Nanoparticle ‘kite’ Performs Unusual 2D Rearrangement Mimicking Rotation

Researchers investigated pseudorotation, an unusual isomerization involving apparent rigid-body rotation, but observed it occurring in two dimensions within an optical matter system composed of metal nanoparticles. John Linderman, Shiqi Chen, and Yanzeng Li, all from the Department of Chemistry at the University of Chicago, alongside Alexandria Hoehn, Stuart A. Rice, and Norbert F. Scherer, also of the University of Chicago, detail how this differs from the three-dimensional motion typically seen in molecular isomerization due to the electrodynamic nature of optical binding. Their work demonstrates that correlated motion between all eight nanoparticles within a kite-shaped optical matter structure, possessing D2(D2h) symmetry, drives this pseudorotation, despite inter-particle separations that would normally lead to destructive interference. Significantly, the team found the kite isomer to be remarkably stable, exhibiting a slower rearrangement rate than other isomers, and revealed that this behaviour stems from crucial N-body interactions and forces, highlighting their importance in active matter systems more broadly.

Scientists have uncovered a surprising instance of two-dimensional pseudorotation within an unconventional system of self-assembled nanoparticles. Pseudorotation, a peculiar form of isomerization typically observed in molecules, mimics the appearance of rotation but arises solely from rearrangements of atoms. This phenomenon extends to optical matter (OM), structures built from interacting metal nanoparticles, but occurs within a flattened, two-dimensional plane rather than the three dimensions characteristic of molecular systems. The distinction in dimensionality stems from the fundamental difference between the light-mediated binding of nanoparticles and the conventional chemical bonding found in molecules. Researchers assembled an eight-nanoparticle structure, dubbed a “kite” due to its shape, exhibiting D2 (D2h) symmetry and a D4 symmetric transition state. This kite isomer, though relatively rare, accounting for only 10% of observed structures, displays a remarkably rapid rate of pseudorotation compared to other, more common isomers like the “teardrop” configuration. The mechanism driving this pseudorotation involves the coordinated movement of all eight nanoparticles, with their interactions evolving smoothly without any particles joining or leaving the assembly. Simulations and experiments reveal that these N-body effects are crucial for maintaining the kite’s integrity and enabling its unique rotational behaviour. Further investigation revealed that other OM isomers, arranged on a trigonal lattice, enhance light interference and induced polarization, but rearrange more slowly than the kite. Despite the kite’s particle arrangement seemingly promoting destructive interference on a two-particle basis, it proves to be the most structurally persistent isomer, reinforcing the significance of N-body forces in dictating the overall stability and dynamics of this optical matter system. Eight-particle optical matter (OM) structures were formed and observed using an inverted microscope optical trapping setup. The use of circular polarization is crucial for inducing rotational motion through the transfer of angular momentum. To visualize the OM structures, a spatially incoherent white light source was directed through a dark-field condenser, illuminating the nanoparticle solution. Scattered light was collected by the same 60× objective and imaged onto a CMOS detector (Andor, Neo) at a frame rate of 450Hz. Single-particle tracking software (Mosaic, Image J) was employed to determine particle positions, with corrections applied to mitigate pixel-locking bias. The research team also utilised electrodynamics-Langevin dynamics (EDLD) simulations, a computational technique that models the movement of particles under the influence of various forces. These simulations were performed using Generalised Multiparticle Mie Theory (GMMT) implemented in the MiePy software. The Langevin equation was numerically integrated, accounting for the mass of each particle, external forces, frictional drag (ζ = 6πηr, where r is the particle radius and η is the viscosity of the medium), and random thermal fluctuations. A simulation time step of 1μs was chosen to accurately capture the overdamped dynamics of the system. Collective coordinates, derived from weighted principal component analysis (w-PCA) of particle position fluctuations from EDLD trajectories, were used to represent the overall motions of the nanoparticle constituents. The 8-nanoparticle optical matter (OM) “kite” structure exhibits pseudorotation, a type of isomerization observed with a rate significantly faster than transitions to other OM isomers. This kite isomer, possessing D2 (D2h) symmetry and a D4 symmetric transition state, constitutes only 10% of the total population of observed OM isomers yet demonstrates a unique dynamic behaviour. Correlated motion of all eight nanoparticles drives this pseudorotation, evolving smoothly without particles entering or leaving the array. Analysis reveals that despite inter-particle separations within the kite structure potentially causing destructive interference on a two-body basis, it remains the slowest isomer to rearrange into any alternative configuration. Simulations and experimental data demonstrate that N-body interactions and forces are crucial in maintaining the kite structure and facilitating its pseudorotational dynamics. These N-body effects, exceeding the influence of simple pairwise interactions, are fundamental to the behaviour of this active matter system. The study identified that the kite isomer’s stability is linked to these collective interactions, which manifest as a rigid-body rotation within the D4 symmetric transition state. Electrodynamics-Langevin dynamics simulations, coupled with experimental observations, confirm the mechanism of pseudorotation and provide insights into transitions between different isomers. These simulations allow evaluation of both two-body and N-body forces, revealing their contributions to the observed dynamics. The observed pseudorotation occurs in two dimensions, a departure from the three-dimensional motion typically associated with isomerization in molecular systems. Furthermore, the relative populations of the various OM isomers, alongside the rate of intra-state pseudorotation, are demonstrably affected by changes in ionic strength, suggesting that electrostatic forces contribute to the stabilisation or destabilization of both the isomers and their transition states. The system was studied using 150nm diameter Ag nanoparticles suspended in water, illuminated by a loosely focused 800nm wavelength optical trapping beam, with images collected at 450Hz, enabling detailed tracking of particle positions and analysis of structural changes. Scientists have long sought to understand how complex behaviours emerge from simple interactions, and this work offers a compelling new perspective on that challenge. The observation of pseudorotation within an optical matter system composed of nanoparticles is particularly noteworthy because it occurs in two dimensions, diverging from the more common three-dimensional isomerizations seen in molecular chemistry. This difference stems from the unique nature of optical binding, where electromagnetic fields dictate interactions rather than traditional chemical bonds. For years, controlling and predicting the behaviour of these ‘optical matter’ systems has been hampered by the difficulty of accounting for the many-body interactions at play. While individual nanoparticle interactions are relatively well understood, the collective effects, how the presence of one particle alters the forces on others, have proven elusive. This research demonstrates that these N-body interactions are not merely a detail, but a fundamental driver of the system’s unusual stability and dynamics. The ‘kite’ structure, despite its inherent instability on a pairwise basis, persists due to these complex, correlated forces. However, the limited range of observed structures remains a constraint. The kite isomer’s low probability of formation suggests that achieving predictable control over optical matter architectures is still some way off. Future work might focus on manipulating the system’s parameters to favour the formation of the kite structure, or exploring other geometries where N-body effects are similarly prominent. More broadly, this research could inspire new approaches to designing active materials with tailored properties, potentially leading to advances in areas like photonics and micro-robotics, though translating these nanoscale observations into macroscopic devices will undoubtedly present significant hurdles.