Static Laser Light Scattering

Static Laser Light Scattering is an established and precise measurement technique for the particle size characterization of both dry and wet samples. Microtrac is a global leader in this technology with over 40 years of experience in the development and manufacture of particle analyzers.

Static light scattering is a phenomenon that occurs when light interacts with particles. It produces characteristic angle-dependent patterns in which light is preferentially scattered by the particles in certain directions. Scattering angle and intensity depend on the size of the particles involved.

Therefore, static light scattering can be used to measure particle size distributions when an ensemble of particles is illuminated with a laser beam and the resulting light scattering pattern is recorded over a wide angular range.

The following is a brief introduction to the physic of static light scattering and how it is used in particle size analyzers.

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Fraunhofer and Mie theory in static light scattering

The characteristic light scattering patterns which are formed when a laser interacts with particles are caused by diffraction, refraction, reflection, and absorption (as shown on the figure).

For large particles, diffraction, which occurs at the contour of particles, is the dominant mechanism. This is sufficiently described by the so-called Fraunhofer theory. "Large particles" in this context means "significantly larger than the wavelength of light".

For the description and evaluation of scattered light patterns of smaller particles, the optical properties, essentially the refractive index, must be considered. This is described by the Mie theory, which, however, also includes diffraction and therefore allows a comprehensive evaluation of light scattering phenomena.

Literature values are available for the refractive indices of almost all solids, so Mie theory can be applied very reliably for static light scattering. Static light scattering is often referred to as laser diffraction or laser diffractometry, even independent of the size of the particles considered and the phenomena that occur.

Static laser light scattering - Figure 1

When light interacts with particles, diffraction, refraction, absorption, and reflection can occur.

Describing static light scattering patterns

The figure shows the scattered light patterns of suspensions with 1 µm and 10 µm particle size, respectively.

For the 10 µm particles, the scattered light pattern shows a characteristic ring structure, which can be explained mainly by diffraction. For larger particles, the diffraction angles would be smaller, and the rings would be closer to the center. Furthermore, the intensity of the diffraction maxima would increase.

For the 1 µm particles these diffraction rings are no longer observed. The light scattering pattern is rather diffuse, but more light is scattered in forward direction than to the side or back. With decreasing particle size, the overall intensity of the scattered light decreases, and less light is scattered in forward direction, and more is scattered to the side. To still evaluate the weak signals from very small particles, scattered light measurement is performed with shorter wavelengths, which generally provides stronger signals.

The figure also shows light scattering patterns from a mixture of 1 µm and 10 µm particles, with the scattering patterns of the two sizes overlapping. Real samples usually contain many different particle sizes, all of which contribute to the total scattered light. This must be taken into account accordingly when evaluating and calculating the particle size distribution.

Static laser light scattering - Figure 2

Static laser light scattering - Figure 2b

Static laser light scattering - Figure 2c

Scattered light pattern of 10 µm particles (left), 1 mm particles (center), and a mixture of 10 µm and 1 µm particles (right). A commercially available laser pointer was used for illumination.

Measurement instruments for static laser light scattering

The instrumental implementation of static light scattering in a measuring device is shown in the Figure. In a particle measurement with a Microtrac analyzer, a laser beam penetrates a dispersed sample, which can be a suspension, an emulsion, or a powder in an air stream.

Since the intensity of the scattered light provides information about the size distribution, Microtrac technology measures this scattered light at various angles up to 163°. The on-axis detector in the forward direction measures the sometimes very low diffraction angles generated by large particles. The high angles are covered by the off-axis detector.

By using three lasers hitting the sample from different angles, a particularly wide range of scattering angles is covered. Data is recorded continuously during the measurement, analyzed and evaluated according to Fraunhofer or Mie. Microtrac's 'Modified Mie' algorithm for static laser light scattering calculates exact particle size distributions even for (semi-)transparent, opaque, round, and non-round particles.

Static laser light scattering - Figure 3

Setup of the Microtrac SYNC particle analyzer for static light scattering analysis with two detector arrays and three laser light sources.

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Static Laser Light Scattering - FAQ

Why is the method called "static light scattering"?

In static light scattering, the observed pattern does not change over time. The term "static" therefore refers to the measurement signal. The particles that generate the scattered light pattern usually move through a measurement cell during analysis, so they are not static. However, if the sample material is well mixed and homogeneous, the size distribution within the volume under consideration is largely constant, and so is the scattering pattern.

What is the difference between dynamic and static light scattering?

In static light scattering, an angle-dependent light pattern is recorded and evaluated. In dynamic light scattering, the fluctuation of the scattered light intensity over a longer period of time is measured at one scattering angle. From both, the size of the light-scattering particles can be determined, whereby the dynamic method is especially suitable for nanoparticles and static light scattering can be used flexibly for a wide range of sizes.

Is the Fraunhofer approximation for static light scattering valid?

The Fraunhofer approximation only considers diffraction but is permissible for the evaluation of particle size distributions if these are significantly larger than the wavelength of the incident laser light. For the related static light scattering standard ISO 13320, 50 µm are specified as the lower limit, but in practice the Fraunhofer approximation is often used reasonably for particles down to about 5 µm.

How is Mie theory related to static light scattering?

Mie theory can be used to describe the light scattering pattern of spherical particles, taking into account their optical properties. It is the basis for particle size analysis with static light scattering. Mie theory is applicable to the entire size range, which is usually between 10 nm and 4 mm. The theory is named after Gustav Mie, who in 1908 described light scattering by solving Maxwell's equations.

How is the static light scattering intensity related to particle size?

Large particles scatter more light than small ones. The decrease in scattered light intensity happens by about a factor of 106, meaning that a 100 nm particle has 10 times less diameter, 1000 times less volume, and a million times less static light scattering intensity compared to a 1000 nm particle.

How is static light scattering angle related to particle size?

In the Fraunhofer approximation, diffraction angles increase with decreasing size. An important implication of Mie theory in static light scattering is that large particles scatter more light in forward direction than small particles.

How is the static light scattering intensity related to wavelength?

The scattering intensity of a particle is much higher for short wavelength light than for long wavelength light. This scattering is inversely proportional to the fourth power of the wavelength, 1/λ4. However, long-wavelength light is better suitable for measuring larger particles with static light scattering technology.