For any solute aqueous solution (binary mixture, solute+water) what is the difference between the Mean Square Displacement (MSD) or Diffusion coefficient (D) for water-water and solute-water? And why the nature of MSD is proportional to ~t^2 in the initial regime ~t in long times ? Does this translational motion depends only on the solute hydration?
These behaviors are an extension of the Fick's law (for high times). For small times, one could apply the Langevin equation equation (ask me in mp if you want more info about that). In general, you can consider that you are in Fick's regime.
Thank you very much. Actually here, I have calculated diffusion coefficients (D) from the MSD, using Einstein equation. Is it not valid in all (time) regime? I want to investigate the diffusion coefficient (D) as function on solute concentration (not temp). What may be the role of the solute hydration. Can I fit the D values as function of concentration by the Arrhenius law and get the idea of activation energy (E) as function of concentration?
Can you please put some references.
No I dont think it is relevant to use Arrhenius as a function of concentration. Einstein's relation is theoretically correct for infinite dilution. When the dilution is not infinite you should take into account co-diffusion and use ma diffusion tensor. I'll look for somme biblio about that if I were you ^^
I looked a bit into it and found some biblio for you :
R. Taylor and R. Krishna. Multicomponent mass transfer. Wiley series in
chemical engineering. Wiley, New York, 1993.
If you dont have access to this : try to find some on the Maxwell-Stefan diffusion
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