Theory for size-dependent surface plasmon resonance of capped metal nanoparticles with atomic steps

A work function (WF) centric theory is developed for the localized surface plasmon resonance (LSPR) energy (in the non-scattering regime) for ligand-capped metal nanoparticles (NPs) with atomic steps. Theoretical LSPR energy is the product of the electrochemical work function (EWF) and the attenuation factor . The semi-microscopic model for the EWF includes a curvature-dependent WF, crystallographic information through the step density (n_s), partial charge of adsorption (δ_a), dipolar orientation, the packing density of the ligand (N₀), and the number of adsorbing contacts (n_L) of the capping ligand. is a function of electronic screening length (l_TF) and attenuation length (l_ed). decays exponentially with the ratio of plasmonic cloud depth (2l_TF) to l_ed. The LSPR peaks (λ_max) of plasmonic metals (the same NP size) follow the reverse order of their EWF values. The LSPR absorption peak red-shifts with an increase in size (2r), n_s, and N₀, while blue-shifts with an increase in the number of adsorbing contacts of the capping ligand (like the citrate ion). Coinage metals, viz. Au, Ag, and Cu, exhibit size (2r < 50 nm)-dependent LSPR peaks in the visible spectrum: 420 nm ≲ λ_max ≲ 520 nm, for n_L = 1. Pt shows anomalous twin peaks, attributed to the distinct number of carboxylic groups of citrate capping on the metal: one for n_L = 2, with size-dependent peaks in the visible spectrum: 430 nm ≲ λ_max ≲ 454 nm and another for n_L = 3, with peaks in the UV spectrum: 378 nm ≲ λ_max ≲ 400 nm. Finally, theory shows agreement with the experimental data for citrate-capped Au and Au/Ag alloy NPs.