Particle Size Distribution

Particle Size Distribution (PSD) is a critical index in material science, indicating the range of particle sizes present in a sample and their relative proportions (usually expressed as a percentage of the total amount). However, the concept is inherently challenging because PSD is highly dependent on the principle of measurement used.

This fundamental problem arises because almost all particles are of complex and irregular shapes—they are not simple spheres or cubes. Because of this irregularity, the particle size cannot be defined directly. Instead, it must be defined by an equivalent sphere diameter, which is calculated based on a specific, measurable property (like volume, surface area, or sedimentation rate).

🛑 The Measurement Dependence Problem

When the principle of measurement differs, the very definition of particle size—the standard or "scale" used to measure it—also differs.

For instance, a sieve measures the shortest dimension a particle can pass through.
Laser diffraction measures an equivalent sphere diameter based on the volume that scatters light.
Sedimentation measures an equivalent sphere diameter based on the rate of settling.

If two analyzers based on different principles are used, they will likely yield completely different PSD results for the same sample, even if the term "particle size distribution" is the same. Therefore, it is generally meaningless to scientifically or subjectively rank the precision or accuracy when comparing various principles of measurement against each other. The principle itself acts as the standard.

Selecting the Right Analyzer

To select the appropriate analyzer (e.g., laser diffraction, sieves, or others), you must:

Clearly understand the target you are measuring and the purpose of the measurement.
Thoroughly examine the analyzer's properties and specifications (e.g., measuring range, resolution, and sample state) to ensure they are suited to that target and purpose.

📊 Understanding Particle Size and Distribution

Particle Size

Particle size is a fundamental concept that pertains to the discrete units in colloids, biological systems, and granular materials (like powders and soils). It provides a contrast between solids, liquids, and gases, as it relates to the physical dimensions of the smallest, inseparable component units in a given system.

Particle Size Distribution (PSD)

The PSD is a rundown of numerical values describing the mass or number of all particles present as a function of size.

In granular materials like soil, the PSD is called a grain size dissemination. Significant energy is typically required to break down soil particles to this level.

Significance of PSD

The PSD is important in determining a substance's physical and chemical properties:

It influences the strength and load-bearing properties of rocks and soils.
It affects the reactivity of solids involved in chemical reactions.
It must be strictly managed in industrial products such as pharmaceuticals, printer toner assembly, and beauty care products, as it controls dosage, solubility, and quality.

🔢 Describing Particle Data

Mean Particle Size

The mean particle size (or mean value) can be calculated from tabulated data. The ISO 9276-2 document describes various methods for calculating this average. A simple method is to:

Multiply the individual particle measurement values for each class by the mean size of that measurement class.
Sum these values to find the mean.

Number and Weight Distribution

When analyzing mixtures with multiple particle sizes, two properties are considered:

Individual particle form and surface area.
Size distributions (the size range and number or weight of particles).

By plotting weights over particle sizes within a certain range, a curve called the frequency distribution curve is obtained. This curve is important because two samples can have the same mean size but drastically different distributions, leading to different behaviors in manufacturing and end-use.

Particle Number ( $N$ )

The particle number ( $N$ ) represents the number of constituent particles in a thermodynamic framework.

It is a key parameter in thermodynamics, formally known as a number of particles, and is linked to the chemical potential.
$N$ is an extensive property (proportional to the size of the system) and is only relevant for closed systems where the number of particles is conserved.
A constituent particle is one that cannot be broken into smaller pieces at the size of energy $k \cdot T$ associated with the interaction, where $k$ is the Boltzmann constant and $T$ is the absolute temperature.