Measuring Non-spherical objects with Dynamic Light Scattering

How can we deal with non-spherical DLS? Nature does not always present us with perfect spheres. Quite often, nanoparticles are only approximately spherical. So what happens if we try to measure the hydrodynamic size of a non-spherical object? How can DLS deal with this scenario? Find out if we can measure non-spherical nanosheets in this highlight of an interesting comparison to TEM data. Let’s dive into non-spherical DLS.

Hydrodynamic size – assumes a sphere – does it?

“The Hydrodynamic size – either the hydrodynamic radius or hydrodynamic diameter – is the size of a sphere that diffuses with the same diffusion coefficient.” So on the face of it, it seems to imply we always require spheres. But that is not so: the hydrodynamic size is an equivalent spherical size. It does not require the object to be spherical. The size is just the theoretical size of a sphere.

Can we do non-spherical DLS? If the object is not spherical we can still simplify and think of it as a sphere, an equivalent sphere. If only for the purpose of interpreting our dynamic light scattering data. So we can certainly do non-spherical DLS, it is just a matter of how we interpret the data correctly.

Non-spherical DLS from Nanosheets – small disks with two dimensions

As an example of a non-spherical particle, we can consider a cylinder or disk: here we have two dimensions, a length/diameter L and a thickness t. The hydrodynamic volume of this object is proportional to size D_h³ and also proportional to t*L². So if we are dealing with non-spherical nanosheets of similar thickness t, the hydrodynamic size is expected to be

D_h ~ L^2/3

In a paper titled “Measuring the lateral size of liquid-exfoliated nanosheets with dynamic light scattering” Mustafa Lotya et al. confirmed this experimentally. They prepared a series of layered materials (graphene, molybdenum disulfide, tungsten disulfide) in N-methyl-2-pyrrolidone (NMP) and N-cyclohexyl-2-pyrrolidone (CHP) by horn tip sonication. Then they centrifuged at various rates to tune nanosheet size, and measure it by TEM and DLS. As a result, they experimentally find for a range of nanosheets that the following relation holds:

= (0.07 ± 0.03) D_h ^(1.5±0.15)

where is the mean lateral sheet size, and D_h is the primary peak hydrodynamic diameter from an intensity size distribution by DLS. The alternative of imaging by TEM or AFM requires much more time and effort. They conclude that this DLS method – even though not highly accurate – can give a fast, simple, and reasonable estimate of the lateral size of any two-dimensional nanosheet dispersed in a liquid.

Want to dive in even more into non-spherical shape?

The latest Zetasizer has two components that may extend the usability of the nanosheet length estimate even further than before:

1. Adaptive correlation can classify steady state data from a somewhat noisy, non-ideal sample
2. Polarization may allow extra information about the shape

It may be surprising that a technique with a few decades of history still provides plenty of areas to discover, and shape is one of them. The above two points are possible through faster processors and through the easy-to-use integration of polarizers into the latest hardware.

If you want to learn even more about non-spherical DLS and how shape affects dynamic light scattering: check out references to the Perrin Shape or Perrin friction factor. A brief summary in “Can you get shape information from DLS?” contains an overview.

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Have any questions about “non-spherical DLS” ? Please email me ulf.nobbmann@malvern.com – Thanks! Opinions are those of the author. Our editorial team modifies them occasionally.