: Theory for Size Dependent Surface Plasmon Resonance of Capped Metal Nanoparticles with Atomic Steps

Abstract

A work function (WF) centric theory is developed for the localized surface plasmon resonance (LSPR) energy (in non-scattering regime) for the ligand-capped metal nanoparticles (NPs) with atomic steps. Theoretical LSPR energy is the product of electrochemical work function (EWF) and attenuation factor (${\cal F}_A$). The semi-microscopic model for EWF includes curvature-dependent WF, crystallographic information through step density ($n_s$), partial charge of adsorption ($\delta_a$), dipolar orientation, packing density of ligand ($N_0$), and number of adsorbing contacts (${\rm n}_L$) of capping ligand. ${\cal F}_A$ is a function of electronic screening length ($l_{TF}$) and attenuation length ($l_{ed}$). ${\cal F}_A$ decays exponentially with the ratio of plasmonic cloud depth ($2\,l_{TF}$) to $l_{ed}$. LSPR peaks ($\lambda_{max}$) of plasmonic metals (same NP size) follow reverse order of their EWF values. The LSPR absorption peak red-shifts with an increase in size ($2r$), $n_s$, and ${\rm N}_0$; while blue-shifts with an increase in the number of adsorbing contacts of capping ligand (like citrate ion). Coinage metals, viz. Au, Ag, Cu, exhibit size($2r\le 50$ nm)-dependent LSPR peak in the visible spectrum: 420 nm $\lesssim\lambda_{max}\lesssim$ 520 nm, for ${\rm n}_L = 1$. Pt shows anomalous twin peaks, attributed to the distinct number of carboxylic groups of citrate capping on metal; one for ${\rm n}_L = 2$, with size-dependent peak in visible spectrum: 430 nm$\lesssim\lambda_{max}\lesssim$ 454 nm; and another for ${\rm n}_L = 3$ with peak in UV spectrum: 378 nm $\lesssim\lambda_{max}\lesssim$ 400 nm. Finally, theory shows agreement with experimental data for citrate-capped Au and Au/Ag alloy NPs.