Rh and Rg measure different properties of the particle and thus provide complementary information. The hydrodynamic diameter will reflect the protective layers on the particle (e.g. surfactant) whereas the radius of gyration will reflect where the mass of the particle is located. Thus for a stable gold colloid Rh is likely to be much larger than Rg. Thus there is no shape information that can logically be deduced. Note too that, from liquid crystal work, particles with an aspect ratio < 3:1 will tumble randomly in a fluid presenting all axes to the measurement and thus will be ‘seen’ or assumed as spherical.

Thank you Dr. Rawle for answering the question.

So in which condition table 3.1 of the book that I attached is true?

Who is Dr. Rafle?

You should remove the attached text for copyright breach.

Even for a polymer where there may be no 'protective layer', aspect ratios of < 3:1 still allow a particle to rotate freely and present all aspects to the impinging laser beam. The hydrodynamic diameter simply reflects the diffusion of an assumed spherical particle diffusing at the same rate as your measured particle.

I have measured Rh=50 nm by using an experimental setup and cumulants algorithm .and also measured Rg=74 nm by Guinier plot for this standard polystyrene nanosphere. I want to be sure that the method and my setup are correct. my DLS measurement is correct because the Rh result is consistent with the manufacturer's report. But how can I understand that my SLS measurement is correct ?

Instruments measure what is given to them. Test the instrument with a certified reference material to verify perfromance.

For a true hard sphere particle the ratio of Rg to Rh should be 0.78.

In your case the Rg is larger than Rh so you probably have some aggregation in your particle size distribution. This should typically also show up in the size distribution obtained from DLS. Rg will always give you just one overall average, and if there is aggregation in your sample, this could lead to a larger Rg than Rh. If you have polymer chains in your sample (which may also be true, maybe your solvent is dissolving some of your particles, or alternatively if you do not have latex particles but innstead polymer chains (long or cross-linked) then you would not expect anything close to hard spheres, and the measured value would indicate something about the structure of your polymer chains.

http://www.materials-talks.com/blog/2012/11/15/size-matters-rh-versus-rg/

concerning cumulants and distribution:

http://www.materials-talks.com/blog/2014/07/10/faq-peak-size-or-z-average-size-which-one-to-pick-in-dls/

thanks a lot. It was so useful to me.

Rg/Rh = 1.6 consistent with an extended rod like shape in solution

Rg/Rh = 1.3 random coil structure

Rg/Rh = 0.77 for monodisperse compact spheres like globular proteins

Hello Adel Aschi, can you please mention the published articles where they have put these ratios. I mean I want to use them to characterize my protein structure but to be sure I need a reference.