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tokens: The stopping time is a measure of the timescale on which the gas transfers its angular momentum to dust and can be expressed as (Perets Murray-Clay 2011 )where is the gas thermal velocity, R s is the radius of the solid particle, ρ s is its density, assumed to be 1 g cm −3 regardless of the size, and v rel is the relative velocity between the gas and the dust grain. The dimensionless drag coefficient C D is a function of the Reynolds number Re of the flow around the particle and derives from an empirical law fitted on recent experimental data (Perets Murray-Clay 2011 ):where Re is the Reynolds number. It is given by (Supulver Lin 2000 )where l g is the mean-free path of the gas. The turbulent diffusion of the grains is modeled using a Monte-Carlo scheme where individual particles are given random impulses to mimic the stochastic transport due to turbulent eddies (see, e.g., Ciesla 2010 , 2011 ). Overall, the new position z d of a dust grain after a timestep dt is computed as follows in the vertical direction:where R 1 ∈ [−1; 1] is a random number, σ 2 is the variance of the random number distribution, D p is the diffusivity of the solid particle, and v adv is the term accounting for the nonuniform density of the gas in which the particles diffuse as well as the nonuniform diffusivity of the particles, and the forces experienced by the particle (see Equation ( 11 )). The diffusivity of the dust grains D p is related to the gas diffusivity through the Schmidt number Sc as (Youdin Lithwick 2007 ):where ν = αH 2 g Ω K is the turbulent viscosity of the gas (assumed to be equivalent to the gas diffusivity) expressed through the nondimensional α parameter measuring the level of turbulence within the disk (Shakura Sunyaev 1973 ) and St is the Stokes number, corresponding to the stopping time multiplied by the local Keplerian frequency. Larger values of α yield a more efficient redistribution of the dust grains through turbulent diffusion. Finally, the advection term in the transport equation is given by Ciesla ( 2010 , 2011 ) as This set of equations allows us to derive the vertical position z d of individual particles at each timestep and to subsequently estimate the dose of irradiation they received. 3. Irradiation of Grains The energy received by water molecules per unit time due to cosmic-ray irradiation W irr ( n ) as a function of the column density of gas n above the particle is taken from Yeghikyan ( 2011 ). These authors computed this term by using the cosmic-ray intensity I ( E ) (cm −2 s −1 st −1 MeV −1 ) from Cooper et al. ( 2003 ) and considering a planar geometry. This leads to a differential flux spectrum inside the disk F ( E ) given by W irr ( n ) is then derived from the molecular cloud material stopping power S ( E ), i.e., its capability to absorb the cosmic-ray energy, as estimated from the Stopping and Range of Ions in Matter program (Ziegler et al. 2010 ). Note that the stopping power mostly depends on the mass density and not