Laser Diffraction for Particle Sizing – Theory Simply Explained in One Figure
Of course. We have very well written notes and instructions. And with our help on method developments, cases are rare when we ponder on the fundamental theories behind the technology of Mastersizer 3000. Nevertheless, we will need to troubleshoot, to challenge the instrument, to customize SOPs…… (And we get curious, too.) Then the comprehension of the theory becomes essential. The only problem is – it seems to be complicated. Therefore, I constantly challenge myself on how to communicate the theory as simple as possible. Now it comes down to “Four Events” and “Four Scenarios”.
Four Events:
- Incident light hits particle
- Light interacts with particle
- Light gets out of particle
- Outcoming light gets detected and analyzed by detectors and the software
Four Scenarios, from simple to complex:
Please read the descriptions in the table correspondingly with the figure down below.
| Opaque | Non-opaque | |
| One particle / one size | 1. An opaque spherical particle only diffracts light at its edge. Light does not enter the particle. Mathematically, it simply follows the rules of a mechanical wave, like a water wave passing a stone. Every size has its unique diffraction pattern. Fraunhofer approximation can be applied, or Mie solution with a very high refractive index (e.g. 2.3, for your reference, steel has a refractive index of around 2.5). | 2. A non-opaque spherical particle scatters light. In this case, the incident light, as an electromagnetic wave, gets into the particle and interacts with its electron clouds. The pattern of the light getting out of the particle is described by the Mie solution to Maxwell’s equations. This scattered light pattern is also unique to a particle with a certain size and certain optical properties. |
| Size Distribution | 3. To find out the size distribution of opaque particles, an iteration algorithm will be applied to find the particle sizes that best fit the detected light pattern. Fraunhofer approximation can be applied, or Mie solution with very high refractive index. | 4. To find out the size distribution of non-opaque particles, an iteration algorithm will be applied to find the particle sizes that best fit the detected light pattern. Mie solution is applied with given optical properties. |
These four scenarios, from simple to complex, represent a historical development of the technology. Nowadays, we are almost always in the fourth scenario – “non-opaque particles with a size distribution profile”. Therefore, Mie solution, which describes light scattering in general, is used in the vast majority of cases. It covers all size ranges and all optical properties. However, we continue to use the terminology – “laser diffraction” – for the historical reason. It can be confusing but hopefully not any more if you’ve read this far. In cases that the particles are opaque (e.g. refractive index > 2) and/or the particle is large enough (e.g. size greater than 10 times the wavelength), Mie solution can converge to Fraunhofer approximation with the benefit of simpler calculations (which is not that appealing to modern computers).
The Limits of the Technology
“Laser diffraction” is a “first-principle” technology with no need for calibrations. This is because the angular dependent profile of the scattered light is directly determined by the particle size and its optical properties. It is possible to measure particle sizes from 0.01µm – 3500µm. Outside this range, the angular dependence of the scattered light becomes too difficult to be detected. At the lower limit, the scattered light becomes too isotropic, while at the upper limit, the incident light hardly deviates from its incident direction.
Non-Spherical Shapes
Besides non-opacity and polydispersity, the non-spherical particle shape is another complexity. For one thing, irregularly shaped small particles (<1μm) depolarize light more strongly in one direction. We have a “Non-Spherical” option in the software which enables the high angle scattering to be correctly interpreted. Otherwise, the software would assume the irregularity as a different particle population. That is why some laser diffraction instruments tend to report bi-modal particle size distributions for non-spherical particles.
Optical Property Optimizer
The optical properties – refractive index (RI) – can be more complicated (than it already is) when it comes to non-spherical shapes. RI has a real part and an imaginary part. The real part accounts for refraction while the imaginary part handles the attenuation, known as the “absorptive index”. An irregularly shaped particle tends to have a higher absorptive index since the irregularities on the surface absorb light. In case we are not sure about the index values, our software has an “Optical Property Optimizer ” which scans a range of index values to find the ones that make most sense. For any further discussions, please do not hesitate to contact me since helping you is the most satisfying part of my job!
Further reading