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The author examines the process of method development, with reference to ISO 13320:2009 and relevant monographs from the United States and European pharmacopoeias.
Particle size is a critical quality attribute for a diverse array of pharmaceutical products, from topical ointments to powders for pulmonary delivery. During recent decades, the unique attributes of laser-diffraction analysis have positioned it as the particle-sizing technique of choice for the resulting spectrum of pharmaceutical applications. Fast, nondestructive and suitable for a broad size range (0.1 to 3000 μm), laser diffraction lends itself to full automation. As a result, for many routine users, particle-size measurement is now simply a matter of loading the sample and pressing a button. However, streamlining measurement to this degree demands the development of a robust secure method that will consistently deliver reliable and reproducible data. This process is given considerable emphasis in the International Organization for Standardization's (ISO) 13320:2009 standard for laser diffraction released at the end of 2009, reflecting that understanding of this technique among industry has grown significantly during the past decade (1). There is a wealth of information to support method development, the success of which depends on a rigorous and systematic examination of the factors known to influence results.
The principles of laser diffraction
Understanding the basic principles of laser diffraction is essential for successful method development. Laser diffraction is an ensemble particle-sizing technique, which means it provides a result for the whole sample, rather than building up distributions from data for individual particles, in the way that, for example, image analysis or microscopy does. Particles illuminated in a collimated laser-beam scatter light over a range of angles. Large particles generate a high scattering intensity at relatively narrow angles to the incident beam, while smaller particles produce a lower intensity signal but at much wider angles. Using an array of detectors, laser-diffraction analyzers record the pattern of scattered light produced by the sample.
With the application of an appropriate model of light behavior the particle-size distribution of the sample can be determined from the scattering data, via a deconvolution step. The Mie theory and the Fraunhofer approximation (of Mie theory) are used routinely. ISO 13320:2009 provides a detailed description of both models but confirms Mie as the method of choice, especially for measurements across a wide dynamic range. The two models return similar results for large particle sizes, but Mie offers improved accuracy for finer materials. Furthermore, the inaccuracies that arise from the use of Fraunhofer are unpredictable. Both models assume that the measured particles are spherical, so for nonspherical samples the size distribution returned is one that is based on spherical equivalence.
Method development involves addressing the wider set of practical issues that flow from this underlying explanation of the basic principles of operation. United States Pharmacopeia (USP) General Chapter <429> states that laser diffraction involves the measurement of "a representative sample, dispersed at an adequate concentration in a suitable liquid or gas" (2). This statement neatly highlights three crucial aspects of laser-diffraction analysis: sampling, dispersion, and measurement conditions.
Obtaining a representative sample from a larger bulk is a major challenge with any kind of laboratory-based particle characterization technique. Sampling issues generate the greatest errors in laser-diffraction analysis, especially when measuring large particles or when the specification is based on size parameters close to the extremes of the distribution, such as the Dv95 (the particle size below which 95% of the volume of particles exists). This is because laser diffraction, as a volume-based technique, is extremely sensitive to small changes in the amount of coarse particles within the selected sample. ISO 13320:2009 expressly discourages the use of specifications based on the Dv100 for this reason. The effect of sampling on reproducibility increases with particle size and the width of the distribution, as the volume of sample required to ensure representative sampling of the coarse particle fraction increases. For this reason, it may be necessary to measure a large sample (often greater than 1–2 g) to ensure reproducible results. For wet-dispersion measurements, this will require the use of a large dispersant volume, to ensure the concentration of material is within the required range for accurate measurements (i.e., to ensure multiple scattering is avoided). A detailed discussion of sampling is beyond the remit of this paper, but ISO 14488 provides an extremely useful summary of the requirements for sampling during particle characterization studies (3).
Laser diffraction is suitable for the analysis of a wide array of sample types, but it is essential to appropriately tailor the sample-preparation method. For sprays, aerosols, and gas bubbles in solution, USP <429> strongly discourages sample preparation, or indeed sampling, because of the difficulty of imposing either step without skewing the measured particle-size distribution. Laser diffraction instruments designed specifically for the analysis of sprays have much to offer here, being able to measure relatively concentrated sprays directly.
For other sample types, there is a choice to be made between wet and dry dispersion. Influencing factors include the natural state of the sample, the ease with which it can be dispersed and the volume of sample to be measured. Where the sample is dry powder, dry dispersion may present the simplest option, but there are several reasons why wet measurement may be preferred. These include:
Because wet dispersion is appropriate for so many samples, it is the method most widely used for laser diffraction measurement.
A further issue to consider alongside the choice of dispersion method is: What should be the goal of the dispersion procedure? While it is the primary particle size of an active ingredient for a tablet blend that will influence its in vivo dissolution and consequent bioavailability, for instance, in other applications, the particle size of agglomerates may be more relevant. A good example of this is the study of suspension stability where, if particles are prone to agglomeration, it is agglomerate size that will control sedimentation rates.
Factors to address in the development of a robust wet dispersion include dispersant choice, conditions for stable dispersion, and sample concentration. The aim is to reliably produce a stable, representative dispersion of suitable concentration for measurement.
Dispersant choice. The dispersants used in laser-diffraction measurement range from highly polar water to very nonpolar long-chain alkanes and alkenes (see Table I). A candidate dispersant should:
Table I: Dispersants in order of polarity.
The dispersant must also be able to wet the sample. Wetting can be assessed by mixing sample and dispersant in a beaker and observing the resulting suspension. A uniform suspension is indicative of good wetting; sedimentation of the sample on the base of the beaker is undesirable. Wetting depends on the surface tension between the particles and dispersant and can, therefore, be modified through the use of surfactants. Other admixtures may also be beneficial, with the pH of the dispersant an important variable for systems having an iso-electric point (4). ISO 14887 is a useful source of further guidance for the dispersion of powders in liquids (5).
When characterizing emulsions, choosing a dispersant as close as possible to the continuous phase minimizes the risk of dissolution shock, which is the modification of droplet size by the dissolution process. Figure 1 contrasts the suitability of tap and de-ionized water for dispersing an example emulsion; 10 measurements were made with each system to assess dispersion stability in each case.
Figure 1: Contrasting emulsion stability in deionized and tap water. (ALL FIGURES ARE COURTESY OF THE AUTHORS)
With tap water, droplet size increases over time, a response attributed to flocculation. Deionized water prevents this and is therefore more suitable. These data highlight the importance of making repeat measurements to assess dispersion stability because initial measurements of particle size are almost identical, with differences becoming increasingly pronounced over time.
Optimizing conditions for stable dispersion. Energy input maintains a stable dispersion with the chosen dispersant. With wet dispersion, the sample is typically made up in a dispersion cell, which is essentially a feed vessel for the analyzer. Energy for dispersion comes from the agitator in this cell, from the pump that transfers the sample to the measurement zone, and from sonication if applied. Effective tuning of these three inputs ensures repeatable dispersion to a size appropriate to the application, avoiding primary particle breakup.
Both USP <429> and ISO 13320:2009 highlight microscopy as a useful tool for determining whether or not suitable conditions have been established. Particle imaging allows for the identification of agglomerates, and can be used to cross-validate the particle size range of the sample.
Figure 2 illustrates the progression of an agglomerated sample toward stable dispersion. Images show agglomeration when only the dispersion cell stirrer and pump are active; however, when ultrasound is applied particle size reduces to a stable level. The leveling of particle size suggests that primary particles are undamaged, and the results provide an indication of required sonication time. When the ultrasound is switched off, the stable dispersion persists, and image analysis confirms the presence of discrete primary particles.
Figure 2: Optimizing conditions for stable dispersion.
For certain types of samples, there are additional factors influencing dispersion conditions. With emulsions for example, excessively high agitation may shear emulsion droplets, in which case droplet size will decrease with increasing agitator speed. On the other hand, for samples containing coarser particles, higher agitator speeds may increase particle size by reducing the tendency to sediment. Finally, where particles have a high aspect ratio, certain agitator or pump speeds may cause flow alignment. Nonrandom alignment can affect the measured particle-size distribution, so this phenomenon should be carefully considered if samples fall into this classification.
Setting sample concentration. The ideal sample for laser-diffraction analysis is sufficiently concentrated to give a stable scattering signal but dilute enough to avoid the issue of multiple scattering. Multiple scattering occurs where the light interacts with more than one particle before being detected, and leads to an underestimation of particle size.
Obscuration is a measure of the percentage of emitted laser light that is lost by scattering or absorption. It is therefore indicative of sample concentration. Carrying out an obscuration titration and plotting particle size as a function of obscuration is an efficient way of identifying a concentration range for reproducible measurement, as Figure 3 illustrates. Data are shown for two samples: one with particles in the submicron region, the other with a Dv50 of > 30 μm.
Figure 3: Obscuration titrations for submicron and larger particle samples.
With the submicron-sized sample, particle size begins to decrease at obscurations above 5%, as multiple scattering begins to have an appreciable effect. For the sample containing larger particles, particle size is stable over a much wider obscuration range. Larger particles scatter light at relatively high intensity and narrow angles so measurement is less influenced by multiple scattering, and the signal-to-noise ratio is less of a challenge. Where larger particles are present, or the particle size distribution is particularly wide, concentration may be set on the basis of sampling requirements (as previously discussed).
Energy to disperse a dry sample is applied by entraining the powder in a compressed air stream. Similar to wet dispersion, the goal is to disperse to an application-relevant degree but no further; air pressure is the lever used to control energy input. ISO 13320:2009 notes that a "pressure/particle-size" titration should in the ideal case identify a region where particle size is nearly constant over a range of pressures, indicating that agglomerate dispersion has occurred without particle breakup. However, it makes clear that this is seldom observed, in which case it becomes important to reference dry results against wet measurements, to avoid breakup and/or milling of the primary particles.
Figure 4 (a) shows a pressure/particle-size titration for a relatively fragile material. Particle size decreases quite steeply as pressure is increased from 0 to 1 bar, but there is no way of telling simply by looking at this plot if this size reduction is the result of agglomerate breakup or the milling of primary particles. Figure 4 (b) shows that close agreement between wet results and dry data is achieved at a dispersion pressure of 0.2 bar, suggesting that pressures above this result in particle milling. As with wet dispersion, images of the particles can be useful in elucidating the effect of entrainment at different air pressures.
Figure 4: Method-development data for a fragile powder sample, (a) a pressure/particle-size titration, (b) a comparison of wet-dispersion data with dry results measured at a dispersion pressure of 0.2 bar.
Figures 5 (a) and (b) show strictly analogous data for a different material—a pharmaceutical powder. Here too, the pressure/particle size titration fails to plateau, giving an unclear indication of optimal air pressure. A comparison of data measured at 3 bar with those from a wet dispersion suggests that dispersion is inadequate—there are larger quantities of material toward the coarse end of the particle-size distribution. The dry results also show, however, a larger proportion of fines. Here then, dispersion and breakup occur simultaneously, rather than sequentially, making dry dispersion problematic. Further increasing the dispersion pressure will reduce the amount of agglomerated material present but will also increase particle damage. For this system, wet dispersion is a better option.
Figure 5: Method-development data for a pharmaceutical powder, (left) a pressure/particle-size titration, (right) a comparison of wet-dispersion data with dry results measured at a dispersion pressure of 3 bar.
The actual process of sample measurement involves recording the scattering pattern produced as the sample passes through the path of the laser. An initial background measurement captures scattering from the cell windows, any contaminant present and, in the case of wet measurement, the pure dispersant. This process assesses cleanliness and allows precise capture of the scattering pattern relating solely to the sample.
With a dry measurement, duration is set to ensure analysis of the entire sample to avoid analyzing an unrepresentative subsample. Obscuration limits can be set to prevent measurement when the powder density is too low to give a reliable signal-to-noise ratio, or, conversely so high that multiple scattering is likely.
For a wet dispersion, measurement duration can be specified to analyze just a small fraction of the sample, or, at the other extreme, to repeatedly measure the same sample, because material being measured can be recirculated through the measurement cell many times. Excessively long measurement times are inefficient but an overly short measurement time may give unrepresentative data, especially if the sample contains coarser particles and/or the distribution is broad, as illustrated by Figure 6. For this sample, the poor repeatability and smaller particle size recorded at low measurement times are attributable to insufficient sampling of the large particles, an issue resolved by extending measurement duration.
Figure 6: Results of tracking Dv90 and measurement variability as a function of measurement duration.
When assessing the validity of measured results and determining whether a defined procedure and associated system are fit for purpose, two concepts are central: repeatability and reproducibility. Assessing repeatability involves duplicate measurements of the same sample. It therefore tests the precision of the instrument and the consistency of the sample. Reproducibility is a broader concept that also encompasses sampling from the bulk.
One aspect of repeatability is the performance of the analyzer. ISO13320 (2009) provides revised accuracy acceptance criteria for performance verification, which typically involves measurement of an appropriate standard. Because laser diffraction is a volume-based measurement technique, sampling errors for large particles will cause greater uncertainty in the Dv90 than in the Dv10. The revised acceptance criteria for reference materials reflect this and are:
To test repeatability for a given application, duplicate measurements of the same sample are performed. The precision of laser diffraction measurements is usually assessed using the term coefficient of variation (%COV) which is defined according to the following equation (1):
ISO 13320:2009 states that repeatability tests should show a %COV of less than 3% on Dv50 and below 5% for Dv10 and Dv90 but indicates that these values can be doubled for samples containing particles smaller than 10 μm, because of the difficulties of dispersion. In ideal conditions, however, much better performance is readily achievable: a %COV of less than 0.5% for samples larger than 1 μm and below 1% for samples finer than this, is realistic.
Reproducibility is assessed by measuring several samples from the same batch of material and therefore tests how representative the sampling procedure is. Both USP and the European Pharmacopoeia recommend acceptance criteria for reproducibility testing of a %COV of less than 10% on Dv50 or any similar central value and less than 15% on values toward the edge of the distribution such as Dv10 and Dv90 (2, 6). Once again, these limits are doubled for samples containing particles smaller than 10 μm.
The highly valued simplicity of routine laser-diffraction measurement belies the relative complexity of method development. During the last decade, considerable progress has been made toward securing a comprehensive understanding of how best to define measurement methods for laser-diffraction analysis and implement them. The new ISO standard and relevant chapters of the USP and the European Pharmacopoeia provide useful summaries of the significant guidance now in place. Instrument manufacturers recognize that helping users to access all available information—through education, direct support and smarter software—is the way to maximize the benefits of this vital analytical technique.
Anne Virden is a product technical specialist in diffraction at Malvern Instruments, Enigma Business Park, Grovewood Road, Malvern, Worcestershire, WR14 1XZ, UK, tel. +44 (0)1684 892456, fax + 44 (0)1684 892789, firstname.lastname@example.org.
1. ISO 13320:2009 Particle Size Analysis—Laser Diffraction Methods. Part 1: General Principles (2009).
2. USP30–NF25 General Chapter <429>, "Light Diffraction Measurement of Particle Size," pp. 1235–1241.
3. ISO 14488:2007 Particulate materials—Sampling and sample splitting for the determination of particulate properties.
4. Application note MRK373: The Use of Zeta Potential Measurements for Improving Dispersion During Particle Size Measurements, www.malvern.com/appnote_particle_size_determination, accessed Sept. 18, 2010.
5. ISO 14887:2000 Sample Preparation—Dispersing procedures for powders in liquids (2000).
6. Ph.Eur. 6.6 General Chapter 2.9.31, "Laser Diffraction Measurement of Particle Size," (EDQM, Strasbourg, France) p. 5103.