Extending Laser Diffraction with PIDS Technology

From Fraunhofer to Mie Theory

Laser diffraction originally relied on Fraunhofer diffraction theory for particle sizing. The technique offered several important advantages. Modern laser diffraction analysers now extend beyond simple diffraction effects. Most systems use Mie theory instead. They also measure scattering intensity across a wide angular range. This wider measurement range improves particle size analysis, especially for smaller particles.

The Challenge of Measuring Nanoparticles

Manufacturers typically use two methods to improve small particle sizing. They increase the scattering angle and use shorter light wavelengths. These methods improve performance for many applications. However, they cannot accurately measure particles only tens of nanometres in diameter.

Increasing the scattering angle further provides little additional benefit. Small particles produce very slow changes in scattering intensity at high angles. Figure 2 illustrates this behaviour with a three-dimensional display. Even with wide-angle detection and short wavelengths, particles below 200 nm remain difficult to size accurately.

Two Different Approaches

Instrument manufacturers developed two different solutions. Some extend measurements below the instrument’s practical detection limit. They estimate particle sizes beyond the theoretical sizing limit, sometimes down to 10 nm. This approach introduces uncertainty. In some cases, it produces incorrect results.

Other manufacturers measure the polarization properties of scattered light. Beckman Coulter pioneered this method through Polarization Intensity Differential Scattering, or PIDS. This patented technique uses polarization to extract additional particle size information.

How Polarization Improves Particle Sizing

Vertically polarized light and horizontally polarized light create different scattering patterns for small particles. These patterns contain subtle structural differences.

Horizontally polarized scattering intensity, Ih, reaches a minimum near 90 degrees. Larger particles shift this minimum toward higher scattering angles. Vertical scattering intensity, Iv, changes only slightly for very small particles. However, the difference between Iv and Ih reveals clearer structural features.

This additional information makes small particle sizing possible. The technique combines polarization effects with wavelength dependence at large scattering angles. Together, these methods extend the practical sizing limit to approximately 10 nm. This performance approaches the theoretical limit of laser diffraction.

Understanding the PIDS Signal

Very small particles behave differently from larger particles when light strikes them. The light’s oscillating electric field induces an oscillating dipole within each particle. Electrons move back and forth while the particle remains stationary.

The electron motion follows the electric field direction. This direction stays perpendicular to the light’s propagation. The oscillating dipole then radiates light in almost every direction. It does not radiate along the oscillation direction. A detector positioned along that direction receives no scattered light from a single dipole.

Changing the light polarization changes the scattering intensity. Vertically polarized light produces Iv. Horizontally polarized light produces Ih. The difference between these values, Iv minus Ih, forms the PIDS signal.

How Particle Size Changes the Signal

Larger particles no longer behave like simple dipoles. Internal interference changes their scattering behaviour. Their scattering patterns become increasingly complex.

Small particles produce a PIDS signal that resembles a quadratic curve centred near 90 degrees. Larger particles shift this pattern toward smaller angles. They also create additional peaks through scattering effects.

Particle size and light wavelength both influence the PIDS signal. Measuring several wavelengths therefore provides additional particle size information. This extra information improves particle size distribution calculations.

Multiple Wavelengths Improve Accuracy

Figure 4 shows how particle size changes the PIDS response. The figure highlights both peak movement and contrast changes. It includes particles measuring 100 nm and 50 nm. Their angular scattering patterns remain distinguishable. Their symmetry axes also shift with particle size.

Longer wavelengths produce flatter PIDS signals. Measuring several wavelengths therefore captures additional scattering information. This information refines the particle size retrieval process.

Theoretical simulations and experimental studies support these observations. Conventional scattering intensity measurements struggle below approximately 200 nm. Adding polarization makes accurate sizing practical. Combining wide angular measurements, multiple wavelengths, and polarization greatly improves submicron particle characterization.

Practical Results

Figure 5 shows a trimodal particle size distribution measured with the PIDS technique. The experiment used wavelengths of 475, 613, 750, and 900 nm. It also measured scattering angles up to 144 degrees.

The solid line represents results that include polarization effects. The dashed line excludes polarization effects. The dotted lines show the nominal latex particle diameters supplied by the PSL manufacturer.

The measurement without PIDS misses the smallest particle population. This limitation remains despite using short wavelengths and large scattering angles. Figure 6 confirms the result with an SEM image. The image clearly shows three distinct particle sizes.

Summary

Accurate measurement of particles down to approximately 10 nm requires three complementary approaches. The instrument must measure over a wide angular range. It must also use multiple wavelengths and polarization effects.

PIDS does not combine unrelated measurement techniques. Every signal originates from the same light scattering process. The software processes all signals together within a single retrieval algorithm. The system therefore performs one integrated laser diffraction measurement instead of combining separate technologies.