Introduction

The laser diffraction technique has evolved such that it is now a dominant method for determination of particle size distributions (PSDs). The success of the technique is based on the fact that it can be applied to a wide variety of particulate systems. The technique is fast and can be automated, and a variety of commercial instruments is available. Nevertheless, the proper use of the instrument and the interpretation of the results require the necessary caution.

Since ISO 13320-1:1999 was first published, the understanding of light scattering by different materials and the design of instruments have advanced considerably. This is especially marked in the ability to measure very fine particles. Therefore, it was replaced with the first edition of ISO 13320 in 2009, and since then the method has been developed for a wider application. Additionally, demands raised recently not only on establishment of accuracy of measurements but also on necessity of evaluation of the accuracy and of qualification of instrument by users. Therefore, this document incorporates the most recent advances in understanding.

Abstract

This document provides guidance on instrument qualification and size distribution measurement of particles in many two-phase systems (e.g. powders, sprays, aerosols, suspensions, emulsions and gas bubbles in liquids) through the analysis of their light-scattering properties. It does not address the specific requirements of particle size measurement of specific materials.

This document is applicable to particle sizes ranging from approximately 0,1 µm to 3 mm. With special instrumentation and conditions, the applicable size range can be extended above 3 mm and below 0,1 µm.

For spherical and non-spherical particles, a size distribution is reported, where the predicted scattering pattern for the volumetric sum of spherical particles matches the measured scattering pattern. This is because the technique assumes a spherical particle shape in its optical model. For non-spherical particles the resulting particle size distribution is different from that obtained by methods based on other physical principles (e.g. sedimentation, sieving).

Principle

The laser diffraction or scattering technique1) for the determination of particle size distributions, PSDs, is based upon the phenomenon that the angular distribution of the intensity of scattered light by a particle (scattering pattern) is dependent on the particle size. When the scattering is from a cloud or ensemble of particles the intensity of scattering for any given size class is related to the number of particles and their optical properties, present in that size class. 

A test sample, dispersed at an adequate concentration in a suitable liquid or gas, is passed through the beam of a monochromatic light source, usually a laser. The light scattered by the particles, at various angles, is measured by an array of photo detectors. The numerical values from each detector are recorded for subsequent analysis. Within certain limits, such as of particle concentration in measuring zone, the scattering pattern of an ensemble of particles is identical to the sum of the individual scattering patterns of all particles. The theoretical scattering patterns of unit volumes of particles in selected size classes are used to build a matrix and together with a mathematical procedure are used to solve the inverse problem, providing a volumetric particle size distribution (PSD), iterated to provide a best fit to the measured scattering pattern.

Theory

The theoretical scattering pattern of a single spherical homogeneous particle is given by Mie-theory in general. If the particle size is relatively large (in terms of size parameter, α = π × nm/λ > 10) and is opaque, Fraunhofer diffraction theory is available only for small angle forward scattering. The Fraunhofer approximation is an analytical method that does not require the optical properties of the material.

Some other theoretical approximations are available for numerical realization of the Mie-theory, and these are called optical models in general. Choosing a relevant optical model for the inverse problem to yield a proper PSD is important.

Laser diffraction records the scattering pattern from the particles presented. This composite pattern is converted to a size distribution of spherical particles that would provide the same composite scattering pattern using an appropriate optical model and data inversion routine. It therefore provides a size distribution of laser diffraction equivalent spheres. If the test sample is not spherical, the same basic procedure is used and the resulting size distribution is formed. Thus, PSD’s for non-spherical particles are likely to be different from other particle sizing techniques measuring the same material. The details of the theory are given in Annex A.

Typical instrument and optical arrangement

The system consists of a monochromatic light source, sample feeder, optical system, light detectors, and control-calculation device. To extend the applicable range of particle size and its analysis, multiple light sources, additional light detecting systems and related optical systems can be used.

The light source is typically a laser or other narrow-wavelength source to generate a monochromatic beam. This is followed by a beam-processing unit producing an extended and nearly ideal, Gaussian distributed beam to illuminate the dispersed particles. The illuminating light beam passes through the measuring zone of the optical system.

A computer is used to control the measurement, to store and to process the data, and to solve the inversion problem from the data of the detected signals to the particle size distribution. It may provide automated instrument operation.

Typical diagrams of the set-up of laser diffraction/scattering instruments are given in Figures 1 to 4.

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