I am doing an experiment with colloidal solution of nanoparticles and would like to measure the Brownian motion velocity of these particles. Can I do it experimentally?
Prajal Chettri You get the diffusion coefficients directly and they can be plotted out - it's these that are transformed to PSD. Indeed in the Stokes-Einstein relationship there's a direct inverse linear relation between hydrodynamic size and diffusion coefficient. so the plots will look identical (except that the x-axis will be different).
Alan F Rawle
Thank you sir for replying. I would also like to know whether the measurement gives me a value for velocity of Brownian motion? Or it uses this property to give the size distribution across the solution.
Prajal Chettri You get the diffusion coefficients directly and they can be plotted out - it's these that are transformed to PSD. Indeed in the Stokes-Einstein relationship there's a direct inverse linear relation between hydrodynamic size and diffusion coefficient. so the plots will look identical (except that the x-axis will be different).
As Alan F Rawle states in his excellent answer, this is the principle of DLS. Another method would be particle tracking such as NTA.
Another representation of the data from either of these techniques is as a Mean Square Displacement as a function of time.
Alexander Malm Thanks for the reminder about NTA. Number (NTA) and intensity (DLS) routes to the Brownian motion.
I am not sure about this, but in order to obtain some sort of particle velocity from knowledge of its Brownian diffusivity, wouldn't one need to divide the latter by some sort of length scale? Please correct me if I am wrong.
Omar Z. Sharaf The units for Brownian motion are the diffusion coefficients (e.g. m2/s in SI units). The term 'velocity of Brownian motion' in the question is an oxymoron as Brownian motion is expressed as diffusion coefficients. Obviously the unit of velocity is m/s. (So you are correct - a length scale (m) separates the units). There is a range of Brownian motion diffusivity values. Particle-particle interactions make a velocity profile more difficult to extract as, of course, there are collisions and other events to slow the particles down.
Thank you Alan F Rawle Omar Z. Sharaf Alexander Malm for your insights.
Is the length scale the interaction length (length of the cuvette) that needs to be divided with the diffusion coefficient to get the Brownian motion velocity?
Prajal Chettri The units of Brownian motion are those of the diffusion coefficient that I mentioned above. There is no concept of 'velocity of Brownian motion'. This is because the motion is possible in 3 dimensions.
Prajal Chettri , I would say that the problem here is that the term 'Brownian motion velocity', which you refer to, is a bit "loose".
It is all a matter of the time and length scales you are interested in.
In particular, this will mainly depend on whether you are interested in looking at your nanoparticles in the 'diffusive' or 'ballistic' regimes.
For the former, you can probably link measured Brownian diffusivity to some sort of averaged particle velocity. The link will be through the MSD calculated over a certain time interval. This is where the Stokes-Einstein model is valid.
As for the latter, particle motion becomes dominated by its 'inertia'. From this perspective, the Stokes-Einstein model is no longer valid, and we cannot make much use of Brownian diffusivity measurements.
In all likelihood, a true 'Brownian velocity' of a particle can be only deduced if we have the means to resolve the very small time and length scales associated with the ballistic regime of Brownian motion. I would say that, only in this regime we can start to think of particles as having some sort of well-defined 'Brownian velocity'.
Please, feel free to correct me where I am wrong, Alan F Rawle , Alexander Malm , and everyone.
I hope this helps!
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