**The particle size is the most important physical property of particulate samples. Particle size measurement is normally needed across a range of industries and is a critical parameter in the manufacture of many products. The particle size has a direct influence on many properties of a material, including the ones listed below along with a typical application:**

- Reactivity or dissolution rate e.g. catalysts, tablets
- Stability in suspension e.g. sediments, paints
- Efficacy of delivery e.g. asthma inhalers
- Texture and feel e.g. food ingredients
- Appearance e.g. powder coatings and inks
- Flowability and handling e.g. granules
- Viscosity e.g. nasal sprays
- Packing density and porosity e.g. ceramics.

The measurement of particle size, and understanding how products and processes are affected by this, can be critical to the success of many manufacturing businesses.

## Definition of Particle Size

Particles are 3D objects and unless they are perfect spheres such as bubbles or emulsions, they cannot be fully described by a single dimension such as a radius or diameter. For regular shaped particles, the equivalent sphere concept works very well.

However for irregular shaped particles, it is not always appropriate where the size in at least one dimension can differ significantly from that of the other dimensions.

**Figure 1. **Illustration of the concept of equivalent spheres.

In the case of rod shaped particles shown in Figure 2, a volume equivalent sphere will give a particle diameter of 198pm, which is not a very accurate description of its true dimensions.

**Figure 2. **Illustration of the volume equivalent rod and sphere of a needle shaped particle.

## Particle Size Distributions

Only if the sample that you have to characterize is perfectly mono disperse, i.e. every single particle has exactly the same dimensions, it will consist of a statistical distribution of particles of different sizes.

It is normal to represent this distribution in the form of either a frequency distribution curve, or a cumulative (undersize) distribution curve. The particle size distributions are classified into:

- Weighted distributions
- Number weighted distributions
- Volume weighted distributions
- Intensity weighted distributions

While comparing particle size data for the same sample using different techniques, it is important to realize that the types of distribution being measured and reported can produce very different particle size results.

## Distribution Statistics

For simplifying the interpretation of particle size distribution data, a range of statistical parameters can be calculated and reported. The choice of the most appropriate statistical parameter for any given sample will depend upon how that data will be used and what it will be compared with. One can choose between the following parameters:

- Mean - 'average' size of a population
- Median - size where 50% of the population is below/above
- Mode - size with highest frequency.

## Means

There are several means that can be defined based on how the distribution data is collected and analyzed. The three most commonly used for particle sizing are outlined below.

- Number length mean D[1,0] or Xnl
- Surface area moment mean D[3, 2] or Xsv
- Volume moment mean D[4, 3] or Xvm

## Percentiles

For volume-weighted particle size distributions, such as those measured by laser diffraction, it is often convenient to report parameters based upon the maximum particle size for a given percentage volume of the sample.

Percentiles are defined as XaB where: X= parameter, usually D for diameter

a = distribution weighting, e.g. n for number, v for volume, i for intensity

B = percentage of sample below this particle size e.g. 50%, sometimes written as a decimal fraction i.e. 0.5

The most common percentiles reported are the Dv10, Dv50 and Dv90, as illustrated in the frequency and cumulative plots in Figure 3.

**Figure 3. **Illustration of volume percentiles in terms of cumulative and frequency plots.

The monitoring of these three parameters shows whether there are significant changes in the main particle size, as well as changes at the extremes of the distribution, which could be due to the presence of fines, or oversized particles/agglomerates.

## Particle Shape

Along with particle size, the particle shape also has a considerable impact upon the performance or processing of particulate materials. Several industries are now also making particle shape measurements in addition to particle size in order to gain a better understanding of their products and processes. Areas in which particle shape have an impact are:

- Reactivity and solubility e.g. pharmaceutical actives
- Powder flow and handling e.g. drug delivery systems
- Ceramic sinter properties e.g. ceramic filters
- Abrasive efficiency e.g. SiC wire saws
- Texture and feel e.g. food ingredients.

One can use particle shape to determine the state of dispersion of particulate materials, specifically if agglomerates or primary particles are present.

## Definition of Particle Shape

Particle shape is most commonly measured using imaging techniques, where the data collected is a 2D projection of the particle profile. Particle shape parameters can be calculated from this 2D projection using simple geometrical calculations e.g. Aspect ratio =width/length

## Particle Form

It is possible to characterize the form of a particle using relatively simple parameters such as the aspect ratio. Aspect ratio can be used to distinguish between particles that have regular symmetry, such as spheres or cubes, and particles with different dimensions along one axis, such as needle shapes or ovoid particles.

Other shape parameters that can be used to characterize particle form including elongation and roundness.

## Particle Outline

Along with the detection of agglomerated particles, the outline of a particle can provide information about properties such as surface roughness. For calculating particle outline parameters, a concept known as the convex hull perimeter is used. This is shown in Figure 4.

**Figure 4. **Illustration of the convex hull for two different shapes of particle.

On determining the convex hull perimeter, parameters based on it can be defined, such as convexity or solidity where:

- convexity = convex hull perimeter/actual perimeter
- solidity = area bound by actual perimeter/area bound by convex hull perimeter

## Universal Shape Parameters

Certain shape parameters capture changes in both outline and particle form. Monitoring these can be useful where both form and outline may influence the behavior of the material being measured. The most commonly used parameter is circularity where:

Circularity = perimeter/perimeter of an equivalent area circle

## Zeta Potential

Zeta potential is a measure of the magnitude of the electrostatic or charge repulsion or attraction between particles in a liquid suspension. It is one of the key parameters known to affect dispersion stability.

Its measurement brings detailed insight into the causes of dispersion, aggregation or flocculation, and can be applied to improve the formulation of dispersions, emulsions and suspensions.

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

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