**The objective of a particle size analysis may be to obtain a bulk powder measurement to explore dusting tendency, filter blockage, or flowability, or to get the primary size of a particle system to gain insights into chemical reactivity, gas absorption, and dissolution rate.**

The following questions need to be considered in a particle size analysis:

- How many analyzes are required for statistical validity?
- How much sample is needed from the bulk in terms of both weight and count of particles to ascertain that the sample taken is representative of the whole?

## Number of Analyzes Required for Statistical Validity

Finding answer to the question “how many analyzes are required for statistical validity?” is much easier. The probable error or standard error (SE) in multiple measurements is described as follows:

SE = 2/3 [Σ(x – x_{m})^{2}/n] ^{0.5}

Where, n is the number of samples; x is any sample measurement; and x_{m} is the mean of the samples. Using the aforementioned formula the total number of samples required can be calculated. For instance, for a precision of ± 1µm, the total number of samples required would be 23. However, this is not the usual condition that needs to be dealt with in particle size analysis.

Standard error varies in proportion to N^{-1/2}, where N is the total number of particles measured. This means that an image analysis may need to analyze on the order of 10000 images to get a satisfactory limit of uncertainty.

## Finding Sample Size

For minimum number of particles and 1% or better SE with knowledge or assumptions about the particle density, a spreadsheet is easily built to get a feel for the sort of sample size needed. Figures 1 and 2 show that sampling became the major error in particle size analysis for maximum size, if a sample size of roughly 1g is assumed for most analytical techniques.

**Figure 1. **Weight of sample versus maximum size.

**Figure 2. **Weight of sample and maximum size.

## Reliability of Sampling Techniques

A spinning riffler is used for sample division or extending the permitted specification. The recommendations in ISO133209 Section 6.4 relating to repeatability take into consideration three successive aliquots with a deviation of 3% for the D50 and 5% for the D10 and D90 in the tails of the distribution.

This could only be possible for samples that have either been appropriately split or were small enough that adequate number of particles was in the highest size band. This is a practical check on the homogeneity of the sample.

## Practical Sampling Methods

For sampling, spinning rifflers have been used for nearly a century. Companies such as Retsch or Microscal provide units capable of dealing with 10 g to 100 kg of sample to divide a primary sample into a size suitable for measurement. Rotary dividing technique must be used to get below 1% coefficient of variation sample-to- sample. Scoop sampling is another alternative (Figure 3). Cone and quartering must never be used.

**Figure 3. **Practical Sampling Methods.

For a large mine dump or a glacial moraine, the golden rules of sampling are as follows:

- Sample needs to be taken when the product packed in a large drum or container is moving. Once in the drum we're then subject to any settling that occurs during transport. If this is not practical then we're back to the option of either spinning riffler or a wider specification or experimental evidence/statistics on the basis or real-world experiments.
- The entire stream is taken for a short period instead of part of the stream for a long period. This is to prevent taking samples say at the edge where air currents could affect what is sampled or in the middle of a pipe where the particle size distribution is different from the value close to the edges. Hence, crosstream and Vezin type samplers must be statistically superior than putting a fixed probe into a stream.

For mines and piles of materials, actual measurements will reveal the widespread of particle sizes in such conditions and would be more realistic when compared to the flippant "Don't/never!" advice.

Slurry sampling is more likely much worse when compared to dry powder sampling wherein segregation or settling is almost certain to be taking place. Sampling from a pipe or in a wet grinding condition needs to be carefully evaluated owing because it is virtually impossible that the system is uniform from a particle size point-of-view. It is recommended to use a Burt sampler for slurry or suspension sampling. The Microscal suspension sampler is shown in Figure 4.

**Figure 4. **The Microscal suspension sampler, 100mL to 10mL.

## Experimental Results

Some practical results of sampling performed at Malvern Panalytical on purified teraphthalic acid (PTA) both as prepared slurry in water and as a dry powder are presented here as illustrative examples for sampling.

The size of the material is huge, thus holding the potential for considerable sampling errors. The recommendations of ISO13320 for riffled samples were followed in that and the complete sampled sub-lot was involved in the measurement.

Repeatability was evaluated for wet measurements by performing 10 successive repeat measurements. The standard deviations for the consecutive scoop sampled aliquots were in good agreement with those noted by Allen. The results of consecutive dry sampling of large material are presented in Figure 5.

**Figure 5. **Consecutive dry sampling of large material. (PTA)

Virtually no effect is observed on the smaller D10 and median, D50, points, but the effect is observed at the D90 end of the distribution. The removal of the larger material is indicated by the gradual decrease in the effect on D90.

For the slurry sample, pipette was used to withdraw the initial samples from a well, and the slurry of the material held in a beaker was continuously stirred using a magnetic stirrer. This material in suspension exhibits a slight change. The step is at the point when no liquid left and one began to sample, by spatula, the paste sitting at the bottom of the beaker. This indicates segregation effects by the gradual increase in key parameters (Figure 6).

**Figure 6. **Consecutive wet sampling of large material. (PTA)

For sampling by spinning riffler, no discernible trends were observed in D90 over the 25 trays of the riffler for measurements of samples in their entirety (Figure 7). The values generated by slurry sampling or simple scoop can be improved and any systematic variation can be removed.

**Figure 7. **Use of spinning riffler.

This information has been sourced, reviewed and adapted from materials provided by Malvern Panalytical.

For more information on this source, please visit Malvern Panalytical.