Light diffraction is one of the most widely used techniques for measuring the size of a wide range of particles from very fine to very coarse. The method is popular because it is quick and easy to use, flexible, and it can be adapted to measure samples presented in various physical forms. The method depends on the analysis of the diffraction pattern produced when particles are exposed to a collimated beam of light. As the patterns are characteristic of the particle size, mathematical analysis can produce an accurate, repeatable picture of the size distribution.

This chapter provides guidance on the measurement of size distributions of particles in any phase system (e.g., powders, sprays, aerosols, suspensions, emulsions, and gas bubbles in liquids) through analysis of their angular light-scattering patterns. Traditionally, the measurement of particle size using laser diffraction has been limited to particles in the range 0.1 µm to 3 mm. Due to recent advances in optics and lens and equipment design and construction, newer instruments are routinely capable of exceeding this range (e.g., 0.1 µm to 8 mm). It is the responsibility of the user to demonstrate the applicability of the instrument for its intended use and to validate any method prior to its adoption for routine use.

For nonspherical particles, an equivalent-sphere size distribution is obtained because the technique uses the assumption of spherical particles in its optical model. The resulting particle size distribution may be different from those obtained by methods based on other physical principles (such as sedimentation or sieving). The laser diffraction technique cannot distinguish between scattering by single particles and scattering by clusters of primary particles forming an agglomerate or an aggregate. If the presence of aggregates is suspected, this can be investigated using other techniques such as microscopy.

The laser diffraction technique is based on the phenomenon that particles scatter light in all directions with an intensity pattern that is dependent on particle size. All present instruments assume a spherical shape for the particles. Historically, the early laser diffraction instruments used only scattering at small angles and, thus, has been known by the following names: Fraunhofer diffraction, (near-) forward light scattering, and low-angle laser light scattering (LALLS).

However, the technique since has been broadened to include light scattering in a wider angular range by application of the Mie theory, in addition to the Fraunhofer approximation and anomalous diffraction.

The measurement of particle size is an important aspect in the characterization of raw materials and drug formulations. To monitor production and particle stability, efficient and rapid methods for particle sizing are needed. The electronic measurement of samples offers a convenient solution to this problem. However, the electronic measurement will often have to be accompanied by microscopical investigation to determine the type of particles being investigated. Modern drug formulations may also be particulate formulations where the particle size will be below 100 µm, and reliable and reproducible methods are needed for the quality control of these drug products.

A representative sample, dispersed at an adequate concentration in a suitable liquid or gas, is passed through the beam of a monochromatic light source, usually from a laser. The light scattered by the particles at various angles is measured by a multi-element detector, and numerical values relating to the scattering pattern are then recorded for subsequent analysis. These numerical scattering values are then transformed, using an appropriate optical model and mathematical procedure, to yield the proportion of total volume to a discrete number of size classes forming a volumetric particle size distribution (e.g., x50 describes a particle diameter corresponding to 50% of the cumulative undersize distribution).

A typical setup for a laser diffraction instrument is shown in Figure 1.

Fig. 1. Typical setup for a laser diffraction instrument.

A representative sample, dispersed at an adequate concentration, is passed through the light beam in a measuring zone by a transporting fluid (gas or liquid); this measuring zone should be within the working distance of the lens used. In some cases the particle stream in a process is illuminated directly by the laser beam for measurement, as in the case of sprays, aerosols, and air bubbles in liquids. In other cases (such as emulsions, pastes, and powders), representative samples can be dispersed in suitable liquids. Often dispersants (such as wetting agents or stabilizers) or mechanical forces (such as agitation or ultrasonication), or both, are applied to deagglomerate particles and to stabilize the dispersion. For these liquid dispersions, a recirculating system is most commonly used, consisting of an optical measurement cell, a dispersion bath (usually equipped with stirrer and ultrasonic elements), a pump, and tubing.

Dry powders can also be converted into aerosols through the use of dry powder dispersers, which apply mechanical forces for deagglomeration. In this case, a dosing device feeds the disperser with a constant mass flow of sample. The disperser uses the energy of compressed gas or the differential pressure to a vacuum to disperse the particles. It outputs an aerosol that is blown through the measuring zone, usually into the inlet of a vacuum pipe that collects the particles.

There are two positions in which the particles can enter the laser beam. In the conventional case, the particles enter the parallel beam before and within the working distance of the collecting lens. In the so-called reversed Fourier optics case, the particles enter behind the collecting lens, and thus in a converging beam.

The advantage of the conventional setup is that a reasonable path length for the sample is allowed within the working distance of the lens. The second setup allows only small path lengths but enables measurement of scattered light at larger angles, which is useful when submicron particles are present.

The interaction of the incident light beam with the dispersed particles results in a scattering pattern with different light intensities at various angles. The total angular intensity distribution, consisting of both direct and scattered light, is then focused by a positive lens or an assembly of lenses onto a multi-element detector. The lens(es) provide(s) for a scattering pattern which, within limits, is not dependent upon the location of the particles in the light beam. Thus the continuous angular intensity distribution is converted into a discrete spatial intensity distribution on a set of detector elements.

It is assumed that the recorded scattering pattern of the particle ensemble is identical to the sum of the patterns from all individual single scattering particles presented in random relative positions. Note that only a limited angular range of scattered light is collected by the lens(es), and thus by the detector.

Prepare a representative sample of suitable volume for the measurement by an adequate sample splitting technique.

Sprays, aerosols, and gas bubbles in liquid should be measured directly, provided that their concentration is at an appropriate level, since sampling or dilution is generally impossible without altering the particle size distribution.

The dispersion procedure is adjusted to the purpose of the measurement: for example, whether agglomerates should be detected or broken down to primary particles.

For the development of a method, it is necessary to check that comminution of the primary particles does not occur, and conversely that a good dispersion of the agglomerates has been achieved. The dry particles may be examined microscopically before and after the addition and dispersion of aliquots of the dispersing liquid to determine if the particle size has changed, and if the agglomerates are dispersed but the primary particles are not fractured. The effect of the dispersion process can usually be checked by changing the dispersing energy and monitoring the change of the size distribution. The measured size distribution does not change significantly if the sample is well dispersed and the particles are neither fragile nor soluble. Microscopy may also be used to investigate primary particle comminution and adequacy of dispersion.

Dispersion Liquids

• be transparent at the laser wavelength and free from air bubbles or other particles,
• be compatible with the materials used in the instrument (O-ring, tubing, etc.),
• not dissolve or alter the size of the particulate materials,
• favor easy and stable dispersion of the particulate material,
• have suitable viscosity to enable calculation,
• have a refractive index that differs from that of the material (for the Mie calculation), and
• not be hazardous to health and meet safety requirements.

Dispersion Gases

Concentration

Setting Up the Instrument and Blank Measurement

Measurement of the Scattering of Dispersed Sample(s)

Selection of an Appropriate Optical Model

Conversion of Scattering Pattern into Particle Size Distribution

Replicates

System Suitability

Reporting of Results

Calibration

Accuracy and Repeatability