Is there a maximum viscosity for DLS measurements?


Diffusion-proportional-to-one-over-eta-rhThe Malvern Zetasizer can determine particle size by dynamic light scattering (DLS). In this technique, the intensity fluctuations are analyzed to find the corresponding diffusion coefficient that led to the fluctuations. The translational diffusion coefficient Dt of a particle is inversely related to its size and the viscosity of the dispersant (or more accurately the hydrodynamic radius rH and viscosity η).

This relationship can be used to predict detectability limits of the technique in general, and this is how we explore the idea of a maximum viscosity (or maximum size) border of applicability.

Diffusion, size, and viscosity

The translational diffusion coefficient obtained from DLS is related to particle size via the Stokes Einstein equation:


where the thermal energy given by the Boltzmann constant kB times absolute temperature T (in Kelvin) is divided by the viscous drag given by 6 times pi times the viscosity times the hydrodynamic radius RH. It is also occasionally seen with a factor 3, when the size is expressed as a hydrodynamic diameter instead of the radius. Since kB is constant and we are interested in measurements at room temperature for now, the above full equation can be reduced to the simplified proportionality, stating that the diffusion coefficient is inversely proportional to viscosity and size.

How can we get the maximum size?

The specifications of the Zetasizer state that the maximum size for particles in water is 10 microns. With the help of the diffusion coefficient equation, we can now translate this to any arbitrary viscosity and predict the corresponding maximum size.

Approx. maximum size by DLS

      Viscosity [cP]                Maximum size [nm]       
                    1.0                   10,000
                    2.5                     4,000
                  10.0                     1,000
                100.0                        100
               1,000.0                          10

What is the maximum viscosity?

The problem to solve is very similar to the maximum size. We can simply look at what the slowest diffusion coefficient for the specification at the limit is (i.e. the large size limit) and then transpose from there.

Approx. maximum viscosity by DLS

       Size                        Maximum viscosity [cP]         
       10 μm                                     1 cP
         1 μm                                   10 cP
     100 nm                                 100 cP
       50 nm                                 200 cP
       10 nm                              1,000 cP

The observant reader may have noticed that we just keep the product of size and viscosity constant, so it is not too challenging to determine the combination for either a different size or a different viscosity.

Hope the above eliminates some confusion about the limits of dynamic light scattering.


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