graft Density on Nanoparticles Using Optical Extinction Spectra

Grafting density is the key parameter governing colloidal stability and structure for polymer-grafted nanoparticles (PGNPs). Existing methods to quantify grafting density either destroy the sample, require prior knowledge of polymer molecular weight Mn, or rely on complex instrumentation. Here, we present a nondestructive optical approach that determines grafting density directly from shifts in the localized surface plasmon resonance peak caused by the grafted polymer changing the local effective refractive index. To interpret this shift, the grafted polymer chains are approximated as cylindrical segments passing through differential spherical shells to obtain radial profiles for the polymer volume fraction and refractive index across the polymer corona. The local refractive-index profile is weighted by the plasmonic near-field decay to calculate the effective refractive index sensed by the nanoparticle. The grafting density is finally determined by iteratively adjusting the effective refractive index until the calculated refractive-index sensitivity of the polymer-grafted nanoparticle matches that of the gold core. The grafting densities obtained from this optical method quantitatively agree with established experimental benchmarks across different polymer Mn, grafting densities, nanoparticle sizes, and solvents. Our approach uses common laboratory equipment, eliminates the need for prior knowledge of polymer Mn, and preserves the sample for further experiments, bypassing challenges provided by existing characterization approaches. Together, these advantages provide a framework for predicting and understanding the physical and chemical properties of PGNPs for specific applications.