As particles become smaller, the ratio of particle dimension to light wavelength (d/λ) is reduced and the scattering pattern becomes smoother and less angularly dependent, causing more difficulty in determining the correct size values. To enhance the ability to measure small particles, there are three approaches one may take to extend the lower size limit when measuring particles using laser diffraction.

The first approach to extend the lower sizing limit is by increasing the angular detecting range. If we use the angular location of the first minimum in the scattering pattern as the criterion to correctly size a sphere, we will find that in order to size a sphere having a diameter smaller than 0.5 µm, the maximum detecting angle has to be greater than 90 degrees. Thus, in order to size a submicron particle, the detection angular range has to be designed to cover angles at least as large as 90 degrees; practically, the maximum detecting angle can be as large as 175°.

Scattering patterns are a function of light wavelength and particle size. Their variations are related to the ratio between particle dimension and wavelength (d/λ). Obviously, if the wavelength of light is shorter the ratio will be greater and the lower sizing limit will be effectively extended. Practically, the shortest wavelength is about 350 nm because most materials exhibit strong absorption at wavelengths shorter than 300 nm. Using a light of λ = 375 nm, the lower sizing limit can be extended to half of that using light of λ = 750 nm.

Pioneered by Beckman Coulter, most laser diffraction manufacturers now use the above two approaches to size small particles. However, for particles smaller than 200 nm, even using wide angular range and short wavelength, it is still difficult to obtain an accurate size. The third approach is to use the polarization effects of the scattered light.

Vertically polarized scattered light has different scattering patterns and fine structures from that of horizontally polarized light for small particles. The main characteristic of the horizontal scattering intensity (I_h) for small particles is that there is a minimum around 90 degrees. This minimum shifts to larger angles for larger particles. Thus, although both vertical scattering intensity (I_v) and Ih have only small contrast in the case of small particles, the difference between them can reveal a more distinguished fine structure, thereby making the sizing of small particles possible. Combining polarization effects with wavelength dependence at large angles, we can extend the lower sizing limit to as low as 40 nm without extrapolation. This combined approach is known as the Polarization Intensity Differential Scattering (PIDS) technique patented by Beckman Coulter¹.

When the light beam is polarized in either the v direction or the h direction, the scattering intensity Iv and Ih for a given angle will be different. The difference between I_h and Ih (I_v - I_h) is termed the PIDS signal. For small particles the PIDS signal is roughly a quadratic curve centered at 90 degrees. For larger particles the pattern shifts to smaller angles and secondary peaks appear due to the scattering factor. Since the PIDS signal is dependent on particle size relative to light wavelength, valuable information about a particle size distribution can be obtained by measuring the PIDS signal at several wavelengths.

Figure 1. displays the shift in the peak value and the change in contrast of the PIDS signal for particles of various diameters. In addition, because the PIDS signal varies at different wavelengths (it becomes flatter at longer light wavelengths), measurement of the PIDS signals at several wavelengths will provide additional scattering information that can be used to further refine the size retrieval process.

From Figure 1., the angular patterns for 100 nm and even for 50 nm particles are recognizable, in addition to the shift in the axis of symmetry. It has been verified through both theoretical simulation and real experimentation that accurate sizing of particles smaller than approximately 200 nm by scattering intensity without the use of the PIDS technique is practically difficult and probably unrealistic. The combination of the three approaches (wide angular range, wavelength variation, and polarization effect) improves the accurate characterization of submicron particles using light scattering. There is no mixing of technologies. All signals are from the same scattering phenomenon and treated integrally in a single data retrieval process just like in an ordinary laser diffraction measurement.

Figure 1. I_v-I_h of small PSL in water (&lambda_o = 450 nm).
Dotted line: d = 150 nm; dashed line: d = 100 nm; and solid line: d = 50 nm.