Unified Description of Diffusion Coefficients from Small to Large Molecules in Organic-Water Mixtures

Diffusion coefficients in mixtures of organic molecules and water are needed for many applications, ranging from the environmental modeling of pollutant transport, air quality, and climate, to improving the stability of foods, biomolecules, and pharmaceutical agents for longer use and storage. The Stokes-Einstein relation has been successful for predicting diffusion coefficients of large molecules in organic-water mixtures from viscosity, yet it routinely underpredicts, by orders of magnitude, the diffusion coefficients of small molecules in organic-water mixtures. Herein, a unified description of diffusion coefficients of large and small molecules in organic-water mixtures, based on the fractional Stokes-Einstein relation, is presented. A fractional Stokes-Einstein relation is able to describe 98% of the observed diffusion coefficients from small to large molecules, roughly within the uncertainties of the measurements. The data set used in the analysis includes a wide range of radii of diffusing molecules, viscosities, and intermolecular interactions. As a case study, we show that the degradation of polycyclic aromatic hydrocarbons (PAHs) by O₃ within organic-water particles in the planetary boundary layer is relatively short (≲1 day) when the viscosity of the particle is ≲10² Pa s. We also show that the degradation times predicted using the Stokes-Einstein relation and the fractional Stokes-Einstein relation can differ by up to a factor of 10 in this region of the atmosphere.