Benchmarking Common Approximations for Determining the Particle-Size Dependence of Adsorbate-Induced Localized Surface Plasmon Resonance Shifts

Abstract

Anomalies are investigated that exist between many long-standing theoretical models of the optical behavior of sensors based on changes in the localized surface plasmon resonance upon analyte adsorption. In particular, we focus on single metal nanoparticles which represent the core building-block of many recent sensing devices. Theoretical approaches include the Retarded Mie theory, the Non-Retarded quasi-static-dipole approximation, and two radiative corrections to the Non-Retarded case (radiative damping and radiative damping + depolarization). We find that the most accurate Non-Retarded approximation to the Retarded Mie theory varies strongly on a case by case basis; anyway, for particle radii beyond a few tens of nanometers, none of the considered approximations represents properly the adsorbate induced plasmon shift. We also find that the size-dependent peak shift has a complex dependence on the metal dielectric function. Accordingly, the trend of the adsorbate-induced plasmon peak shift as a function of the particle radius reveals an unexpected nonmonotonic behavior. We eventually identify an interesting range of particle radii over which the adsorbate-induced plasmon shift is unaffected by the particle size. Moreover, we give examples where nanoparticle batches with large size dispersion provide higher sensor reproducibility than monodisperse samples. On the other hand, in light of our findings, single particle measurements are pivotal to disclose the exact structure of the peak shift trend as a function of the particle radius