Breaking the Brownian Barrier: Models and Manifestations of Molecular Diffusion in Complex Fluids

Abstract

Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent when applied to molecular self-diffusion in fluids. The foundational principles of Gaussianity and Markovianity, central to the Brownian diffusion paradigm, are insuf- ficient for describing molecular diffusion, particularly in complex fluids characterized by intricate intermolecular interactions and hindered relaxation processes. This perspective delves into the nu- anced behavior observed in diverse complex fluids, including molecular self-assembly, deep eutectic solvents, and ionic liquids, with a specific focus on modeling self-diffusion within these media. We explore the potential of extending diffusion models to incorporate non-Gaussian and non-Markovian effects by augmenting the Brownian model using non-local diffusion equations. Further, we vali- date the applicability of these models by utilizing them to describe results from quasielastic neutron scattering and MD simulations.