Understanding Time-Dependent Surface-Enhanced Raman Scattering from Gold Nanosphere Aggregates Using Collision Theory.

Aggregates or clusters of primary metal nanoparticles in solution are one of the most widely used platforms for surface-enhanced Raman scattering (SERS) measurements because these nanostructures induce strong electric fields or hot spots between nanoparticles and as a result, SERS signals. While SERS signals are observed to vary with time, the impact of cluster formation mechanisms on SERS activity has been less studied. Herein, variations in time-dependent SERS signals from gold nanosphere clusters and aggregates are considered both experimentally and theoretically. An excess of the Raman reporter molecule, 2-naphthalenethiol, is added to induce rapid monolayer formation on the nanoparticles. In this diffusion-limited regime, clusters form as loosely packed fractals and the ligands help control nanoparticle separation distances once clusters form. By systematically varying gold nanosphere concentration and diameter, the reaction kinetics and dynamics associated with cluster formation can be studied. Dynamic light scattering (DLS), localized surface plasmon resonance (LSPR) spectroscopy, and SERS reveal that aggregates form reproducibly in the diffusion-limited regime and follow a self-limiting cluster size model. The rate of cluster formation during this same reaction window is explained using interaction pair potential calculations and collision theory. Diffusion-limited reaction conditions are limited by sedimentation only if sedimentation velocities exceed diffusion velocities of the clusters or via plasmon damping through radiation or scattering losses. These radiative loses are only significant when the extinction magnitude near the excitation wavelength exceeds 1.5. By evaluating these responses as a function of both nanosphere radius and concentration, time-dependent SERS signals are revealed to follow collision theory and be predictable when both nanosphere concentration and size are considered.