Micromeretics


The science and technology of small particles is called micromeretics. (Ansel page 167)

Particles of different size behave differently and are evaluated differently. The table below gives some indication as to the relationship between particle size and examples of which products might contain that size particle. The smallest particles are found in Colloids while the largest particles of interest to the pharmaceutical industry are those used in making tablets and capsules.
 

Particle Size Examples
Micrometeres millimeters seive size
<0.5  <.0005  Colloids, Tobacco Smoke, Microorganisms
0.5 - 10 .0005 - 0.01 Suspensions, Emulsions, Bacteria & Red Blood Cell
10 to 50  .01 to .05  Flocculated Suspension & Pollens
50 to 100 .05 to .10 325 to 140 Fine powders, Flour, Mist, Thickness of a human hair
150 to 1000 .15 to 1 100 to 18 Coarse Powder, Drizzle, Beach Sand
1000 to 3360 1. to 3.36 18 to 6 Granule Size
In the area of tablet and capsule manufacture control of the particle size and the nature of the distribution of particle size in the mixture is essential if we wish to achieve the necessary flow properties and mixing characteristics.
 

Particle Size Determination


Rarely do we have a powder that is not a collection of particles of different sizes. It is therefore important to know both the average particle size and shape and the distribution of the particle size range in the powder. Too many small particles will not allow the powder to mix well or flow through the tablet and capsule manufacturing equipment. Please remember that when we discuss a pharmaceutical powder it is normally a mixture of chemicals ( the active drug and excipients) not just a pure chemical.

Edmundson has derived a general equation for the average particle size whether it be an arithmetic, geometric, or harmonic mean diameter.
 

d = {(SUMndp+f)/(SUMndf)}1/p


Where n is the number of particles in a size range, d is the average diameter of the particles in that range, p is an index related to the size of the particle, and f is a frequency index. (The pharmaceutical uses of each of the possible values of "p" and "f" in different situations are also included in the table below.) I have also included a second table with an example of some data collected on a sample of powder.

Statistical Diameters

p f Type of mean Size Parameter Frequency Comments
1 0 Arithmetic Length Number Useful if size range is small.
2 0 Arithmetic Surface Number Average Surface Area
3 0 Arithmetic Volume Number Average weight of particles
1 1 Arithmetic Length Length Of no use
1 2 Arithmetic Length Surface Important Pharmaceutically
1 3 Arithmetic Length Weight Sometimes useful

 

Calculation of Statistical Diameters - data from microscopic measurements

Size Range Mean Size Number of Particles nd nd2 nd3
.5 to 1 .75 2 1.5 1.13 0.85
1 to 1.5 1.25 10 12.5 15.63 19.54
1.5 to 2 1.75 22 38.5 67.38 117.92
2 to 2.5 2.25 54 121.5 273.38 615.11
2.5 to 3 2.75 17 46.75 128.56 353.54
3 to 3.5 3.25 8 26 84.5 274.63
3.5 to 4 3.75 5 18.75 70.31 263.66
Sum 118 265.5 640.89 1645.25

Edmondson value for p = 1 and f = 2 is 2.57

There are several other methods for evaluating the powder sample based on its particle size distribution. All have some uses but none are perfect. As long as each subsequent sample of the powder is evaluated in the same way we can make predictions as to its performance in the equipment and in use.
 

Methods for determining Particle Size


Optical Microscope
Sieving
Sedimentation - Andreasen Apparatus - This uses a modification of stokes law.

d = SquareRoot {[18Viscosity h]/[(rho - rho)gt]}

Other properties of powders that are important

Porosity - why is this information useful??
Density - True and Apparent - what is the difference??
Flowability - Angle of repose - How do we measure it??
Compressability - Elastic vs plastic deformation - which one is needed in tablet manufacture??