Tunable Localized Surface Plasmon Resonance in Misaligned Truncated Silver Nanoprism Dimers

Background

Silver and gold nanoparticles are renowned for their exceptional optical properties, arising from localized surface plasmon resonance (LSPR) of their conduction electrons [1, 2]. The resonance can be modulated by altering particle size, shape, material, and the surrounding medium [3–5]. Among them, nanoprisms (NPs) are particularly attractive due to their anisotropic geometry, which concentrates oscillating charges at the prism tips, enhancing the local electric field [6–9]. LSPR in nanoprisms is typically categorized into in‑plane dipolar, in‑plane quadrupolar, and out‑of‑plane dipolar modes, with the dipolar resonance red‑shifting as the prism edge length grows [10, 11]. When two nanoparticles are brought into close proximity, their individual plasmonic fields couple, concentrating the electric field within the interparticle gap—a phenomenon known as the hot‑spot effect. Dimers exhibiting strong hot spots can be fabricated by e‑beam lithography, nanosphere lithography, or self‑assembly [12–18]. Self‑assembly is especially attractive because the inter‑particle gap can be controlled down to the length of the linking molecule, thereby maximizing the hot‑spot intensity [16–18]. While most studies focus on tip‑to‑tip dimers [19–23], the self‑assembly process frequently produces edge‑to‑edge configurations with random misalignment [15]. Misaligned edge‑to‑edge gold NP dimers have been shown to exhibit broken symmetry, yielding dual‑peak resonances that can be toggled by varying the misalignment length [24]. However, gold’s high atomic mass locks the dimer geometry after fabrication, limiting post‑processing tuning. Silver, being more chemically reactive, suffers from tip oxidation during synthesis, leading to truncated nanoprism (TNP) structures [8, 25]. Truncation introduces additional symmetry breaking, opening new avenues for tunable plasmonic behavior. In this work, we investigate how truncation and misalignment jointly influence the LSPR of edge‑to‑edge Ag TNP dimers using finite‑element modeling.

Methods

Structural Model of Misaligned Truncated Ag Nanoprism Dimer

The computational model (Fig. 1) is based on Ag NPs synthesized via seed‑induced growth, where the edge length can be tuned by reaction conditions while maintaining a constant thickness T = 8 nm [26]. Two identical TNPs are arranged edge‑to‑edge with a fixed molecular gap G = 2 nm, representative of self‑assembly linkers. Each TNP has an initial edge length L = 130 nm, with a truncation length l₂ = 10 nm along the prism tips. The misalignment length l₁ defines the offset between the two prisms; the misalignment ratio R = l₁/L is varied from 0 to 1.5 to probe the effect of misalignment. When R approaches 0 or 1, the TNP is effectively transformed into a hexagonal nanoplate (HNP) as its edge length L₁ equals l₂ = L/3. HNP dimers are also simulated with R₁ ranging from 0 to 3.

Schematic diagram of the Ag TNP dimer showing a specific misalignment length l₁

Finite Element Method for Misaligned Truncated Ag Nanoprism Dimer

We employed COMSOL Multiphysics to solve Maxwell’s equations for the TNP dimer. The relative permittivity of silver follows the Drude model:

ε(ω) = ε∞ – ωp²/[ω(ω + iγ)]

Results and Discussion

The extinction cross‑section (ECS) intensity map of the TNP dimer as a function of misalignment ratio R and wavelength is shown in Fig. 2. For R = 0, two resonances of equal strength appear. As R increases to 1, the short‑wavelength resonance (peak 1) becomes dominant, blueshifting, while the long‑wavelength resonance (peak 2) weakens and redshifts. The peak‑1 wavelength initially decreases and then stabilizes; its intensity rises gradually, with a sharp drop at R = 1/8 due to the loss of a higher‑order LSPR mode. Peak 2’s wavelength first increases then decreases, and its intensity diminishes monotonically. Beyond R = 1.5, the two peaks coalesce into a single resonance matching the monomer’s wavelength, indicating negligible inter‑particle coupling.

ECS spectra of Ag TNP dimers. a ECS intensity distribution map as functions of R and wavelength. b ECS resonant wavelength (dark scatter line) and intensity (red short dotted line) spectra versus R. The square and triangle lines denote peak 1 and peak 2, respectively.

Electric‑field snapshots (Fig. 3) reveal the underlying mode structure. At R = 0, peak 1 corresponds to a higher‑order mode with field enhancement at the gap center and termini. Increasing R suppresses this mode, breaking the dimer symmetry; peak 1 then arises from an antisymmetric coupling mode with fields mainly at the lateral tips. Conversely, peak 2 consistently represents a symmetric coupling mode, with fields concentrated in the gap. The transition from a strong gap‑localized field (≈900 V/m) at R = 0 to a more tip‑centric field at larger R demonstrates how misalignment attenuates the hot‑spot effect.

Calculated electric field distributions of Ag TNP dimers and monomer. Panels a–g> correspond to points A–G in Fig. 2a. Peak 1: a R = 0; b R = 0.5; c R = 1; d R = 1.5. Peak 2: e R = 0; f R = 0.5; g R = 1. h Monomer.

We further examined how truncation length l₂ influences the switching behavior (Fig. 4). For R = 0, increasing l₂ from 0 to 43.3 nm (the point at which a TNP becomes an HNP) suppresses peak 1 and gradually reduces peak 2 until the two resonances merge into a single mode. For R = 1, the trend is similar, but the higher‑order mode disappears earlier, indicating that misalignment accentuates truncation effects.

ECS spectra of Ag TNP dimers with l₂ changing from 0 to 43.3 nm. a R = 0; b R = 1. The dark scatter and red short dotted lines indicate resonant wavelength and intensity spectra, respectively. The square and triangle lines represent peak 1 and peak 2.

When the TNP truncates into an HNP (edge length L₁ = 43.3 nm), the ECS intensity map (Fig. 5) shows that the two‑peak system becomes even more responsive to misalignment. The symmetric mode (peak 2) vanishes rapidly as R₁ exceeds 1, while the antisymmetric mode (peak 1) dominates. The resulting single‑peak spectrum can still be switched by adjusting R₁, confirming that truncation and misalignment synergistically enable tunable plasmonic behavior.

ECS spectra of the Ag HNP dimer. a ECS intensity distribution map versus R₁ and wavelength. b Resonant wavelength spectra of the two peaks.