Suppose I have two neutrally-buoyant macromolecules diffusing in water. They have the same radius of gyration (i.e. same root-mean-square distance from their center of mass), but one of them is compact (its mass is roughly the cube of its size) and the other is extended (its mass is roughly the square of its size).
Since these molecules are the same size, do they have roughly the same diffusion coefficient?
Alternatively, their root-mean-square velocities should be different since they have different mass. Does this lead to substantially different diffusion coefficients?