Stokes number of the largest grain size (St_max), dust-to-gas ratio (ϵ), and Rosseland mean opacity per gram of protoplanetary disk material for a range of fragmentation velocities within and beyond the water-ice line, as well as three different turbulence strengths after 1 Myr of evolution. The fragmentation velocity v_frag takes values in the range 0.1–10 m s⁻¹ for ice-free grains and 1–50 m s⁻¹ for icy grains (Blum & Wurm 2008; Gundlach & Blum 2015). The ice line is located at 0.75 au in all of our models.