A particle population which consists of spheres or equivalent spheres of the same diameter is said to be monodisperse or monosized, and its characteristics can be described by a single diameter or equivalent sphere diameter.

However, it is unusual for particles to be completely monodisperse, and such a sample will rarely, if ever, be encountered in a pharmaceutical system. Most powders contain particles with a range of different equivalent diameters, i.e. they are polydisperse or heterodisperse. To be able to define a size distribution or compare the characteristics of two or more powders comprising particles with many different diameters, the size distribution can be broken down into different size ranges, which can be presented in the form of a histogram plotted from data.

Frequency Curve Representations of Particle Size Distribution (Histogram)

Such a histogram presents an interpretation of the particle size distribution and enables the percentage of particles having a given equivalent diameter to be determined. A histogram allows different particle size distributions to be compared.

For example, the histogram in Fig. 1a is a representation of particles that are normally distributed symmetrically about a central value. The peak frequency value, known as the mode, separates the normal curve into two identical halves, because the size distribution is fully symmetrical.

Not all particle populations are characterized by symmetrical, ‘normal’ size distributions, and the frequency distributions of such populations are said to be skewed. The size distribution shown in Fig. 1b contains a large proportion of fine particles. A frequency curve such as this, with an elongated tail towards higher size ranges, is said to be positively skewed; the reverse case exhibits negative skewness. These skewed distributions can sometimes be normalized by the replotting of the equivalent particle diameters with use of a logarithmic scale, and are thus usually referred to as log-normal distributions.

In some size distributions more than one mode occurs: Fig. 1c shows a bimodal frequency distribution for a powder which has been subjected to milling. Some of the coarser particles from the unmilled population remain unbroken and produce a mode towards the largest particle size, whereas the fractured (size-reduced) particles have a new mode lower down the size range.

Cumulative Percent Frequency Curve Representations of Particle Size Distribution

An alternative to the histogram or frequency curve representations of particle size distribution is obtained by sequential addition of the percent frequency values, to produce a cumulative percent frequency distribution. If the addition sequence begins with the coarsest particles, the values obtained will be cumulative percent frequency undersize (or more commonly cumulative percent undersize); the reverse case produces a cumulative percent oversize.

It is possible to compare two or more particle populations by means of the cumulative distribution representation. Fig. 2 shows two cumulative percent frequency distributions. The size distribution in Fig. 2a shows that this powder has a larger range or spread of diameters (less steep gradient) than the powder represented in Fig. 2b. The median particle diameter corresponds to the point that separates the cumulative frequency curve into two equal halves, above and below which 50% of the particles lie (point a in Fig. 2).

Reference:

• Aulton, M. (2018). Aulton’s pharmaceutics, the design and manufacture of medicines. Edinburgh. : Elsevier