Temperature-Dependent Translation-Rotation Diffusivity Divergence in Hot Brownian Motion Directly Observed by Single-Particle T-Jump Tracking

A nanoscale heat source suspended in fluids constitutes a highly localized yet mobile system that is far from equilibrium. Remarkably, its translational and rotational dynamics can still be theoretically described by Brownian-type equations of diffusion, a “hot Brownian motion” framework (HBM), while the original formulation of diffusive dynamics premises a system that is at or near thermal equilibrium. The HBM theory predicts a steeper temperature dependence for the nanoscale heat source’s rotational dynamics over its translational movements─a breakdown of the equipartition principle. Here, we present the first experiment that consistently assessed the HBM prediction by evaluating the diffusivities resulting from both types of motion on an equal footing. We simultaneously tracked the dynamics of all six translational and rotational degrees of freedom for single gold nanoparticles after laser-induced temperature jumps up to ∼30 K above ambient. Without the need for adjustment parameters, the experimental data were recapitulated by the HBM theory across a panel of particle sizes and heating-laser intensities. Our results thus corroborated the translation-rotation diffusivity divergence predicted by the theory, solidifying its underlying microscopic picture which is expected to have important implications in such applications as photothermal imaging, molecular thermobiology and biophysics, nonequilibrium physics and active matters, as well as chemical dynamics, to name a few.