Mie or Fraunhofer?

For determination of particle sizes a validated method is necessary. Laser diffraction is known to be a robust method – but one very dangerous pitfall exist: By laser diffraction you do not obtain a “direct” measure of the particles: The signals from the measurement is “translated” into a particle size by different calculation methods – these calculation methods are known as “Fraunhofer” and “Mie”. If you are not using the right calculation method and correct parameters, this might lead to large over- or underestimation – especially of the presence of small particles! The consequence might be severe – as for instance a too high or too low exposure in vivo. To our experience, many people use a “default” value in their “validated” method which might give a very misleading picture of the actual size distribution. A method validation should always include evaluation of the calculation method used – even though the suppliers of the instruments usually recommend one of the two calculation methods. Otherwise, a complementary method confirming the results from the laser diffraction should always be applied (i.e. microscopy).

Thus, when using laser diffraction for determination of particle size distribution, the results are translated into a given particle size using either Fraunhofer or Mie theory:

The use of Mie theory is more correct than Fraunhofer when there are small particles in the sample. However, use of Mie theory requires knowledge of the optical parameters (refractive index and absorption) as these are included in the transformation from measured signal to particle size distribution. Several procedures are described in the literature for determination of the refractive index and absorption. Some of them are used for this material, but the values found can only be considered as estimations and not the true parameter values.

The parameters are optimised by:

Becke lines test

  • Recalculation of laser diffraction measurement using the Malvern software with varying absorptions (refractive index is set to a value within the interval found by the Becke line test).
  • Estimation of suitable absorption based on:
    • The residual from data to mathematical model is low.
    • D10%, D50% and D90% are not significantly affected when small changes in the absorption are introduced.
  • Recalculation of laser diffraction measurement using the Malvern software with varying refractive indices.
  • Control of the suitability of the refractive index used for estimation of absorption by checking that:
    • The residual from data to mathematical model remains low when small changes in the refractive index are introduced.
    • D10%, D50% and D90% are not significantly affected when small changes in the refractive index are introduced.

SEM and microscopy are used for correlation of the particle sizes to the laser diffraction result and confirmation of the final result. The figure below show how quite different results are obtained when the two different models are applied to the same laser diffraction measurement.