Quantifying water diffusion in high-viscosity and glassy aqueous solutions using a Raman isotope tracer method

Abstract. Recent research suggests that under certain temperature and relative humidity conditions atmospheric aerosol may be present in the form of a glassy solid. In order to understand the impacts that this may have on aerosol–cloud interactions and atmospheric chemistry, knowledge of water diffusion within such aerosol particles is required. Here, a method is described in which Raman spectroscopy is used to observe D₂O diffusion in high-viscosity aqueous solutions, enabling a quantitative assessment of water diffusion coefficients, D_water, as a function of relative humidity. Results for sucrose solutions compare well with literature data at 23.5 ± 0.3 °C, and demonstrate that water diffusion is slow (D_water ~5 × 10⁻¹⁷ m² s⁻¹), but not arrested, just below the glass transition at a water activity of 0.2. Room temperature water diffusion coefficients are also presented for aqueous levoglucosan and an aqueous mixture of raffinose, dicarboxylic acids and ammonium sulphate: at low humidity, diffusion is retarded but still occurs on millisecond to second timescales in atmospherically relevant-sized particles. The effect of gel formation on diffusion in magnesium sulfate solutions is shown to be markedly different from the gradual decrease in diffusion coefficients of highly viscous liquids. We show that using the Stokes–Einstein equation to determine diffusion timescales from viscosity leads to values which are more than 5 orders of magnitude too big, which emphasises the need to make measurements of diffusion coefficients. In addition, comparison of bounce fraction data for levoglucosan with measured diffusion data reveals that even when particles bounce the diffusion timescales for water are a fraction of a second for a 100 nm particle. This suggests a high bounce fraction does not necessarily indicate retarded water diffusion.