Microtrac Ultrafine Particle Analyzer Utilizing Dynamic Light Scattering Theory

Using light for particle size measurement

Light has properties that can be used for determining particle size and particle size distributions. In the case of diffraction instruments, such as the Microtrac S3000, the angle at which the light is diffracted depends upon the wavelength of the light and the particle size. The angle of diffraction is measured to determine size. For a particular particle size, should the wavelength change, the angle will change. There is another feature of light that can be used for determining the particle size – it is the frequency. Frequency is a measure of how many waves pass through a given point during one second. The more waves that cross the point or the closer the distance between the waves, the higher the frequency. Frequency change or shift information is used in Dynamic Light Scattering.

Dynamic light scattering

Dynamic light scattering (DLS) theory is a well established technique for measuring particle size over the size range from a few nanometers to a few microns. The concept uses the idea that small particles in a suspension move in a random pattern. A microbiologist by the name of Brown first discovered this effect while observing objects thought to be living organisms, by light microscopy. Later it was determined that the “organisms” were actually particles, but the term has endured. Thus, the movement of small particles in a resting fluid is termed “Brownian Motion” and can easily be observed for particles of approximately (0.5 to 1.0) sing a microscope at a magnification of 200 - 400X. Observation of larger particles compared to smaller particles will show that the larger particles move more slowly than the smaller ones if the temperature is the same. (Use the link to the applet to observe an animation of the effect of solvent molecules on particles). According to Einstein’s developments in his Kinetic Molecular Theory (applied to heat), molecules that are much smaller than the particles can impart a change to the direction of the particle and its velocity. Thus water molecules (0.00033 microns) can move polystyrene particles as large as a couple of microns. The combination of these effects is observed as vibrations and an overall movement of the particle.
 

Demonstration of Brownian Motion
 

When a coherent source of light (such as a laser) having a known frequency is directed at the moving particles, the light is scattered, but at a different frequency. The change in the frequency is quite similar to the change in frequency or pitch one hears when an ambulance with its wailing siren approaches and finally passes. The shift is termed a Doppler shift or broadening, and the concept is the same for light when it interacts with small moving particles. For the purposes of particle measurement, the shift in light frequency is related to the size of the particles causing the shift. Due to their higher average velocity, smaller particles cause a greater shift in the light frequency than larger particles. It is this difference in the frequency of the scattered light among particles of different sizes that is used to determine the sizes of the particles present.

Heterodyne and homodyne configurations

 

Commercial DLS instruments use either homodyne or heterodyne configurations. Microtrac invented (introduced in 1990) the use of the heterodyne configuration as used in conjunction with development of a power spectrum and more advanced mathematical treatment of the scattered light information. Figure 1 illustrates the two measurement configurations, which can be employed to obtain the Brownian motion information from the frequency shifted light. As shown on the right (heterodyne measurement) the frequency-shifted light is mixed (thus the term heterodyne) with stable, unshifted light. The unshifted light originates from the laser, a part of which is reflected in the instrument to the detector. This light acts as a stable reference point or baseline for the scattered, shifted light from each particle. The interaction (interference) of the reflected and shifted light allows for removal of the high optical frequency present in the particle-scattered light. This leaves only the lower shifted frequencies, which are the values that are related to the size of the particles. A similar approach is used in homodyne measurement, but the reference is, in effect, light shifted by other randomly moving, unstable particles. In both cases the interference signal frequencies are indicative of the Doppler frequency shifts due to the particles' Brownian motion and are the basis of the particle sizing measurement by DLS.

UPA Technical concepts

The following is a more technical description of the heterodyne process and how the UPA is different from other DLS instruments that use homodyne detection.

The expressions for P(w) shown in Figure 1 represent the power spectra which are the distributions of power as a function of frequencies. They therefore show distributions of frequencies. These are Lorentzian functions of angular frequencies, w, for both homodyne and heterodyne detection. The particle size is determined by the analysis of these power spectra. The constant g appears as a particle characteristic frequency of the response and is a function of the wavelength,l, scatter angle, q, and the diffusion coefficient, D. The diffusion coefficient, D, is a value that describes the movement of a particle in suspension relative to other particle sizes. The value D depends on the temperature, “T”, the suspending medium viscosity, “h”, and particle radius (size), “a”.

Note that there are two differences between the power spectra for the two cases. First, the homodyne detection power spectrum depends upon twice the characteristic frequency, 2g, while the heterodyne detection power spectrum depends upon just g. Second, the homodyne power is proportional to the scattered light intensity squared, (Is)², while the heterodyne power is proportional to the product of the scattered intensity and reference (laser) intensity, (I_s)(I_o). The latter means that the heterodyne signal level can be made many orders of magnitude larger than the homodyne signal by providing a large reference, I_o, using the reflected laser. This concept allows for measurement of very dilute suspensions and very small particles when observing light scattered at 180^o (back-scattered).

Microtrac Ultrafine Particle Analyzer measurement approach

The Microtrac Ultrafine Particle Analyzer (UPA) operates with heterodyne detection. Figure 2 is a diagram of the UPA measurement system. A magnified view shows the region of light interaction with the suspended particles. The UPA has an optical wave guide (fiber optic) focused on the outer surface of an integral sapphire window, which is immersed in the suspension. The sapphire window delivers the laser beam to the sample. The sapphire window and waveguide combination also collects the backscattered light. The reflection (Fresnel) of the original laser, at the interface between the window and the medium, is mixed with the back-scattered light. The reflection is unshifted in frequency and provides the local oscillator (reference) for heterodyne detection. The high index of refraction of sapphire produces a reflected reference beam having adequate intensity.

Two important features should be noted. First, the high intensity reflected reference allows the heterodyne component to dominate the power spectrum and to provide a signal many orders of magnitude higher than the equivalent homodyne signal. The high signal allows for the use of a silicon photo detector and a solid-state laser diode source. The all solid-state source-detector combination is very stable and reliable.



The second important feature is the very short path length that the scattered light signal travels in the suspension. The short path length allows measurement of high particle concentration while preventing effects of multiple optical scattering effects (re-scattering of light by the presence of too many particles that can lead to errors).

 

Also shown in Figure 2 is the balance of the measurement system for the UPA. The stainless steel probe contains the waveguide. The waveguide contains three arms. One arm of the waveguide transmits the laser to the tip of the waveguide and is focused onto the front surface of the sapphire window. A portion of the light is reflected while the remaining light exits the probe (second arm) and interacts with the particles. The probe tip is immersed in the suspended particles much the same as one would a pH electrode. The directional “Y” optical splitter not only delivers the laser to the tip, but also collects and returns the scattered and the reflected beams to the photodetector. The latter is done through the third arm of the three-port waveguide. The power spectrum of the interference signal is calculated with high speed FFT digital signal processor hardware. The power spectrum is then subjected to further calculation (inversion) to give the particle size distribution. Specialized mathematics packages are not needed to obtain particle size distributions. The heterodyne Controlled Reference Method of the UPA technology overall permits a dynamic measuring range that is both higher and lower than the homodyne concepts

A copy of the publication describing further details of the Ultrafine Particle Analyzer technology is available from Microtrac, Inc through this website.

“A New Approach to particle Sizing by Dynamic Light Scattering”, P.J. Freud and M.N. Trainer, Microtrac, Inc.

“High-concentration submicron particle size distribution by dynamic light scattering”, M.N. Trainer, P.J. Freud and E.M. Leonardo, American Laboratory, July 1992.
 

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