Extended Discrete Interaction Model: Plasmonic Excitations of Silver Nanoparticles

Abstract

We present a new atomistic model for plasmonic excitations and optical properties of metallic nanoparticles, which collectively describes their complete response in terms of fluctuating dipoles and charges that depend on the local environment and on the morphology of the composite nanoparticles. Being atomically dependent, the total optical properties, the complex polarizability, and the plasmonic excitation of a cluster refer to the detailed composition and geometric characteristics of the cluster, making it possible to explore the role of the material, alloy mixing, size, form shape, aspect ratios, and other geometric factors down to the atomic level and making it useful for the design of plasmonic particles with particular strength and field distribution. The model is parameterized from experimental data and, at present, practically implementable for particles up to more than 10 nm (for nanorods even more), thus covering a significant part of the gap between the scales where pure quantum calculations are possible and where pure classical models based on the bulk dielectric constant apply. We utilized the method to both spherical and cubical clusters along with nanorods where we demonstrate both the size, shape, and ratio dependence of plasmonic excitations and connect this to the geometry of the nanoparticles using the plasmon length.

An atomistic description of alloys and core shells nanoparticles

“…The extended Discrete Interaction Model (ex-DIM) 9,11 , is a further development of the DIM model 12,13 where significant improvements in the description of the surface topology, geometric dependence and parameterization of the SPR(s) are introduced. The ex-DIM model has a special applicable edge for systems in the 1 − 15 nm size range, where quantum mechanical models cannot be applied, due to the scaling of these methods, and where the concept of a bulk dielectric constant used in classical models breaks down.…”

“…Due to the inability of extrapolating data from quantum mechanical methods and classical methods into the 1 − 15 nm size range the ex-DIM must be parameterized directly from experimental data. 9 We will in Sec. 3.1 briefly show how a new element easily can be parameterized for the ex-DIM and in Sec.…”

“…The interaction energy E[{µ, q}] in this way captures all different types of interactions involving fluctuating dipoles µ, charges q and an external field and described in greater detail in ref. 9 .…”

“…In Eqs. ( 2) and (3), R i,bulk is the bulk radius of the atom, R i ( f cn ) the coordination number scaled radius 9 , α i,s,kl the static atomic polarizability 15 , d = 0.1 a scaling factor and L(ω, P) a sizedependent Lorentzian. The polarizability and capacitance of alloys will in this way not only have a spacial dependence from the discrete structure from the interaction but also a small one from the modified surface atoms.…”

“…Since the atomic radius for different atoms is slightly different the plasmon length P i is not a constant even when the same discrete structure is used for alloys though the change is only in the difference between the atomic radii of the constituents. ω a and A are the only fitted parameters in the ex-DIM model 9 .…”