Dynamic Light Scattering Technique

Particle size distribution analyzers based on measuring the phenomenon of Brownian motion can be broadly classified as being based on either autocorrelators or on power spectrums. For the purpose of this document, systems using autocorrelators will be called Photon Correlation Spectroscopy (PCS) systems. Power spectrum analyzers such as the HORIBA LB-550 are designed to examine the differences in frequency of light scattered off particles.

The LB-550 technique is designed to analyze fluctuations in the intensity of any
scattered light from a body in relation to the incident light. This method is also
referred to as the frequency analysis method. PCS analyzers are based on the method in which the number of photons per time unit is counted, assuming that light consists of a series of photons.

As described above, the PCS instrument is designed to count moving particles
in terms of the number of photons. Therefore, it must simultaneously measure particles which are moving at both fast and slow speeds. The simultaneous measurement requires that fast-moving particles be determined at high speeds, and slow-moving ones over extended periods of time. In actual practice, however, it is very difficult to create an instrument that combines the above functions with continuous data multiplication capability.

Conclusions on Building a State of the Art Laser Diffraction Analyzer

The HORIBA LA-950 particle size analyzer uses the laser diffraction method to measure size distributions. This technique uses first principles to calculate size using light scattered off the particle (edge diffraction) and through the particle (secondary scattering refraction). The LA-950 incorporates the full Mie scattering theory to cover the widest size range currently available. Wide measurement ranges, fast analyses, exceptional precision, and reliability have made laser diffraction the most popular modern sizing technique in both industry and academia.

Building a State of the Art Laser Diffraction Analyzer

There’s a wide gulf between bare minimum and state of the art. The latter is always the industry leader in accuracy, repeatability, usability, flexibility, and reliability. The current state of the art in laser diffraction is the Partica LA-950 featuring two high intensity light sources, a single, continuous cast aluminum optical bench (see the figure below), a wide array of sample handling systems, and expert refinements expected from the fifth revision in the 900 series.



Using two light sources of different wavelengths is of critical importance because
the measurement accuracy of small particles is wavelength dependent. Figure A (below) shows the 360° light scattering patterns from 50nm and 70nm particles as generated from a 650 nm red laser. The patterns are practically identical across all angles and the algorithm will not be able to accurately calculate the different particle sizes. Figure B (below) shows the same experiment using a 405nm blue LED. Distinct differences are now seen on wide angle detectors which allows for accurate calculation of these materials. Integrating a second, shorter wavelength light source is the primary means of improving nano-scale performance beyond the bare minimum laser diffraction analyzer.

The Importance of Optical Model

In the beginning there was the Fraunhofer Approximation and it was good. This
model, which was popular in older laser diffraction instruments, makes certain
assumptions (hence the approximation) to simplify the calculation. Particles are
assumed…

- to be spherical
- to be opaque
- to scatter equivalently at wide angles as narrow angles
- to interact with light in a different manner than the medium

Practically, these restrictions render the Fraunhofer Approximation a very poor
choice for particle size analysis as measurement accuracy below roughly 20
microns is compromised. The Mie scattering theory overcomes these limitations. Gustav Mie developed a closed form solution (not approximation) to Maxwell’s electromagnetic equations for scattering from spheres; this solution exceeds Fraunhofer to include sensitivity to smaller sizes (wide angle scatter), a wide range of opacity (i.e. light absorption), and the user need only provide the refractive index of particle and dispersing medium. Accounting for light that refracts through the particle (a.k.a. secondary scatter) allows for accurate measurement even in cases of significant transparency. The Mie theory likewise makes certain assumptions that the particle…

- is spherical
- ensemble is homogeneous
- refractive index of particle and surrounding medium is known

These figures show a graphical representation of Fraunhofer and Mie models using
scattering intensity, scattering angle, and particle size (ref. 13). The two models
begin to diverge around 20 microns and these differences become pronounced below 10 microns. Put simply, the Fraunhofer Approximation contributes a magnitude of error for micronized particles that is typically unacceptable to the user. A measurement of spherical glass beads is shown in Figure 19 and calculated using the Mie (red) and Fraunhofer (blue) models. The Mie result meets the material specification while the Fraunhofer result fails the specification and splits the peak. The over-reporting of small particles (where Fraunhofer error is significant)is a typical comparison result.

Bench-top Instruments

Bench-top laser diffraction instruments became practical with the advent of high
intensity, reasonably priced lasers and sufficient computing power to process
the scattered light data. Once these barriers to market entry were eliminated
the advantages of laser diffraction over other techniques were apparent: speed
of analysis, application flexibility, small particle accuracy, and ease of use. The
ability to measure nano, micro and macro-sized powders, suspensions, and emulsions, and to do it within one minute, explains how laser diffraction displaced popular techniques such as sieving, sedimentation, and manual microscopy.

Such an instrument consists of at least one source of high intensity, monochromatic
light, a sample handling system to control the interaction of particles and incident light, and an array of high quality photodiodes to detect the scattered light over a wide range of angles. This last piece is the primary function of a laser diffraction instrument: to record angle and intensity of scattered light. This information is then input into an algorithm which, while complex, reduces to the following basic truth:

LARGE PARTICLES SCATTER INTENSELY AT NARROW ANGLES

SMALL PARTICLES SCATTER WEAKLY AT WIDE ANGELS

The algorithm, at its core, consists of an optical model with the mathematical
transformations necessary to get particle size data from scattered light. However,
not all optical models were created equally.