Emergent tetratic ordering in autophoretic rods mediated by torque

Chemically driven nanorods offer a powerful platform for studying emergent pattern formation in synthetic microswimmers, where hydrodynamic, electrokinetic, and phoretic interactions play key roles. This study integrates experiments, finite element modeling, and Brownian dynamics simulations to investigate how torque-mediated interactions influence the clustering behavior of self-propelled autophoretic Au-Rh nanorods. At low particle fractions (ϕ < 1%) and high fuel concentrations (5 wt% H₂O₂), the nanorods transiently form dynamic wedge-shaped clusters, aligning along two arms of a V-shaped structure due to torque-driven interactions. As the particle fraction increases (ϕ > 1%), stable dimers, trimers, and higher-order clusters emerge, eventually transitioning to tetratic clusters at (ϕ ∼ 10%) under low-fuel conditions (1 wt% H₂O₂). This tetratic ordering, where rods align along two orthogonal axes, appears at intermediate densities, differing from its typical occurrence in denser systems. Finite element simulations reveal that hydrodynamic and electrokinetic interactions generate a net torque of 8.23 × 10^-20 Nm, driving rotational motion that promotes clustering. Meanwhile, Brownian dynamics simulations highlight the interplay between self-propulsion and pairwise rotational interactions in cluster formation. These findings underscore the crucial role of hydrodynamic and phoretic torques in shaping collective behaviors and provide valuable insights for designing active materials and synthetic microswimmer systems capable of self-assembling into functional, high-density structures.