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tokens: to fit the blue wing of the bulk water absorption. The original dOH band and the shifted one are each fit using a Gaussian function. This fitting scheme is applied to each spectrum collected in the whole experiment to trace the diffusion of N 2 in the ASW. The band area of the shifted dOH band at 3672 cm −1 and the original dOH band at 3694 cm −1 during the isothermal experiment at each target temperature are shown in Figures 3 and 4 , respectively. It is evident that the shifting of dOH strongly depends on the target temperature. Figure 2. RAIR Spectra of: (1) 200 ML pure water ice deposited at 10 K; (2) after annealing at 70 K for 30 minutes; (3) after cooling down to 10 K and deposition of 16 ML N 2 on top; (4) after the isothermal experiment. The dashed lines are the fit while the solid circles are the experimental data. Spectra are offset for clarity. Figure 3. The band area of the 3672 cm −1 peak during isothermal experiments of N 2 on ASW at different target temperatures. The lines are fits using the model described in the Section 4 . Figure 4. The band area of the 3694 cm −1 peak during the isothermal experiment of N 2 on ASW at different target temperatures. 4. Modeling Fick’s law of diffusion was used to obtain the diffusion energy barrier as well as the pre-exponential factor D 0 , similar to other studies (Mispelaer et al. 2013 ; Karssemeijer et al. 2014 ; Lauck et al. 2015 ). The one-dimensional Fick’s law of diffusion is described by the following equation:where C ( z , t ) is the coverage (unitless) at depth z into the ice. If the amount of N 2 at depth z is just enough to cover the whole pore surface at that depth, then C ( z , t ) = 1. D ( T ) is the temperature dependent diffusion coefficient. We assume that 1 ML of water corresponds to a thickness of 0.3 nm. Therefore the total water ice thickness is h = 60 nm. Right after N 2 deposition at 10 K, N 2 should only cover the top few layers. We denote this initial penetration depth as d . After sufficient diffusion, N 2 penetrates into the ASW and evenly covers the pore surfaces. We have the following equations: The values of d , C 0 , and C inf can be obtained from Figures 3 and 4 . We denote the area of the original dOH band at 3694 cm −1 before and after isothermal experiment (such that N 2 covers the pore surface evenly) to be O i and O f , respectively. Similarly, we denote the area of the shifted dOH band at 3672 cm −1 before and after sufficient diffusion to be S i and S f , respectively. Figure 5 illustrates how the two dOH bands change with the fraction of pore surface covered by N 2 . Simple calculations show that In the model, we do not consider desorption, because in all of the isothermal experiment, the ice temperature is always below the temperature at which desorption occurs. Solving Equation ( 2 ) yieldsFigure 6 shows the solution at t = 0, 200, and seconds. At t = 0 s, N 2 molecules penetrate only to depth d . The shifted dOH band area should be proportional