Number and Volume Distributions

The most appropriate representation for the particle size distribution measured using a given technique will depend on the technique’s sensitivity. Laser diffraction reports the volume of material of a given size, since the light energy reported by the detector system is proportional to the volume of material present. This contrasts with counting-based techniques such as image analysis, which measure and report the number of particles of a given size.

In comparing number and volume distributions, it is important to remember that there is a cubic relationship between the size of a particle and its volume. The volume of a 500 micron particle will therefore be 1 million times that of a 5 micron particle. If a sample containing one 500 micron particle and one million 5 micron particles was analysed using a volume-based technique, the contribution of these particle sizes to the overall distribution to be equivalent. If this distribution were expressed in terms of numbers of particles the presence of the 500 micron particle would be viewed as insignificant within the overall distribution.

The above example helps in understanding the sensitivity of number and volume based techniques. Volume-based methods are very sensitive to the appearance of a few large particles with a given distribution due to their large volume. Such techniques are therefore applied to detecting agglomeration or monitoring milling processes where the end-point is defined by monitoring the coarse particle fraction. Conversely, number based techniques are very sensitive to the appearance of fine particles within a sample, as these are normally present in large numbers. Given this, it is generally the case that number based techniques report a finer particle size compared to volume-based techniques.

It is possible to convert between from number distributions to volume distributions and vice versa. However, in doing this the errors involved in each technique are cubed. As such, the distributions produced following conversion should only be considered to be indicative of the actual distribution.