Azimuthally averaged radial profiles of the maximum radius a_r in models with different α-parameters and fragmentation velocities as indicated in the panels. The evolution time in all panels is t = 0.2 Myr. The solid blue lines are the model results, and the dashed black lines are the maximum grain radius a_frag set by the fragmentation barrier defined in Eq. (26). The red solid lines show the Toomre Q-parameter calculated using Eq. (33). The red dashed lines mark the Q = 2.0 threshold for convenience.