Number Distribution

The number distribution is the number of particles counted of each size, shown as a differential across total number of counts. I.e. if there were nine particles spread evenly over three sizes the number differential would be 33.3% for each size.

Volume Distribution

The volume distribution is the distribution per volume of the particle sizes, shown as a differential of total volume of all counts.  Volume is a cubic function of the particle size and is representative of the distribution in a column fill. I.e. a 100 µm bead will occupy 1000 times the volume of a 10 µm bead.

A Simplified Example

The difference between number and volume distribution is best conceptualized in either tabular format or graphically and there are illustrations given here in Table 1, Fig 1 and Fig 2.

For a simplistic distribution of 9 particles, 3 of which are 10 µm in diameter, 3 of which are 50 µm in diameter, and 3 of which are 100 µm in diameter the number and volume distribution differential can be readily shown. 

Table 1: Tabulated data for number and volume distribution

Conclusion

In the above example there are equal numbers of each particle, but 88.8% of the volume of the nine beads is occupied by the three beads which are 100 µm. The three 10 µm beads each only occupy 0.1% of the total volume, so upon viewing the volume differential there are, apparently, no fines visible in the distribution.

In a column, not all the space is occupied. For random packing of equal or mixed size
spheres the void volume itself is approximately 1/3rd of the volume of the column and these voids are referred to as interstitial voids.

 

The volume distribution itself may not indicate any fine materials in the column fill, but small particles sit in the interstitial voids between larger particles, disrupting the flow between these particles. In addition, these fines also block meshes and frits on the column. Both of these factors can limit the flow performance of a packed column and can lead to increased back pressure and packing issues. For agarose media this can lead to head spaces being formed in the column which would require that the column be re-packed. Fines also accelerate resin fouling.
 
Resolution of the distribution is dependent on the number of beads counted alongside bin size,
i.e. size range of each count.

A More Complex Example

For a more complex distribution of a 50 µm chromatography resin, the difference between volume and number distribution can be more significant.

Traditionally,
batchwise emulsification technology is used to produced chromatography resins, whether it is an agarose, styrenic or acrylic polymer back bone. This resin produced has a wide distribution and the course and fine material must be removed by a screening (or similar process) step, which is both time consuming and reduces yield of the resin.

Typically, the particle size distribution quoted after screening is greater than 95% between two screen sizes.

In the following 
example 3096 particles are counted in 10 µm bins from 10 to 110 µm with a particle size distribution greater than 95% within 40 - 100 µm specification range.

Table 2: Tabulated data for number and volume distribution of a typical 50 µm chromatography resin

Conclusion

Despite 96.1% of the resin by volume being within the 40 - 100 micron range, 48.5% of the total number of particles are between 10 - 20 micron which can lead to reduced flow performance, increased back pressure issues and potential sites for fouling.

These fines are created as part of a stirred batch emulsification process, and are not present in resins produced using Jetting technology.

The Solution

If a technology is used which produces only resin of the desired size, such as Purolite’s proprietary Jetting technology, this can significantly alter the number distribution but not have a noticeable impact on the volume distribution, this is illustrated in figures 5 and 6 respectively.

The particle size distribution within the range is increased from 96.1% to 98.2%, which is modest, with virtually no difference overall in the volume distribution (Fig 8) The number distribution reduced from 48.5% to circa 2.5% by removing most particles 20 micron and under thereby eliminating the need for screening and reducing the blocking of the interstitial void (Fig 7).

A Real World Example

All previous data sets have been for illustrative purposes only, but a real-world example of this is the comparison of Praesto® Jetted A50 (a 50 µm bead) and MabSelectPrismA (a 60 µm bead), as shown in Figures 9 and 10 respectively.  Measurements were taken via optical microscopy, with a minimum bead count of 2500 particles per measurement and bin sizes of 0.25 micron. 

Conclusions

When comparing only the volume distribution there is minimal difference in the particle size distribution of Praesto® Jetted A50 and MabSelectPrismA. However, there is stark contrast in the number distribution of the two resins.

Praesto® Jetted A50, which is made using Purolite’s proprietary Jetting technology, has no fines and very little course material, therefore it does not require screening. It is a uniform particle size 50 µm bead with an average particle size distribution of 95% within 35 - 90 µm. MabSelect
PrismA is a 60 µm bead, with an average particle size distribution of 95% within 20 -100 µm.

In the tested sample of MabSelect
PrismA, which is produced by a batch wise emulsification technology, approximately 25% of all particles present are smaller than 25 microns, which can block column nets and the interstitial voids of a packed bed.