Procedures to be followed for particle size determination by laser light diffraction instruments are to a great extent specific to the instrument being used and are usually very well defined by the manufacturer. The procedures are designed to work best with the algorithms used in the instrument and are optimized for the instrument set-up. As a result, these procedures vary from one instrument to another. This also requires a fair amount of work by the user to find the set of parameters (e.g., real and imaginary components of refractive index, solids loading, signal collection time) that appears to work best for that instrument. However, irrespective of the instrument being used there are certain general procedures that can be adopted in order to minimize various systematic errors. Some of these general procedures are discussed in this section. Figure 1 shows the general steps involved in the determination of the particle size and size distribution of a powder system by laser light scattering.

1. Sampling

Powder sampling is conducted in a manner which ensures that the specimen being examined is representative of the entire batch. While most laser diffraction instruments are set up for batch samples, there are numerous instruments that are set-up for on-line sampling or have accessories that can sample from an on-line stream. An example of an on-line sampling system would be the use of laser diffraction instruments in a cement production plant where tight control of the powder size during grinding operations is desired. In such instances, wherever practical, the guideline of sampling the entire stream for some time, rather than the some of the stream all the time, should be practiced. In case of batch samples, it should be ensured that the specimen is representative of the powder system under study.

Flowchart Indicating Steps Involved in Particle Size Determination by Laser Light Diffraction Technique

2. Dispersion and Homogenization

The state of the powder being sampled also plays a role in deciding the sampling procedure to be used. Flow of dry powders may be significantly different from that of powders dispersed in a liquid. Powders in both cases may segregate in the case of a broad size distribution causing some size fractions to be present in a non-representative manner. Agglomeration of these powders may be observed depending upon the surface characteristics of these powders and the stability of the dispersions. Sampling procedures that are followed should take into account these factors. Development of suitable dispersion procedures during or immediately prior to the analysis helps ensure that powders are well dispersed and agglomeration is minimized. Most instruments are designed for analyzing samples dispersed in fluids such as water or isopropanol or other low hazard fluids. Instruments have special cells designed for flammable liquids or explosive vapors. Accessories may be available from the instrument manufacturer for analysis of powders in a dry state, obviating the need for dispersion in a fluid. While using such an accessory it is still essential to ensure that the powders are not agglomerated and particle-particle bridging is minimized. Procedures recommended by the manufacturer should be followed in such instances. Additional procedures to prevent agglomeration or segregation may be designed and implemented by the user.

Ensuring a good degree of dispersion prior to sample analysis is an important step to ensure reliable and reproducible size analysis. Due to the inability of the instrument to distinguish between agglomerates and primary particles, this process can help reduce some bias and other systematic errors in the calculated powder size distribution. Sample dispersion can be achieved by numerous methods including ultrasonication, milling, pH stabilization, addition of dispersion agents, etc. Regardless of the technique followed, it is critical to ensure that the process of dispersion does not lead to creation of stable air bubbles, fracture of brittle particles or agglomeration. The occurrence of any of these will lead to skewed particle size distribution results. The use of ultrasonic probes to disperse powders is well suited for this technique due to the small quantities of sample powders needed for analysis. While ultrasonication does lead to dispersion, the specimens may still need to be stabilized in such a state by either controlling the pH of the suspension or adding dispersion agents. After stabilization, it is preferable to keep the suspension agitated to prevent any settling or agglomeration. Instrument manufacturers are making available ultrasonic kits that can be attached to the specimen chamber to ultrasonicate the specimens prior to analysis.

Important factors that are to be considered for determining ultrasonication parameters are the ultrasonication duration, energy, diameter of the probe/horn and coupling between horn and sample. Time and power output to be used for ultrasonication are dictated by the nature of the material being dispersed. Ultrasonication duration can extend from a few seconds to a few minutes. Ultrasonication should be carried out until no further reduction in particle size distribution is observed. In some instances, this might call for ultrasonication durations of a few minutes. For systems that tend to generate heat upon ultrasonication for such lengths of time, the energy can be applied in fractional duty cycles (e.g., 50 % on and 50 % off during the duty cycle), or the beaker containing the sample being ultrasonicated can be placed in an ice bath. Close attention should be paid to the nature of the coupling observed between the ultrasonic probe and the sample. The nature of the coupling defines the efficiency of power transfer from the probe to the material system. The depth of the probe into the sample influences the coupling. It has been observed that glass beakers provide better reflection of ultrasonic energy and thus lead to better coupling than polystyrene beakers. Determination of ultrasonication parameters is mostly by a trial-and-error process, designed to ensure minimization of the particle size distribution, without causing fracture of the primary particles.

Figures 2 and 3 (studies at NIST) indicate the need to create and maintain stable dispersions for particle size analysis by laser diffraction. Figure 2 shows the influence of the duration of ultrasonication on a suspension of nominally 1 um spherical SiO2 powder system. The specimens were ultrasonicated for 15 s, 1 min, 3 min and 6 min and then stabilized at a pH value of 8. The graph represents the observed size distribution (d10 , d50 or median size and d90 ) and a measure of the mean size as a function of ultrasonication duration. A significant difference is observed upon increasing the ultrasonication duration from 15 s to 1 min. Ultrasonication for 3 min causes a small reduction in the mean particle size and size distribution. Ultrasonication for 6 min does not produce any significant improvement in the results. However, ultrasonication for 6 min causes significant heating of the suspension. Thus, excessive ultrasonication may cause changes in the physical and chemical state of the powder system being analyzed. From this information, ultrasonication duration of 3 min was chosen to be the desired value for this material system.

Figure 3 shows the change in the measured size of a nominally 1 um spherical SiO2 powder system that has been ultrasonicated for 3 min. at 30 W and adjusted to different pH levels prior to size analysis by laser diffraction. As this powder system has an i.e.p near 2.5, it is expected that the particles will agglomerate at pH values close to the i.e.p and be well dispersed at pH values further away from the i.e.p. Thus, at low pH values of the dispersion, the measured mean and median sizes are significantly larger than the expected values. At higher pH values this size is closer to the expected value. Furthermore, the associated uncertainty in the measured value is significantly higher at lower pH values. Each point represents the average value of 3 sets of measurements.

After dispersing the powders, it is essential to ensure that the dispersions are stabilized in such a state. Stabilization is usually achieved by addition of suitable additives to the dispersion. Controlling pH by addition of a suitable acid or base to keep the pH of the dispersion well away from the i.e.p of the system constitutes a technique of electrostatic stabilization. Addition of suitable deflocculants to physically prevent the coagulation of particles is known as steric stabilization. Some polyelectrolytes often used as deflocculants include sodium polyacrylate, ammonium polyacrylatae, sodium silicate, sodium carbonate, tetrasodium pyrophosphate, sodium polysulfonate and ammonium citrate. For milling techniques of size reduction and dispersion, it is desirable to use polyelectrolytes with short polymeric chains. This prevents damage to the polymeric chains during the milling operations, which would reduce the efficacy of the deflocculant.

Figure 2. Influence of Ultrasonication Duration Upon Particle Size Distribution, Measured by a Laser Diffraction Instrument

Figure 3. Graph Representing Variation in Measured Size of Nominally 1 um SiO2 Powder System After Ultrasonication and Stabilization at Varying pH Levels

3. Optical Alignment and Other Instrument Checks

Other general procedures to be followed prior to analysis include ensuring optical alignment and establishing a background or threshold signal level. It is absolutely critical to perform these procedures as any deviations will lead to significant errors in the calculated results. Optical alignment includes corrections in vertical, horizontal or angular positions of the laser source, the optical elements including lenses and the sample cell and the detector arrays so that the incident beam is aligned with the optic axis of the instrument. Loss of alignment occurs primarily due to ambient vibrations transmitted through the structures such as laboratory benches, tables, etc., and those introduced during the sample pumping process. Alignment procedures are instrument-specific and clearly defined by the instrument manufacturer. In some cases, the alignment procedure may require manual intervention by the operator, or may be conducted electronically with minimal operator intervention.

4. Background Signal Collection and Determination of Obscuration Levels

A background signal or threshold should be obtained immediately after optical alignment. By obtaining a background signal the current levels at each detector element in the absence of diffracted light is established. When analyzing a specimen, the current signals at the detector due to diffraction are compared with those determined during the background scan. Furthermore, the intensity of the laser beam in the absence of a specimen is determined during the background scan. By comparing the signal intensity of the laser beam without any sample present to the signal intensity with a specimen loaded in the sample cell, the obscuration level (extent of attenuation of incident beam intensity due to presence of particles) can be calculated.

Obscuration values are required to calculate the sample concentration present in the specimen. Most instruments are designed to operate within a particular obscuration value range. Means to determine whether the sample loading is within this range are specified by the instrument manufacturer. This includes either a number range or a bar graph specific to that instrument. Higher particle concentrations that may cause high levels of obscuration can lead to multiple scattering, while low solids loading corresponding to low levels of obscuration may cause inadequate signal strength at the detector elements. The impact of changes in the obscuration level on the determined particle size distribution is a function of the particle system being studied, the optical model used, and the algorithm used for deconvolution and inversion. Figure 4 (studies at NIST) indicates the effect of varying obscuration levels on the calculated particle size distribution of a nominally 1 urn SiO2 powder system. In the case of the instrument used in this study, the manufacturer recommended range indicates obscuration levels of 7 % to be low and 13 % to be high. An obscuration level of 10 % is in the middle of the range specified for the instrument. As is observed there are small differences in the calculated size distribution at these varying obscuration levels. Though the observed differences are small for the quoted example, these difference can be significant for other material systems.

Figure 4. Effect of Varying Obscuration Levels on Calculated Particle Size Distribution of Nominally 1.0um SiO2 Powder System

5. Sample Analysis

In numerous cases, the results of the particle size analysis are only as good as the optical model chosen to interpret and convert the diffraction pattern into particle size distributions. Instruments are set up to enable the user to select from a predetermined set of optical models. These optical models are usually a combination of values representing the real and imaginary components of the refractive index of the material being analyzed. In some instruments, the user may be asked to make some selections about the expected shape and width of the size distributions. Some instruments allow the operator to create optical models based on their choice of real and imaginary components of the refractive indices. Instruments that are designed for size analysis of powders coarser than about 2 um may not have these requirements, as the algorithms in these instruments are based on a Fraunhofer diffraction model and thus totally independent of material properties. Figure 5 (studies at NIST) shows how changes in optical models can create significant changes in the calculated particle size distribution. The graphs show the powder size distribution of a hydroxyapatite powder system represented as a differential volume distribution. The five curves represent size distribution results calculated using different optical models including the Fraunhofer model, labeled as such. The remaining four graphs are based on Mie models, and in this case the real component of the refractive index of the powders was reliably determined to be 1.63. However, there was some  uncertainty about the correct value for the imaginary component. As is observed, significant differences are observed in both the shape and magnitude of size distribution depending upon the refractive index value chosen. For imaginary values of and 0.01, the lower range of the distribution is calculated to be in the vicinity of 1 um. For the Fraunhofer model and the Mie models with imaginary components of 0.1 and 1.0, the lower range is found to be smaller than 0. 1 um. The choice of the "correct model" in this case has to be made with the aid of other techniques, such as microscopic determination, that would enable a direct examination of the powder system.

Figure 5. Influence of Optical Model on Calculated Particle Size and Size Distribution

6. Data Output and Post-Processing

Particle size distribution results are typically expressed as a function of the equivalent spherical diameter. This is based on the assumption of spherical particles giving rise to the diffraction process. Size distributions are typically expressed on a volume basis. This basis though not always accurate does simplify matters to a great extent. A very precise representation would require the distribution to be expressed on the scattering cross-sectional area basis. If the particles are spherical or are assumed to be so, then the volume representation can be easily converted to a cross-sectional area, and vice versa. Size distributions can also be expressed in terms of a number or surface area basis, but it should be remembered that such expressions are derived from the volume basis. Thus, any deviations from the spherical nature of the powders will introduce significant error and/or bias in the particle size distribution representation. For these very reasons, when reporting size distributions in a quantitative manner (e.g., using the mean value and the d10, d50 and d90 values), these numbers should be calculated from the volume basis distribution graph.

It is a good practice to represent the results of the particle size distribution as both a cumulative finer than and fraction distribution graph as a function of the observed particle size. This enables the user to observe the nature of the distribution (unimodal, bimodal, etc.) the fraction of the distribution in a particular size range of interest, and be able to determine the size corresponding to a particular fraction (d10, d50 or d90, etc.). Availability of this information enables conversion from one format or distribution (e.g., volume based distribution to mass based or number based distribution) to another with relative ease.