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out, the particles may be partially separated or more of less completely separated. The difference is crucial when high-resolution results are required. As a class, the fractionation techniques are relatively slow.


Ensemble averagers include Fraunhofer Diffraction (FD) and all forms of light scattering. The signal, from which the size distribution information is calculated, is a sum over all the signals from all the particles during the entire measurement. Thus, the results are an average over an ensemble of particles. As a class, ensemble averagers are fast, easily automated, and can be, at least in principle, put on-line. In general the resolution is, however, poor.


Weighting: A size distribution has two coordinates. The size, which is, most often, an equivalent spherical diameter, is plotted on the x-axis; and the amount in each size class, which is plotted on the y-axis. The amount is usually given as either the number or volume or mass of particles. If the particle density is the same for all sizes, then the volume and mass descriptions are equivalent.


Each particle sizing technique weights the amount observed differently. For example, light scattering on really small particles is weighted by the intensity of scattered light, which varies as the 6th power of the diameter. A few large particles can dominate the scattered light signal obscuring the presence of small particles. Electrozone techniques weight by the volume of the particle, which varies as the cube of the diameter.


Although it is a simple matter to write the equations for converting from one type of weighting to another, the results calculated this way are often in error. Perhaps some particles were not measured at all. Perhaps the measured distribution is significantly broader than the true distribution. Or, in the hybrid techniques, different ranges are weighted differently. In all these cases the errors in the transformed data are much exaggerated due to weighting.


Whenever possible use a particle sizing technique that gives the desired weighting without transformation. If absolute counts are needed, then get a single particle counter. If mass is important, then get an instrument that responds to mass. If a few particles in the tail of the distribution are important, then get an instrument that is capable of identifying these.


Information Content: The last major classification includes the amount of information required to solve a particular problem in particle sizing.


Frequently only a single number is required to answer a question in particle sizing. That number might be the average size or it might be a cumulative specification, such as 90% of the particles are less than a stated size. For quality assurance or process control, this single number may be sufficient. Techniques that give only a single number include the following: a turbidity measurement at one wavelength; end-point titration of the surface groups; and the Blaine test for large particles in a powder sample.


Sometimes a second number is required. Perhaps it is the width of the distribution (testing for monodispersity) or two cumulative sizes, for example the 90th and 10th percentile values (characterising the usefulness of rutile as a pigmenting agent). In the submicron range, DLS is a technique, which reliably yields a measure of the width as well as an average of the size distribution.


Additional size distribution information, often hard to come by reliably, might be the skewness of a single, broad distribution; the size and relative amounts of several peaks in a multi-peaked distribution; or the existence of a few particles at one extreme of the distribution. Where the distribution has several, closely spaced features, a high-resolution technique is necessary. More complete size distribution information is often required in the pigment and coatings industry.


Finally, a word of caution: Many of the modern methods of particle size analysis purport to give complete size distribution information. Often they don't. Computers are marvelous devices for storing, retrieving, and massaging data. With the exception of, perhaps, image enhancement, rarely can a computer improve resolution in particle sizing applications. That is the job of the basic technique.


First, there are theoretical limitations with any single technique. Diffraction is normally limited to sizes much larger than the wavelength of the light source. Sedimentation is limited at the high end by turbulence (large Reynolds numbers) and at the low end by diffusion. In fact, it is not hard to find the theoretical limitations in any technique. They lie either in the basic assumptions or in the resulting equations used to calculate the results.


Second, there are limitations associated with the implementation of the technique in practical instruments. To ensure a good dynamic signal response, the detectors in diffraction devices are located in such a way that the raw size classes are, typically, logarithmically spaced. This may mean that the last size class covers fully half the total size range. Accelerating a centrifuge is useful for speeding up the measurement, but it often broadens the real size distribution.


Third, there are limiting cases, which become, incorrectly, generalised to cover all types of samples. DLS is a useful technique for particles that remain suspended. Low density materials stay suspended long enough to make useful measurements, but high density materials may not. Colloidal gold can be measured with a centrifuge down to about 0.01 micron because of its high density. Colloidal polystyrene, whose density is very low, cannot be measured much below 0.05 micron using the same centrifuge. Diffusion makes the results suspect, and the measurement is painfully slow.


Fourth, there are limitations when subranges, or different techniques, are spliced together. Usually each subrange requires a change in something: a lens, an aperture and a speed of rotation. In principle this is possible. In practice it is difficult to splice distributions together without producing artifacts. These are often taken to be real by novices. Some manufactures use smoothing to hide these artifacts, yet this may then result in a significant loss of resolution. Different techniques use different weightings and are subject to different theoretical limitations, especially at their extremes. Yet it is at the extremes where they are spliced together.


Although instrument makers often claim they have the perfect, universally applicable instrument, the ‘zero to infinity’ machine, the vast majority are limited, in particular at the extremes of the size range.


Recommendation:


Estimate an average and a range for your particular problems. Have a few test measurements made to support your estimates. Look for an instrument that can cover the range without using the extremes claimed in the specifications. Choose an instrument that is suited to the task. There are no free lunches, and there are no zero-to-infinity particle sizers.


Specifying a Particle Sizer


Specifications are of two types: quantitative and qualitative. If you need to run 30 samples each day, then you have quantified a throughput specification. One example of a qualitative specification is ease-of-use.


Short lists of both types of specifications follow. The lists are by no mean definitive. They do, however, provide a good starting point for focusing on questions you will need to answer before an informed choice can be made.


Quantitative specifications: size range; throughput; accuracy; precision; reproducibility; and resolution.


Qualitative specifications: support; ease-of-use; versatility; and life cycle cost.


Size Range: Everyone wants the zero-to-infinity machine. It appears to solve lots of problems: only one instrument is required, now and for the future; less bench space is required; operator learning curves are reduced to one. Its universality is so appealing that zero-to-infinity machines are currently the rage. Witness the birth of the hybrid instruments. They combine more than one technique. But there are several limitations with the zero-to-infinity machines, not the least of which is: they do not exist.


Throughput: The concept of throughput is most important to a quality control laboratory where a large number of samples must be run in one day. Speed of analysis is sometimes a consideration even for one measurement. Process control applications are an example.


Some techniques are relatively slow: Image analysis and sedimentation on small, low density particles, are but two examples. Some techniques are relatively fast: most forms of light scattering. In some particle sizing applications, throughput is not even a consideration. In others, it is a dominant consideration. The novice often assumes that the measurement duration is sufficient to characterise the typical time per sample. This is a mistake. The total time includes: sampling, sample preparation, measurement, calculation, formatting and printing, and clean up. In some cases warm-up or calibration or instrument adjustment may also add significantly to the overall time per experiment. Automated instruments may need time-consuming wash/rinse cycles. Sometimes the measurement duration is only a fraction of the actual time per sample.


Recommendation:


Estimate the throughput you require. Compare to vendor claims. Be sure to consider the total duration as defined above.


Accuracy: Accuracy is a measure of how close an experimental value is to the true value. Often, the true value is not known. Perhaps the particles are not spherical. Perhaps no truly accurate measurements have been made by which to compare the results. In these cases, accuracy becomes difficult to assess.


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