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Secondary organic material (SOM) constitutes a large mass fraction of atmospheric aerosol particles. Understanding its impact on climate and air quality relies on accurate models of interactions with water vapour. Recent research shows that SOM can be highly viscous and can even behave mechanically like a solid, leading to suggestions that particles exist out of equilibrium with water vapour in the atmosphere. In order to quantify any kinetic limitation we need to know water diffusion coefficients for SOM, but this quantity has, until now, only been estimated and has not yet been measured. We have directly measured water diffusion coefficients in the water soluble fraction of α-pinene SOM between 240 and 280 K. Here we show that, although this material can behave mechanically like a solid, at 280 K water diffusion is not kinetically limited on timescales of 1 s for atmospheric-sized particles. However, diffusion slows as temperature decreases. We use our measured data to constrain a Vignes-type parameterisation, which we extend to lower temperatures to show that SOM can take hours to equilibrate with water vapour under very cold conditions. Our modelling for 100 nm particles predicts that under mid- to upper-tropospheric conditions radial inhomogeneities in water content produce a low viscosity surface region and more solid interior, with implications for heterogeneous chemistry and ice nucleation.