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

TL;DR

This paper reviews the limitations of classical Brownian motion models for molecular diffusion in complex fluids and proposes extended models incorporating non-Gaussian and non-Markovian effects validated by experimental and simulation data.

Contribution

It introduces extended diffusion models that account for complex fluid behaviors, moving beyond traditional Gaussian and Markovian assumptions.

Findings

Classical Brownian models are insufficient for complex fluids.

Non-local diffusion equations better describe molecular self-diffusion.

Models are validated with neutron scattering and MD simulations.

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 insufficient for describing molecular diffusion, particularly in complex fluids characterized by intricate intermolecular interactions and hindered relaxation processes. This perspective delves into the nuanced 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 validate the applicability of these models by utilizing them to describe results from quasielastic neutron scattering and MD simulations.