I want to understand how can two spheres of different materials but the same hydrodynamic size and in the same solution have identical diffusion coefficients? Like shouldn't it also depend on the material the spheres are made of? Or at least the molecular weight, i.e., what if one of the spheres is hollow or a nanocomposite? Does none of this change D (as defined in the S-E eqn.) ?
Arti Tyagi Good question. The bombardment of the particle by external solvent molecules causes the Brownian motion and the density or composition of the particle plays no role here as the acceleration to the diffusion speed is virtually instantaneous. Essentially the particle slips into 'holes' in the continuous phase - and that's why the motion is random. A similar question might be 'why does a spherical particle move at all with solvent molecule bombardment? One could imagine that the random bombardments would cancel out and the particle would not move at all. Obviously this is not the case...
Alan F Rawle thank you for the explaination.. so what about at very low concentrations when we consider that particles do not essentially interact with each other?
Arti Tyagi Assumptions of infinite dilution in theories are to avoid particle-particle interactions i.e. hindered mobility. This doesn't apply to particle-continuous phase interactions. This applies to both Brownian motion (absence of an electrical field) and zeta potential (presence of an electrical field). In these ('infinite dilution') instances a true mobility is calculated or measured unencumbered by other concentration dependent effects. All the international standards (ISO and ASTM) in this area advise the use of a concentration ladder to try to gauge the effect of such interactions.
Dear Arti Tyagi
In addition to the very explicative answer by Prof. Alan F Rawle ,
I would like to add to this thread, the following link powered by Comsol.:
https://www.comsol.com/multiphysics/diffusion-coefficient
The link shortly gives a review about the D dependence on several physical variables for different physical situations. In the case of the stokes Einstein eq. will inversely depend on μ---the solvent viscosity.
Pedro L. Contreras E. yes I knew the S-E equation parameters, that is T and μ. I was just wondering why there shouldn't be a term to account for the particle composition. I understand now, thank you.
Because diffusion coefficient is the property of solution in which the solvent is added. It does does not depend on either the nature or concentration of the solvent, unless the external solvent is reactive.
Dear Arti Tyagi and Readers,
The answer is provided in the attached file.
Thank you Arti Tyagi for your comment.
To advance our understanding, it is useful to consider the problem from a historical perspective. I believe that the attached collection of short essays is an excellent source of information on the problem of Brownian motion. I find this material to be one of the best discussions on the subject and I hope it will help you in your future studies.
Arti Tyagi If you need more diffusion stuff, here's a webinar:
The importance of the measurement of diffusion in 2-phase systems
https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W150813DiffusionColloidalSuspension.html
[Registration needed]
Thank you, Prof. Alan F Rawle I'll go through this as well. My initial question has been answered but it would be better for my understanding to read as much as I can on this topic.
Hello Arti Tyagi : yes, as you indicated the Stokes Einstein equation is independent of the material properties of the sphere: thermal energy divided by viscous drag.
The diffusion coefficient of a 50nm lead nanoparticle in water is exactly the same diffusion coefficient as the one of a 50nm oxygen nanobubble in water. It only depends on the temperature and the viscosity of the surrounding medium.
Where the confusion might set in is: you can come up with an empirical relationship between molecular weight and hydrodynamic size - and this relationship is different for different materials.
You might find https://www.materials-talks.com/blog/2014/09/16/faq-molecular-weight-estimate-from-dls/ of interest.
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