Fig. 4: Self-limited assembly of single-patch prisms by patch‒patch interpenetration.

a TEM images of nano-bowties, trimers, and tetramers exhibiting tip-to-tip connection. Schematics of a nano-bowtie labeled with interparticle angle γ and tip-to-tip distance d (inset). b TEM tomograph of a nano-bowtie and 3D reconstruction of merged patches. c Curvature analysis of merged patches. d Heatmap of γ and d by the kernel density estimation overlaid with the scatter plot obtained from experiment: γ = 39.9 ± 30.4°, d = 33.6 ± 6.7 nm. e Theoretically calculated monomer density profiles \({{{{{\rm{\varphi }}}}}}(r)\) before (black line) and after merging (black line with a green shadow) as a function of the distance away from a tip r normalized by Kuhn monomer size \({b}_{l}\) at interparticle angle γ of 0°. Inset: schematics of the theoretical model of patch‒patch interpenetration. The crossover distance Г divides a patch into inner and outer regions, where intrapatch and interpatch chain‒chain interactions are dominant, respectively. \({{{{{{\rm{\varphi }}}}}}}^{*}\) refers to the equilibrium monomer concentration after merging. f Normalized histograms of d (purple bars) and doubled patch thickness 2\({t}_{{{{{{\rm{m}}}}}}}\) (gray bars) measured from experimental TEM images and from simulations (solid lines of corresponding color). g Plasmonic near-field LSPR maps calculated by solving Maxwell’s equations using Finite Element Modeling (FEM) of the trimer boxed in (a) at excitation energies corresponding to the modes (2.81 eV: face; 2.69 eV: edge; 2.29 eV: tip antibonding; 2.25 eV: tip bonding). The orientation of the electric field is averaged in-plane, with incident excitation impinging on the particles from perpendicular to the plane. Scale bars: 50 nm (a), 10 nm (c).