Laser Diffraction is a popular and cost-effective particle sizing technique capable of determining the particle size of a properly dispersed material from approximately 0.2 µm to 3500 µm depending on the instrument. This technique calculates particle size distribution by analyzing the angle of light scattered as a cloud of particles move through a light source. The information is then translated into a volume distribution under the assumption that the particles are all spherical.
While highly useful, the accuracy of this method is dependent on user-defined optical property parameters and the assumptions embedded in the manufacturer’s proprietary algorithm.
Still wondering what makes up an optical model and how to achieve representative results based on your selection? Continue reading to learn more!
What is Mie and Fraunhofer Theory?
Laser Diffraction relies on two light scattering theories, Mie and Fraunhofer, to determine particle size. Both theories simplify the scattering data captured from the instrument into a particle size distribution. To learn more about the mathematical calculations behind each of these theories, ISO 13320 delves into the specifics.
Mie theory assumes that all particles are spherical, and utilizes a user-defined absorption value and refractive index for both the material and dispersion medium. An absorption value is considered to be an imaginary value that represents the reduction of intensity of a light beam that is not due to scattering. A refractive index is the degree that the light bends while passing between mediums. A refractive index of 1 is assumed for air when a sample is analyzed on a dry basis.
Fraunhofer theory is best used for large opaque particles over 50 µm, as this theory assumes that all particles scatter light equally, the particles are much larger than the laser’s wavelength, and that the particles have an opaque appearance and do not transmit light. Neither an absorption value nor a refractive index is needed for this theory. If this theory is selected for smaller material, there is the potential for a large margin of error as it makes many assumptions.
At PTL, we have multiple manufacturers for laser diffraction instrumentation including, Malvern, Beckman Coulter, and Sympatec. Each manufacturer handles optical models differently.
For Sympatec, Mie theory is generally not used. The default optical model is FREE (Fraunhofer Enhanced Evaluation) or HRLD (High Resolution Laser Diffraction). Both use the same assumptions as Fraunhofer theory. Beckman Coulter and Malvern are similar in that both manufacturers allow a user to select Fraunhofer or Mie Theory. Refractive index and absorption values are commonly displayed as: RI, Absorption. As discussed above, Fraunhofer theory does not rely on a refractive index or absorption value and is denoted as: 0,0; whereas Mie theory may be denoted as: 1.52, 0.1.
How Do We Select a Refractive Index Value?
If there is a known refractive index for a sample from published literature, that value is used. If there is no known refractive index, PTL uses a default value. Alternatively, if the material is not well known and has suitable characteristics, it is possible to generate an approximate refractive index by utilizing Becke Line refractive index testing, or the Saveyn method.
How Do We Select an Absorption Value?
A particle’s surface texture, roughness, reflectivity, color, or opaqueness can affect the beam intensity therefore influencing the absorption value. As there is no commercially available method to measure absorption, the value is inferred. When a sample is analyzed via Laser Diffraction at PTL, the sample is observed under a bench-top microscope to help determine an appropriate absorption value. Depending on the appearance of the sample, an absorption value is typically chosen between 0 and 1.0 as noted in the table below. This value as it is a user-defined parameter is subjective and based on our expertise.
| Sample’s Appearance | Absorption |
| Spherical, transparent (glass beads) | 0 |
| Spherical, not completely transparent (milk, oil, emulsions) | 0.001 |
| Transparent, surface texture (crystalline milled powders) | 0.01 |
| Gray appearance under the microscope (slightly colored powders | 0.1 |
| Black appearance under the microscope (colored powders, metal powders) | 1.0 |
Ensuring a Representative Distribution
Looking at the sample under a microscope before analysis also helps to determine a general particle size range to ensure the instrument’s generated histogram is representative of the sample. A sample’s distribution can shift depending on the refractive index or absorption value chosen. Below is an example of results from the Malvern Mastersizer 3000.
Depending on the user-selected absorption value, the distribution can shift. Additional peaks can appear in the distribution for absorption values that are not the best fit for the material. To confirm if a peak at the lower end of the distribution is representative of the sample, PTL can filter the sample preparation using a filter size in the peak’s range. After filtering, a laser is shone through the vial and if particles are seen in the laser beam, then the peak is confirmed to be most likely real; known as the Tyndall Effect. PTL strives to ensure a representative particle size range is captured for each material.
Absorption of 1.0
Absorption of 0.1
Absorption of 0.01
Absorption of 0.001
Absorption of 0
Conclusion
Selecting an appropriate optical model helps to ensure we obtain representative results. If you have a known refractive index or an absorption value you would like used, please let us know when submitting samples. Otherwise, PTL evaluates each sample to select the best absorption and refractive index based on our observations and expertise. We look forward to assisting with all your particle sizing needs. Contact us today for a quote!
By Fiona Hamilton, Particle Characterization Chemist II.
