Particle Size Distribution (PSD) characterizes the dimensions of particles within a sample. Every material, from pharmaceutical powders to construction aggregate, is composed of tiny pieces of matter, and the size of these individual particles profoundly affects the material’s overall behavior. Understanding the PSD involves determining the proportion of particles that fall into specific size ranges. This measurement is the basis for predicting and controlling the performance of countless manufactured products.
Defining Particle Size Distribution
Particle size distribution is a statistical function that describes the relative quantities of particles present according to their size. It reveals the range of sizes, from the smallest to the largest particle in the sample, and how the material is spread across that spectrum. The distribution is commonly represented based on the number of particles, surface area, or volume/mass, with each representation emphasizing different material aspects.
The uniformity of a sample is described by the width of its distribution. A narrow distribution indicates a monodisperse system where particles are similar in size, while a broad distribution signifies a polydisperse system with a wide variety of sizes. Central tendency measures, such as the mean, median, and mode, characterize the average size. However, the full distribution curve is necessary because a single average value rarely tells the whole story.
Visualizing and Interpreting the Data
Data collected from particle size measurements is typically presented using two primary graphical formats: the frequency distribution and the cumulative distribution. A frequency distribution, often shown as a histogram, plots the relative amount of material (usually volume or mass percentage) within a specific size band. This curve is useful for identifying the modal size, which is the most frequently occurring particle size in the sample.
The cumulative distribution curve, also known as an S-curve, is useful for interpretation and quality control. This curve plots the total percentage of the sample that is smaller than a given particle size, accumulating the material from the smallest size up to the largest. From this curve, specific statistical indicators known as D-values are easily determined, characterizing the distribution’s shape and limits.
The most common indicators are $D_{10}$, $D_{50}$, and $D_{90}$. These percentile values represent the particle diameter below which 10%, 50%, and 90% of the sample volume falls, respectively. The $D_{50}$ is the median particle size, dividing the population into two equal halves by volume. Monitoring the $D_{10}$ tracks the presence of fine particles, while the $D_{90}$ indicates the coarsest fraction of the material, providing a clear picture of the distribution’s span and extremes.
Common Techniques for Measurement
Generating the raw data for a particle size distribution relies on various analytical methods, each suited to different size ranges and material properties.
Sieve Analysis
Sieve Analysis is one of the oldest and simplest techniques, used primarily for larger, coarser particles, typically ranging from 1 millimeter down to 25 microns. The sample is agitated through a stack of woven wire mesh sieves with progressively smaller openings. The mass of material retained on each screen determines the size fraction. The lower size limit is constrained because particles finer than about 25 micrometers tend to clump together due to electrostatic and cohesive forces, preventing accurate passage through the mesh.
Laser Diffraction
For a much broader size range, from sub-microns to several millimeters, Laser Diffraction is the most widely adopted modern technique. This method does not measure the particle directly. Instead, it uses the principle that a particle passing through a laser beam scatters light at an angle inversely proportional to its size. Large particles scatter light at small angles, while small particles scatter light at wide angles. A complex mathematical model converts the resulting light pattern into a volume-based particle size distribution.
Microscopy and Image Analysis
Microscopy and Image Analysis offers a direct, particle-by-particle approach, which is useful for analyzing materials with irregular or non-spherical shapes. An optical or electron microscope captures high-resolution images of dispersed particles, and specialized software measures various dimensions and shape factors. This technique provides detailed shape parameters like circularity, elongation, and aspect ratio, which are not captured by light-scattering methods that assume a spherical shape.
Practical Importance in Industry and Science
Controlling and monitoring particle size distribution is required for maintaining quality and performance across many industries.
Pharmaceuticals
In the Pharmaceuticals sector, PSD directly governs the dissolution rate—the rate at which a tablet or capsule dissolves and releases its active ingredient. Smaller particles offer a larger surface area, leading to faster dissolution and improved bioavailability. This ensures the drug is effectively absorbed into the bloodstream.
Construction Materials
The PSD of cement powder dictates its reactivity, which influences the strength and setting time of concrete. A finer cement powder with a smaller $D_{50}$ generally leads to higher early compressive strength due to increased surface area for hydration. However, a balance must be struck to prevent excessive water demand and shrinkage.
Food Science
In Food Science, PSD is directly related to sensory experience, particularly mouthfeel. To achieve the characteristic smooth texture of high-quality chocolate, for example, cocoa and sugar particles must be refined to a narrow range, typically between 15 and 25 microns. Particles much larger than this range are perceived as an undesirable gritty sensation on the tongue.