## Laser diffraction theory

By laser diffraction analysis it is possible to measure particles sizes between 0.02 and 2000 µm. The sample is dispersed in either air or a suitable liquid media. The laser passes through the dispersion media and is diffracted by the particles. The sample is dispersed well and it is ensured that the particles pass the laser beam in a homogeneous stream. When particles are exposed to a collimated beam of light a diffraction pattern is produced: The laser beam consists of two light sources (He-Ne) having different wavelength.

The blue laser is used for measuring the small particles, while the red detects the larger particles. The diffraction pattern is measured by detectors, and the signal is then transformed to a particle size distribution based on an optical model: The pattern is characteristic of the particle size and using mathematical analysis the result is transformed into an accurate, repeatable picture of the size distribution.

• Models for determination of particle size distribution

Most often the Fraunhofer approximation or the Mie theory is used for transforming the measured data to a particle size distribution (read more about Mie and Fraunhofer). The use of Fraunhofer is suitable for large particles, but in the small particle end the Mie theory provides the greatest accuracy – however, the refractive index must be known. There is a wide disagreement on where the limit is for the suitability of the Fraunhofer approximation – some says no particles must be below 2 µm, while others say below 100 µm. However, if the real and imaginary parts of the refractive index are not known for sure, the use of the Mie theory can be just as incorrect – if not more – as the Fraunhofer approximation.

• Refractive index

The refractive index is a value that describes how a material refracts light. For liquids this value is easy to determine with a refractometer. The refractive index of solid powders can be expressed as: n=ik-m (read more about refractive index)

•  Disadvantages and pitfalls in laser diffraction

In the performance of laser diffraction for determination of particle size distribution one should be aware of the many pitfalls.

• The sample can be soluble in the dispersion.
• The sample can agglomerate in the dispersion media giving larger particle sizes than are the actual sizes in the product.
• If a part of the particles have high density, it is possible that sedimentation will occur, and thus, the whole sample will not be measured.
• Creaming is the case where a part of the sample floats on the dispersion media.
• The total amount of sample will then not be measured and the result will most likely not be representative for the product.
• A common error in laser diffraction is the application of too much sonication of the dispersion. Sonication is applied to disperse loose agglomerates, but fragile primary particles can be destroyed as well.
• Air bubbles in the system will appear at the result as large particles
• The concentration of sample must be sufficiently high to give an acceptable signal to noise ratio in the detector.
• A too high concentration can cause multiple scattering.
• Sample withdrawal must be representative for the entire batch.
• The background signal can change due to e.g. temperature changes. Variations in the background during measurement will influence the results.
• The use of Mie theory presupposes knowledge of the light refractive index of the particles and the dispersion media and the imaginary part of the refractive index of the particles.
• If the refractive index of the sample and of the dispersion media is the same, the laser beam can not be diffracted.
• Clear particles can reflect light, which is detected as small particles
• Due to the wavelength of the laser light, some colored samples can not be measured.
• The materials in the instrument (eg. O-rings, tubings, etc.) must be resistant to the dispersion media.