Introduction

Particle size analysis in the submicrometre size range is performed on a routine basis using the dynamic light scattering (DLS) method, which probes the hydrodynamic mobility of the particles. The success of the technique is mainly based on the fact that it provides estimates of the average particle size and size distribution within a few minutes, and that user-friendly commercial instruments are available. Nevertheless, proper use of the instrument and interpretation of the result require certain precautions.

Several methods have been developed for DLS. These methods can be classified in several ways:

a) by the difference in raw data acquisition (autocorrelation, cross-correlation and frequency analysis);

b) by the difference in optical setup (homodyne versus heterodyne mode);

c) by the angle of observation.

In addition, instruments show differences with respect to the type of laser source and often allow application of different data analysis algorithms (e.g. cumulants, NNLS, CONTIN, etc.).

Scope

This document specifies the application of dynamic light scattering (DLS) to the measurement of average hydrodynamic particle size and the measurement of the size distribution of mainly submicrometre-sized particles, emulsions or fine bubbles dispersed in liquids. DLS is also referred to as “quasi-elastic light scattering (QELS)” and “photon correlation spectroscopy (PCS),” although PCS actually is one of the measurement techniques.

This document is applicable to the measurement of a broad range of dilute and concentrated suspensions. The principle of dynamic light scattering for a concentrated suspension is the same as for a dilute suspension. However, specific requirements for the instrument setup and specification of test sample preparation are required for concentrated suspensions. At high concentrations, particle-particle interactions and multiple light scattering can become dominant and can result in apparent particle sizes that differ between concentrated and dilute suspensions.

Principle

Particles suspended in a fluid are in constant Brownian motion as the result of the interaction with the molecules of the suspending fluid. In the Stokes-Einstein theory of Brownian motion, particle motion of smooth spheres at very low concentration is determined by the suspending fluid viscosity and temperature, as well as the size of the particles. Thus, from a measurement of the particle motion in a fluid of known temperature and viscosity, the particle size can be determined.

The DLS technique probes the particle motion optically. The suspended particles are illuminated with a coherent monochromatic light source. The light scattered from the moving suspended particles has a time-dependent phase imparted to it from the time-dependent position. The time-dependent phase of the scattered light can be considered as either a time-dependent phase shift or as a spectral frequency shift from the central frequency of the light source. Measured over time, random particle motion forms a distribution of optical phase shifts or spectral frequency shifts. These shifts are determined by comparison either with all scattered light (homodyne or self-beating mode) or by using a portion of the incident light as reference (heterodyne mode). Regardless of the setup, the optical signals received from the particles are related to the scattering efficiency of the particles and are thus scattered intensity-weighted.

Sedimentation of particles, dependent on their density, sets an upper limit to the particle size that can be assessed by the technique; typically, the upper limit is much less than 10 μm. DLS was developed for static suspensions. Provided that orthogonal flow and observation axes are adopted, flowing samples may, under some circumstances, be measured if the procedure is properly validated (see Annex C).

Different modes of diffusion, particle-particle interaction, multiple scattering and fluorescence can significantly influence the apparent particle diameter calculated from a DLS experiment. Annex B should be consulted.

Apparatus

A typical apparatus consists of the following components:

6.1 Laser, emitting coherent monochromatic light, polarized with its electric field component perpendicular to the plane formed by the incident and detected rays (vertical polarization). Any kind of lasers may be used, e.g. gas lasers (He-Ne laser, Ar-ion laser), solid-state lasers, diode-pumped solid-state lasers and laser diodes.

6.2 Optics, lenses and equipment used to focus the incident laser light into a scattering volume and to detect scattered light. Optical fibres are often used as a part of the detection system and for lightdelivering optics.

The use of a coherent optical reference allows using interference between the scattered light and the reference to measure the frequency shift of the scattered light. Two methods of referencing are commonly used and are illustrated in Figures 1 a) and b).

— In homodyne detection (also referred to as “self-beating detection”) [Figure 1 a)], the mixing at the optical detector of all of the collected scattered light provides the reference for frequency- or phasedifference measurement.

— In heterodyne detection [Figure 1 b)], the scattered light is mixed with a portion of the incident light. The unshifted incident light provides the reference for the frequency- or phase-difference measurement.

NOTE In DLS, “heterodyne” is understood as mixing of scattered light with unscattered light from the same source. This convention differs from, for example, the use in optical interferometry. 

— In a cross-correlation setup [Figure 1 c)], two homodyne scattering measurements are performed simultaneously in such a way that the two scattering vectors and scattering volumes are the same, but the corresponding wave vectors are not coincident. These two laser beams produce two correlated fluctuation patterns. The correlation is not perfect, since on the one hand, both detectors collect light from the other scattering experiment, and on the other hand, multiply scattered light of the incoming laser beams is totally uncorrelated. The two contributions of the multiply scattered light to the detector signal, however, do not contribute to the time-dependent signal but to an enhanced background.

6.3 Test sample holder, allowing fluctuations of the sample temperature to be controlled to within ±0,3 °C. While precise knowledge of the sample temperature is required for evaluation, it is not necessary to regulate the temperature to any defined value.

6.4 Photodetector, with an output that is proportionally related to the intensity of the collected scattered light. A photomultiplier tube or an (avalanche) photodiode is typically used. Detectors can be placed at any angle. Data collection can be performed in a linear or logarithmic manner.

6.5 Signal processing unit, capable of taking the time-dependent scattered light intensity signal and outputting the autocorrelation function, cross-correlation function or power spectrum of the input signal. This correlation can be performed by hardware and/or software correlators, operating linearly, logarithmically or in a mixed mode.

The resulting output from either mode contains a distribution of characteristic frequencies or timedependent phases representative of the particle size of the suspended particles. Photon detection has a probability distribution of photon arrival times, which means that a fluctuating signal is obtained even if the intensity of the incident light is constant. The intensity of the photons arriving at varying time intervals is superimposed on this already fluctuating signal. In correlation analysis, the uncorrelated signal is constant, whereas the signal associated with the diffusing particles decays exponentially.

In spectrum analysis, the uncorrelated signal is akin to a DC or zero frequency term which is not recorded. The time-dependent component is analysed to determine the particle-size distribution using the theory of DLS.

6.6 Computation unit, capable of signal processing to obtain the particle size and/or particle size distribution. Some computation units also function as the signal processing unit.

— Evaluation via the autocorrelation function allows determination of a mean diameter without determination of the particle size distribution, but determination of the distribution is also possible.

— Evaluation via the frequency distribution determines the particle size distribution using the power spectrum of the signal.

— Evaluation via photon cross-correlation allows quantification/minimization of the effects of multiple scattering, thus extending the useful concentration range towards higher concentrations (however, the effect of particle-particle interaction cannot be eliminated). The disadvantage of this method is that it requires a more complex optical setup.

6.7 Instrument location, placed in a clean environment, free from excessive electrical noise and mechanical vibration and out of direct sunlight. If organic liquids are used as the suspension medium, there shall be due regard to local health and safety requirements, and the area shall be well ventilated.

The instrument shall be placed on a rigid table or bench to avoid the necessity for frequent realignment of the optical system.

WARNING — DLS instruments are equipped with a low- or medium-power laser whose radiation can cause permanent eye damage. Never look into the direct path of the laser beam or its reflections. Ensure highly reflecting surfaces are not in the path of the laser beam when the laser is on. Observe local regulations for laser radiation safety.

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