Investigating the effect of Ag nanocube polydispersity on gap-mode SERS enhancement factors

High Raman enhancement factors (EFs) have been observed for surface-enhanced Raman spectroscopy (SERS) substrates fabricated from colloidal metal nanoparticles. Electrodynamic models of single nanoparticles often do not accurately predict the Raman EFs measured experimentally for such colloidal substrates, which often consist of nanoparticles that exhibit heterogeneity in both size and shape. Here, we investigate the size and shape dispersity of colloidal Ag nanocube samples and their effect on Raman EF. We generate an analytical model that incorporates nanocube size dispersion and calculates the Raman EF associated with an ensemble of differently sized nanocubes. For nanocubes that are ∼70-80 nm in size, this model is sufficient to correct the inaccuracies for electrodynamic simulations of a single nanocube model. For nanocubes >90 nm, size dispersity alone fails to account for the high EFs observed when these substrates are excited off-resonance. We hypothesize that shape defects may play a significant role in optical response at these larger sizes and discuss how these factors can play a role in our analytical model.