Decoupling three-dimensional rotational diffusion of anisotropic nanoparticles using small-angle approximation

Accurately characterizing the three-dimensional rotational dynamics of anisotropic nanoparticles remains challenging due to the limitations of both experimental techniques and conventional simulation methods, which often fail to capture the intricate details of rotational motion. We propose a small-angle approximation method to decouple the nanoparticle rotational dynamics about each of its three principal axes, while simultaneously resolving decoupled angular displacements. Validation through rotational autocorrelation functions and scaling analyses confirms that the proposed method accurately captures rotational diffusion coefficients for both nanorods and nanosheets in unentangled polymer melts. Building on the newly decoupled angular information, calculations reveal partial coupling between nanoparticle rotation and polymer chain dynamics and Gaussian characteristics in angular probability density distributions. This robust approach may be extended to biomolecular systems, like protein rotational diffusion and DNA conformational dynamics, and even to the analysis of dynamic systems in robotics.