# Quick Guide to Particle Size Distribution

## What is particle size distribution?

Particle size distribution (PSD) is the means of measuring the number of particles by mass and size to calculate a size and mass range. This process can be applied to powders, granules, and particles dispersed in fluids. In theory, a particle size distribution is obtained by taking the minimum diameter and standard deviation of  a perfect sphere, assuming a normal distribution.

In pharmaceuticals, the process of determining PSD is generally more complex as particles are rarely perfect spheres, do not conform to a normal distribution due to blends of different sized materials, and can contain large numbers  of small  particles (fines).  For   these   reasons,   it   is   necessary   to   have   a   particle   size quantification system better suited to the specific requirements of the pharmaceutical industry, and D-values fit this requirement well.

## What is d10 d50 d90 in particle size distribution?

D-values can be thought of as a mass division diameter. It is the diameter  which,  when  all  particles  in  a  sample  are  arranged  in order of ascending mass, divides the sample's mass into specified percentages.   The   percentage   mass   below   the   diameter   of interest is the number expressed after the "D". The D10 diameter is the diameter at which 10% of a sample's  mass  is  comprised  of  smaller  particles,  the  D50  is the  diameter  at  which  50%  of  a  sample's  mass  is  comprised  of smaller  particles, and the D90 is the diameter at which 90% of a sample’s mass is made up of smaller particles.  ## Importance of particle size distribution?

Knowing the PSD is highly important as it allows for far greater process control. With increased control, dissolution rates, drug uniformity, drug bioavailability, and quality targets can be achieved more easily.

## How to determine particle size?

D-values are relatively simple to compute but are challenging to  determine  for  a  real  product in real-time. The main obstacle is quantifying the size of the particles.

A  novel method  to  determine particle size  is  direct imaging, like our Eyecon2 Particle Size Analyzer.  In  direct  imaging,  particles  are  illuminated  and  imaged from the same side. This allows the method to be easily used both in  bench-top  and  in-line  applications.

A major advantage of this method is it non-invasive with no product contact and it is non-destructive. Direct imaging affords greater flexibility with adjustable max and min diameters to shape measurement detection and it negates false detection of shadowing particles, where small fine particles hide in front of larger particles.

## How to calculate particle size?

While D-values are based on a division of the mass of a sample by diameter, the actual mass of the particles or the sample does not need  to  be  known.  A  relative  mass  is  sufficient  as  D-values  are concerned  only  with  a  ratio  of  masses.  This  allows  the  optical measurement  systems  to  be  used  without  any need for sample weighing. From  the  diameter  values  obtained  for  each  particle  a  relative mass can be assigned. Assuming that ρ is constant for all particles and cancelling all constants from the equation: Each  particle's  diameter  is  therefore  cubed  to  give  its  relative mass. These values can be summed to calculate the total relative mass of the sample measured. The values may then be arranged in ascending order and added iteratively until the total reaches 10%,  50%  or  90%  of  the  total  relative  mass of  the  sample. The corresponding D-value  for each of these  is the diameter of the last particle added.

For more information on particle size determination using direct image analysis, get in touch!

Uses direct imaging processed in real-time, with ellipses fitted to each particles boundary, shape and size reported back, highlighting variations 