Number and Volume Distributions in Particle Size Analysis

In the field of particle science and characterization, understanding the distribution of sizes within a sample is fundamental. However, "particle size" is rarely a single number; it is a distribution. The way this distribution is reported depends heavily on the measurement technique used and the mathematical basis of the calculation. The two most common ways to represent these data are Number Distributions and Volume (or Mass) Distributions.

Defining the Distributions

To understand the difference, consider a sample containing two particles: one with a diameter of 1 micrometer and one with a diameter of 10 micrometers.

If we report this by number, we simply count the particles. We have two particles, so 50% of the particles are 1 m, and 50% are 10 m. The number distribution focuses on the count of individual entities regardless of their physical size.

If we report this by volume, we look at the space each particle occupies. Assuming spherical particles, the volume is proportional to the cube of the radius. The 10 m particle has a volume 1,000 times greater than the 1 m particle. Consequently, the 10 m particle accounts for over 99.9% of the total volume of the sample. In a volume distribution, the 1 m particle becomes virtually invisible, while the 10 m particle dominates the plot.

Why Number Distributions Matter

Number distributions are most useful when the process of interest depends on the count of particles rather than their total mass. For example, in contamination studiessuch as counting particles in cleanroom air or identifying impurities in a pharmaceutical injectionthe number of particles is the critical metric. If one large particle is present, it may be less harmful to the application than the presence of thousands of tiny, undetected particles.

Techniques like optical microscopy and automated image analysis typically provide data on a number basis. These methods are excellent for detecting small populations of fine particles that might otherwise be masked in a volume distribution.

Why Volume Distributions Matter

Volume distributions are the standard for most industrial applications, such as paint manufacturing, ceramic processing, and powder coating. In these industries, the bulk properties of the materialsuch as rheology, flowability, and coverageare dictated by the total volume or mass of the powder.

Laser diffraction is the most common technique used to determine volume distributions. Because these instruments measure the scattering of light from a large ensemble of particles simultaneously, they naturally weight the results by the cross-sectional area or volume of the particles. This makes laser diffraction highly reproducible for bulk characterization but relatively poor at detecting small numbers of fine particles.

Choosing the Right Metric

The choice between number and volume distribution should be dictated by the physical mechanism of the application:

• Choose Number Distribution if: You are investigating trace contamination, assessing the efficiency of a filter, or studying the potential biological effect of particles where individual particles act as discrete points of impact.
• Choose Volume Distribution if: You are interested in the material properties, the processing efficiency, or the bulk performance of a powder product.

The "Sensitivity Trap"

It is important to acknowledge that number distributions are extremely sensitive to the "fines" (the smallest particles in a distribution). Because there can be millions of tiny particles that occupy negligible volume, any small error in counting or detecting the smallest fraction of a sample will drastically shift the number distribution. Conversely, volume distributions are sensitive to "oversize" particles. Even a few large, aggregated particles can shift the volume distribution curve significantly toward the right, even if those particles represent a negligible fraction of the total count.

Ultimately, neither distribution is "correct" in a vacuum; they are simply different ways of viewing the same sample. A comprehensive particle analysis often involves looking at both to gain a complete picture of the material's behavior.