Plasmonic Response of Complex Nanoparticle Assemblies

Abstract

Optical properties of nanoparticle assemblies reflect distinctive characteristics of their building blocks and spatial organization, giving rise to emergent phenomena. Integrated experimental and computational studies have established design principles connecting the structure to properties for assembled clusters and superlattices. However, conventional electromagnetic simulations are too computationally expensive to treat more complex assemblies. Here we establish a fast, materials agnostic method to simulate the optical response of large nanoparticle assemblies incorporating both structural and compositional complexity. This many-bodied, mutual polarization method resolves limitations of established approaches, achieving rapid, accurate convergence for configurations including thousands of nanoparticles, with some overlapping. We demonstrate these capabilities by reproducing experimental trends and uncovering far- and near-field mechanisms governing the optical response of plasmonic semiconductor nanocrystal assemblies including structurally complex gel networks and compositionally complex mixed binary superlattices. This broadly applicable framework will facilitate the design of complex, hierarchically structured, and dynamic assemblies for desired optical characteristics.

Hierarchically Doped Plasmonic Nanocrystal Metamaterials

“…The mixing trends in the extinction spectra and effective dielectric response were successfully reproduced in simulations using a mutual polarization method (MPM) that we recently developed to efficiently compute the optical response of structurally and compositionally complex nanoparticle assemblies (Figure c and Figures S4 and S5). − In fact, the predicted resonances in the dielectric functions were useful to guide and ultimately improve the quality of the fits to the IR-VASE data, especially for doped metasurfaces, the optical responses of which were more spectrally complex. We define the metamaterial’s effective dielectric response ε eff (ω) through the relation ⟨ D ⟩ = ε eff ·⟨ E ⟩, where ⟨ E ⟩ and ⟨ D ⟩ are the average electric field and electric displacement throughout the metamaterial, respectively (see details in the Supporting Information).…”

Structural Control of Plasmon Resonance in Molecularly Linked Metal Oxide Nanocrystal Gel Assemblies

“…Nanocrystal gels were first assembled using Brownian dynamics simulations of particles with strong, short-range attractions at fixed thermodynamic volume fraction. MPM simulations at varying gap distances were then performed by fixing the particle centers and varying the radius of the optical cores. , The thermodynamic volume fraction and nanocrystal dielectric function were chosen to be qualitatively representative of the suite of experimental ITO nanocrystal gels (see Figure S12 and Table S1 in the Supporting Information), but the decay length τ does not change significantly if these parameters are varied.…”

“…The computational challenge of simulating disordered assemblies has also hampered the understanding and predictive design of their optical properties. 17,18 Nanocrystal gels are percolated networks of linked colloidal nanocrystals lacking long-range order, which show great promise as tunable and responsive optical materials if these challenges can be overcome. 17,19−23 In contrast to close-packed nanocrystal assemblies, 24,25 nanocrystal gels can incorporate nanocrystals with different compositions and without specific size or shape constraints, enabling the emergence of collective properties from diverse building blocks.…”

“…We find that the red-shift in the LSPR peak when forming gels from nanocrystal dispersions increases gradually with higher tin doping concentration, larger nanocrystal size, and shorter ligand molecules, parameters that are conveniently adjustable through synthetic tuning of the inorganic core and the surface ligands. We use Brownian dynamics simulations to extract the gap distance from small-angle X-ray scattering (SAXS) data, , leading to the observation of a universal scaling relationship between the relative plasmonic peak shift and scaled gap distance, establishing a “plasmon ruler.” The approximate exponential scaling is verified by simulating the optical response of gels with variable gap spacing using a highly efficient mutual polarization method (MPM) that we recently developed to compute properties of assemblies containing many thousands of nanoparticles . Analogous to previous analyses of plasmon coupling between pairs of noble-metal nanoparticles, − the plasmon ruler we derive can be used to predict the plasmon peak frequency in a gel from the characteristics of the nanocrystal and molecular components.…”

“…Disordered assemblies of nanoparticles also exhibit a collective optical response, but they typically lack the precise and reproducible structural control needed to fully rationalize their spectra. The computational challenge of simulating disordered assemblies has also hampered the understanding and predictive design of their optical properties. , Nanocrystal gels are percolated networks of linked colloidal nanocrystals lacking long-range order, which show great promise as tunable and responsive optical materials if these challenges can be overcome. ,− In contrast to close-packed nanocrystal assemblies, , nanocrystal gels can incorporate nanocrystals with different compositions and without specific size or shape constraints, enabling the emergence of collective properties from diverse building blocks. , Discrete, disordered assemblies of nanoparticles, like clusters and strings, have been shown to exhibit a collective plasmonic response that varies with their structural attributes, − yet their spectra could be only qualitatively compared to simulations, because of structural heterogeneity. , In our own recent work, we showed that thermoreversible metal-coordination links , result in reproducible structures and consistent assembly-induced optical changes in single-component and multicomponent gel networks of ITO nanocrystals, but we lacked a mechanism to systematically tune gel structures and the resulting optical properties. , …”