Brownian Dynamics Simulations of Rotational Diffusion Using the Cartesian Components of the Rotation Vector as Generalized Coordinates

Abstract

AbstractHere, we report on the first Brownian dynamics (BD) simulations of rotational diffusion using the Cartesian components of the rotation vector as the generalized coordinates. The model system employed in this study consists of freely rotating and non‐interacting rigid particles with arbitrary surface topography. The numerical BD algorithm contains no singularities and yields numerical results that are in full agreement with known theoretical results. Because of the absence of singularities, this new algorithm is several orders of magnitude more efficient than a simple BD algorithm employing the Euler angles as the generalized coordinates. The general theory for using generalized coordinates in studies of more complex systems involving both translation, rotation, and fluid dynamic interactions is well known. Consequently, the benefits reported here can readily be extended to such systems. Important examples are segmented polymer chains, with and without holonomic constraints, and liquid crystals.magnified image