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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?

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The mass will play the role in the relaxation time to go from a ballistic regime in the Langevin equation to an overdamped regime where only diffusion matters.

The bigger the mass, the higher the inertia and therefore the longer the time it takes to reach the overdamped regime.

Once the overdamped regime is reached or, to phrase it differently, if your time window allows you to only see the overdamped regime in both cases then you will see no difference between the two.

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